Research ArticleColor Image Denoising Based on Guided Filter andAdaptive Wavelet Threshold

Xin Sun1 Ning He1 Yu-Qing Zhang2 Xue-Yan Zhen2 Ke Lu3 and Xiu-Ling Zhou4

1Smart City College Beijing Union University Beijing 100101 China2Beijing Key Laboratory of Information Service Engineering Beijing Union University Beijing 100101 China3University of Chinese Academy of Sciences No 19A Yuquan Road Beijing 100049 China4Beijing City University Beijing 100083 China

Correspondence should be addressed to Ning He xxtheningbuueducn

Received 29 May 2017 Revised 20 August 2017 Accepted 21 August 2017 Published 6 November 2017

Academic Editor Ridha Ejbali

Copyright copy 2017 Xin Sun et al This is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

In the process of denoising color images it is very important to enhance the edge and texture information of the images Imagequality can usually be improved by eliminating noise and enhancing contrast Based on the adaptive wavelet threshold shrinkagealgorithm and considering structural characteristics on the basis of color image denoising this paper describes a method thatfurther enhances the edge and texture details of the image using guided filtering The use of guided filtering allows edge detailsthat cannot be discriminated in grayscale images to be preserved The noisy image is decomposed into low-frequency and high-frequency subbands using discrete wavelets and the contraction function of threshold shrinkage is selected according to the energyin the vicinity of the wavelet coefficients Finally the edge and texture information of the denoised color image are enhanced byguided filteringWhen the guiding image is the original noiseless image itself the guided filter can be used as a smoothing operatorfor preserving edges resulting in a better effect than bilateral filteringThe proposedmethod is compared with the adaptive waveletthreshold shrinkage denoising algorithm and the bilateral filtering algorithm Experimental results show that the proposedmethodachieves superior color image denoising compared to these conventional techniques

1 Introduction

During their acquisition and transmission images areadversely affected by noise Color images contain better visualeffects than gray image in terms of visual perception andthe edge information of color images is more abundant thanin gray images Ideally when removing the additive noisefrom an image as many of the important features as possibleshould be retained The denoising of color images oftenresults in the loss of some edge and texture informationmaking the image blurred and creating a poor visual effect

Denoising methods of color image commonly Wienerfilter and Gaussian filter denoising have edge blurred sit-uation Bilateral filtering [1] is the most intuitive nonlinearsmoothing filter although it suffers from the gradient inver-sion effect which uses a histogram-based approximationto calculate the weight and it is computationally complexRecently Zhang et al [2] develop an improved bilateral filter

based framework which is capable of effectively removinguniversal noise Bilateral filter takes spatial information andgrayscale similarity into account and achieves both denoisingand edge-preserving Bilateral filter preserves toomuch high-frequency information but however does not denoise thehigh-frequency noise in color images Thus bilateral filterhas better denoising effect for low-frequency noise merelySometimes bilateral filter suffers from gradient reverse Thereason is that when an edge pixel has few similar pixelsaround it the Gaussian weighted average is unstable In thispaper proposedmethodbased on local linearmodel has goodedge-preserving smoothing properties like bilateral filter butit does not suffer from the gradient reverse

Wavelet threshold denoising [3ndash8] is a simple and effec-tive denoising method This technique effectively involvesthe decomposition of a signal into a set of independentspatially oriented frequency channels The discrete waveletthreshold [9] can be used to decompose the original image

HindawiApplied Computational Intelligence and So ComputingVolume 2017 Article ID 5835020 11 pageshttpsdoiorg10115520175835020

2 Applied Computational Intelligence and Soft Computing

into a sequence of images of different spatial resolutionsDong and Ding [10] proposed a method that can alwaysachieve better performance with lower computation cost andfewer decomposition scales than a high-frequency denoisingmethod Elyasi and Zermchi [11] proposed several adaptivewavelet denoising methods Bayes Shrink Modified BayesShrink and Normal Shrink

In recent years many algorithms have improved andstudied the wavelet threshold denoising Like Bhandari et al[12] developed an optimized adaptive thresholding functionwhich selects the appropriate threshold values to separatenoise from the actual image and preserve edge details Inthis paper a new adaptivewavelet shrink denoising algorithmis proposed Compared with other threshold algorithms theproposed approach improves the denoising performance andhas lower complexity than existing adjacent pixels methods[13 14]

In the process of color image denoising we comparedthe proposed method with the algorithms mentioned above(bilateral filter Wiener filter Gaussian filter and waveletthreshold methods) Proposed method achieves superiorcolor image denoising to these conventional algorithms Thereason is that classic algorithms could suppress the Gaussiannoise effectively but at the same time these methods fail tomaintain the quality of denoised color images (like texture)and may blur edges in the image To address these shortcomings this paper proposes a method based on imagestructure using adaptive wavelet threshold and guided filtertomaintain edges when denoising Itmakes edges continuousand the color of image more brightly Because guided filterusing a local linear model to enhance the image the edgedetails remain In particular the details in color image liketexture are more abundant and saturation is more greater

On this basis this paper presents a new color imagedenoising method based on the adaptive wavelet thresholdshrinkage algorithm combined with image structure-basedguided filtering [15] The method uses the discrete wavelettransform to calculate the energy near thewavelet coefficientsand then uses the adaptive threshold shrinkage functionto denoise the image The threshold function depends onthe energy of adjacent pixels Further using guided filterenhances the image after denoising Experiments show thatthe proposed technique enables better preservation of edgeinformation during the denoising process

The rest of the paper is organized as follows Section 2reviews the related work Algorithm analysis and the struc-ture of proposed method are presented in Section 3 Thenexperimental results and analysis are shown in Section 4Section 5 concludes the paper

2 Related Work

Numerous works have been proposed for image denoising Inthis part we review previous and related work about waveletthreshold algorithms and guided filter

21 Wavelet Threshold Shrinkage Algorithm Wavelet thresh-old denoising is done by Donoho in 1994 which is basedon thresholding the discrete wavelet transform (DWT) of

the signal Hard threshold and soft threshold are traditionalthreshold algorithm Donoho [5] proposed wavelet softthreshold denoising and the threshold VisuShrink algorithmThis method for image denoising obtains a series of waveletcoefficients from the wavelet transform and applies a thresh-old to determine the smaller coefficients (which correspondto noise) Denoising and an inverse wavelet transformationyield the reconstructed image with reduced noise Hard andsoft threshold functions are defined as follows

The hard threshold function is expressed in

119884 = 119883 |119883| ge 1205820 |119883| lt 120582 (1)

The soft threshold function on the other hand is expressed in

119884 = sgn (119883) (|119883| minus 120582) |119883| ge 1205820 |119883| lt 120582 (2)

where 120582 is a threshold value 119883 is wavelet coefficients valueafter the DWT of images and 119884 is output value using waveletthreshold shrinkage function

Normally hard threshold function can preserve thewavelet coefficients well generated by the useful informationfrom images but it is discontinuous at |119883| = 120582 afterreconstruction An alternative approach to hard threshold isthe soft threshold which has advantages of continuity Softthreshold function is smooth and continuous relatively at thethreshold But sometimes there are defects that decreased thewavelet coefficients generated by the effective signal

An appropriate threshold 120582 is the most important roleof discrete wavelet denoising In the process of denoising ifthe threshold 120582 is too small the wavelet coefficients containtoo many noise components and cannot denoise effectivelyOtherwise the threshold 120582 is particularly large resulting inthe loss of useful components that causes distortion Thusnew methods are proposed and some of them have beendelivered to real applications

Adaptive wavelet threshold method first assigns zeroeswhen the wavelet coefficients are smaller than the giventhreshold As the threshold increases the number of coef-ficients below the threshold will increase rapidly When thenumber of nonzero coefficients reaches a certain value thethreshold is further enlarged and the number of nonzerovalues slowly decreases this method can remove most ofthe noise and improve the compression efficiency Nasri andNezamabadi-pour [16] proposed a new thresholding functionto be further used in a new subband-adaptive thresholdingneural network to improve the efficiency of the denoisingprocedure Liu et al [17] found that a wavelet denoising usingneighbor coefficients and level dependency was proposed toseparate spikes from background noise

22 Guided Filter Theguided filter is based on a dual integralimage architecture VLSI [18] (Very Large Scale Integration)The filteringmethod computes the output image based on theinput guiding image which preserves the edges of the imagewell this is an accurate and fast edge-preserving filtering

Applied Computational Intelligence and Soft Computing 3

algorithm He et al [15] proposed a new explicit local linearguided filtering model which is a fast and nonapproximatelinear time algorithm Their model senses the edges andenhances the texture detail Gadge and Agrawal [19] usedguided filtering to color images

Guided filter of image is a linear transformable filteringprocess where the guidance image 119868 needs to be presetaccording to the specific application and 119868 could be identicalto the input image 119901 The output value at pixel 119894 is calculatedas follows

119902119894 = sum119895

119882119894119895 (119868) 119901119895 (3)

where 119894 and 119895 are pixel indexes 119882119894119895 is filter kernel functionwhich defined in [15] expressed by

119882119894119895 (119868) = 1|120596|2 sum119896(119894119895)isin120596119896

(1 + (119868119894 minus 120583119896) (119868119895 minus 120583119896)1205902119896+ 120576 ) (4)

where 120596119896 is the local window that center of 119896 |120596| is count ofpixels in the local window120583119896 and1205902119896 aremean and variance ofguidance image 119868 in the window and finally 120576 is a smoothingfactor

A local linear model (3) is used in guided filter Thislinear relationship ensures that output 119902119894 has the same edgeinformation with guidance image 119868 Thus guided filter hasa better edge-preserving smoothing and avoids the gradientreverse In addition its algorithm computed efficiently andnonapproximately

3 Proposed Algorithm

In this paper we describe an adaptive wavelet transformmethod to remove noise from a color image and use theinverse discrete wavelet transform to obtain the denoisedimage The guided filter is then applied for edge and texturerecovery and enhancement producing a better color imageeffect

31 Overview of Method Structure The framework of pro-posed method contains two main stages (Figure 1) The firststep is to obtain preliminary denoised image 119901 using adaptivewavelet threshold shrinkage algorithm which is based onimage structure feature to shrinkage wavelet coefficients Thewavelet coefficients are decomposed by two-level discretewavelet transform (DWT)The second step is further denois-ing and enhancing by using guided filter to the previous result119901 In guided filter the guidance image 119868 should be presetSetting 119868 and 119901 is identical and can perverse edge and textureof image

In the ideal case the wavelet threshold shrinkage algo-rithm subtracts Gaussian noise from the image and itsdenoising effect is obvious Natural image denoising using thewavelet threshold is very effective because it can capture theenergy of the converted images

Proposed denoising algorithm has the following steps indetail

(1) Transform the noisy image into the frequency domainusing DWT

(2) Apply the adaptive wavelet threshold shrinkage algo-rithm to the local window on each subband and thenuse inverse DWT to obtain preliminary denoisingimage 119901

(3) Apply guided filter on image 119901 to obtain furtherdenoise image 119902

(4) Enhance 119902 and output image

32 Adaptive Wavelet Threshold Algorithm The discretewavelet transform (DWT) applied to image processinghas two main components decomposition and reconstruc-tion We use DWT to decompose the noisy image into asequence of images of different spatial resolutions Two-dimensional images can be decomposed in two-degreedirections resulting in different frequency bands LL (Low-Frequency) LH (Horizontal High-Frequency) HL (VerticalHigh-Frequency) and HH (Diagonal High-Frequency)

In Figure 2 using DWT to decompose the noisy imageinto a sequence of images of different frequency bands Low-Frequency (LL) is decomposed using DWT And decom-posing it produces four different frequency subbands (LL2HL2 LH2 and HH2) using two-level wavelet decompositionfunction On the basis of these frequency subbands thedifferent wavelet threshold shrinkage algorithm can be usedto denoise from the image

After the two-level wavelet decomposition of the image(Figure 2) an adaptivewavelet transform is used to extract thestructure information in the multiresolution image and thecorresponding shrinkage function is applied to the structurefeatures of the image In fact the natural image structureof the wavelet coefficients in the resolution scale exhibits acertain similarity so there is a certain degree of redundancyin the wavelet decomposition scale For example the waveletcoefficients of the edge region are usually concentratedtogether indicating that there is a certain degree of depen-dency in the adjacent wavelet coefficients corresponding tothe edge region

The structure information of the image can be obtained bycalculating the energy of the local area in the wavelet domainThe smoother the image the lower the energy A thresholdrange is determined based on the local energy calculated bythe wavelet decomposition and a different function is usedwithin the corresponding threshold The specific algorithmtakes the average of the square of each pixel value in thelocal window to calculate the energy of the center pixel of thewindowThe appropriate shrinkage factor120572 120573 is then selectedaccording to the corresponding shrink function (6)

In practice we select the local window 119877 lowast 119877 (ie 119877 = 5)using (5) to calculate the local window center pixel energyvalue 1198782119895119896 and then use (6) to calculate the local shrinkagefunction

1198782119895119896 = 11198772119898=119877sum119898=minus119877

119899=119877sum119899=minus119877

1198892119898119899 (5)

119889119895119896 = 119889119895119896(1 minus 120572 lowast 12058221198782

119895119896

) if 1198782119895119896 ge 120573 lowast 12058220 else

(6)

4 Applied Computational Intelligence and Soft Computing

Adaptive

Noise image Image p

waveletthreshold

Input

Guide

I = p

p

Left Right

Output

q

qi = aIi + b

ＩＨＭＮＬＣＨＮＭ qi = pi minus ni

Figure 1 Illustration of the proposed method It contains two main parts Left part is denoising by adaptive wavelet threshold algorithm toobtain denoise image 119901 Right part is using guided filter to enhance edges of image 119901

LL HL

LH HH

LL2

LH2 HH2

HL2

Figure 2 Two-level decomposition of the image Obtaining Low-Frequency image (LL) from the noise image and decomposing it resultingin subbands LL2 HL2 LH2 and HH2 The adaptive wavelet shrink algorithm is applied to each subband to denoise the image

1205902 = [Median (1003816100381610038161003816100381611988411989411989510038161003816100381610038161003816)06745 ] (119884119894119895 = subband HH) (7)

where 1205822 = (41205902 log119877) Equation (7) gives the noise variance1205902 and 119889119895119896 is the central pixel of the local window If 119889119895119896 is atthe boundary of the second wavelet coefficients a boundarycondition is required In the experiments we set 120572 = 01 120573 =03 Finally the reconstructed image is denoised

This denoising algorithm uses the DWT to calculate theenergy near the wavelet coefficients and then applies theadaptive wavelet threshold shrink function to denoise theimage In the experiments we added Gaussian noise withvariances of 1205902 = 001 and 1205902 = 003 to the images Adap-tive wavelet threshold shrink function denoising noise and

getting denoised image 119901 From the experimental results itcan be seen that when the noise variance is large the image 119901is not very clear after denoising in particular the effect of tex-ture is not obvious Therefore we need to enhance the image119901 after this processing step Thus the proposed techniqueuses the guided filter to enhance the image after denoising

33 Guided Filter to Further Processing Guided filtering is aspatial enhancement technique for the spatial domain andthe filtered output is a linear transformation of the localizedimageThefiltering algorithmuses a guiding image to processthe edges of the noisy image The guiding image can be theimage itself At this time their structures are the same thatis the edges of the original image are the same as the edges ofthe guiding image The output pixel values take into account

Applied Computational Intelligence and Soft Computing 5

the statistics of the local spatial neighborhood in the guidedimage Hence using guided filtering the output image ismore structured This can be used for image dehazing andso onThe guided filter adopts an exact linear algorithmThealgorithm is efficient and fast and is considered to be one ofthe fastest edge-preserving filters

For both grayscale and color images the guided filteringalgorithm has 119900(119873) time complexity regardless of the localwindow radius (119903)331 Algorithm of Guided Filter

Guided Filter Theguide image can be a separate image or theoriginal input image when the guiding image is the originalinput image the guided filter retains the edges for imagereconstruction

Assume that the input image is 119901 the output image is119902 and the guiding image is 119868 119902 and 119868 have a local linearrelationship in the window 120596119896 centered on pixel 119896

119902119894 = 119886119896119868119894 + 119887119896 forall119894 isin 120596119896 (8)

where 119886119896 119887119896 are linear (constant) coefficients in the localwindow and the window radius is 119903 Equation (8) calculatesthe guidance of the guiding image to be nabla119902 = 119886nabla119868 Thereforethe linear equation is only guaranteed if 119868 is in the presenceof an edge and the output image 119902 will contain edges Todetermine the coefficients we require constraints from theinput image 119901 The output 119902 is the input 119901 with a number ofnoise components 119899119894 subtracted that is

119902119894 = 119901119894 minus 119899119894 (9)

To minimize the difference between the output 119902 and theinput 119901 and ensure the linearity of (8) the function 119864(119886119896 119887119896)is minimized in the window 120596119896 where 120576 is the regularizationparameter

119864 (119886119896 119887119896) = sum119894isin120596119896

((119886119896119868119894 + 119887119896 minus 119901119894)2 + 1205761198862119896) (10)

In order to minimize the value of the model 119864(119886119896 119887119896) we canderive 119886119896 and 119887119896 respectively and (10) can be solved usinglinear regression

119886119896 = ((1 |120596|) sum119894isin120596119896 119868119894119901119894) minus 1205831198961199011198961205902119896+ 120576

119887119896 = 119901119896 minus 119886119896120583119896(11)

where 120583119896 and 1205902119896 represent the mean and variance in the localwindow 120596119896 respectively |120596| is the number of pixels in thewindow and 119901119896 represents the mean value in the window 120596119896of 119901 After obtaining 119886119896 and 119887119896 in Figure 3 the output 119902119894 is

119902119894 = 1|120596| sum119896|119894isin120596119896

(119886119896119868119894 + 119887119896) = 119886119894119868119894 + 119887119894 (12)

where 119886119894 = (1|120596|) sum119896isin120596119894 119886119896 119887119894 = (1|120596|) sum119896isin120596119896 119887119896 Convert119886119896 and 119887119896 into weights forms which is the general form offiltering

21

qi

qi

Figure 3 Illustration of (12) When the window 120596 is sliding in theimage a pixel is involved in many windows that covers pixel Forinstance windows 1205961 and 1205962 are different local windows that coverthe same pixel 119894Therefore the output 119902119894 should average all the valuesof pixel 119894 in different windows

Therefore the guide filter algorithm proceeds as followsTraverse the entire image via each local window implement-ing the following calculation where 119891 is the mean filter withlocal window radius 119903 input image is 119901 guidance image is119868 corr is the correlation coefficient var is the variance 120576 issmoothing factor and cov is the covariance

mean119868 = 119891mean (119868 119903)mean119901 = 119891mean (119901 119903)corr119868 = 119891mean (119868 lowast 119868 119903)corr119868119901 = 119891mean (119868 lowast 119901 119903)var119868 = corr119868 minusmean119868 lowastmean119868

cov119868119901 = cov119868119901 minusmean119868 lowastmean119901

119886 = cov119868119901(var119868 + 120576)119887 = mean119901 minus 119886 lowastmean119868

mean119886 = 119891mean (119886 119903)mean119887 = 119891mean (119887 119903)

119902 = mean119886 lowast 119868 +mean119887

(13)

332 Edge Preservation When 119868 = 119901 the guided filterbecomes an edge-preserving filter At this point we have

119886119896 = 1205902119896(1205902119896+ 120576)

119887119896 = (1 minus 119886119896) 120583119896(14)

Therefore when the local window variance is large thecenter pixel value remains unchanged In smoother areas theaverage value of the neighboring pixels is used as the centerpixel value

6 Applied Computational Intelligence and Soft Computing

333 Guided Filter for Color Image When the guided filter isapplied independently to the three color channels of the colorimage (8) can be rewritten as

119902119894 = 119886119879119896 119868119894 + 119887119896 forall119894 isin 120596119896 (15)

where 119868119894 is a 3 times 1 color vector 119886119896 is a 3 times 1 coefficient vectorand 119902119894 119887119896 are scalarsThus the color image of the guided filteris

119886119896 = (sum119896

+120576119880)minus1

( 1|120596| sum119894isin120596119896 119868119894119901119894 minus 120583119896119901119896) 119887119896 = 119901119896 minus 119886119896119879120583119896119902119894 = 119886119894119879119868119894 + 119887119894

(16)

where sum119896 is the 3 times 3 covariance matrix of 119868 in 120596119896 and 119880 isthe 3 times 3 identity matrix

Because the local linear model is more effective in thecolor space the edges of gray images cannot be identified butthrough the color image of the guided filter it can be well-preserved Thus the image edges have a significant effect

34 Image Enhancement For images with more texture (ieImage 5) the above denoising method may cause someregions to appear too smooth Therefore it is necessary tofurther enhance the image texture detail Using (17) thedenoised image 119902 is subtracted from the original noiselessimage to yield the details of the loss in 119902 Positive number 119888 isto control and balance the degree of its stacking

119902 enhanced = (119868 minus 119902) lowast 119888 + 119902 (17)

The proposed algorithm uses the characteristics of the imagestructure In the wavelet domain threshold shrinkage is usedto denoise the image and then the guided filter enhances theedges of the denoised image to better reflect the texture detailsof the image

4 Experimental Results and Analysis

We conducted a series of experiments using MATLABR2015b and images in Figure 4 Images in Figure 4 Image 9Image 10 Image 11 and Image 12 are rich in texture Firstvariance of 001 and 003 Gaussian noise was added to thecolor images in Figure 4 This produced the noisy imagesshown in Figures 5(a) 6(a) 7(a) 8(a) 9(a) 10(a) 11(a) and12(a) The proposed method based on image characteristicsand the adaptive wavelet threshold shrinkage algorithm wasthen applied to obtain the denoised images 119901 shown inFigures 5(c) 6(c) 7(c) 8(c) 9(c) 10(c) 11(c) and 12(c) Weused the ldquosym4rdquo two-level wavelet decomposition function todecompose the noisy images with a local window 119877 = 5 lowast 5120573 = 03 and 120572 = 01 to control the degree of shrinkage in thewavelet coefficients

The guided filter was used to denoise the image 119901 withthe guiding image 119868 set to the original image without noiseThis was intended to give the image a better edge effect after

denoising The local window radius was set to 119903 = 8 and 120576 =0022 The image 119901 was denoised after the adaptive waveletthreshold algorithm In image 119901 the 119903 119892 119887 channels wereindividually subjected to the guide filterThe texture and edgeinformation of the images were enhanced and we obtainedthe output 119902 The parameter 119888 in (17) was found to give bettertexture effects and undistorted images when 119888 = 15 Thefinal results 119902 enhanced images are presented in Figures 5(f)6(f) 7(f) 8(f) 9(f) 10(f) 11(f) and 12(f) From Figures 9(f)10(f) 11(f) and 12(f) it can be concluded that the textureand the edge of images had a good performance in proposedmethod

The peak signal-to-noise ratio (119875119878119873119877) of the proposedmethod is presented in Table 1 These 119875119878119873119877119904 indicate thatthe method proposed in this paper is superior to bilateralfiltering the adaptive wavelet threshold algorithm nonlocalmeans [20] algorithm and BM3D [21] method When thenoise level increases the denoising effect of all five methodsdecreases but the proposedmethod gives better performancethan the other four

The 119875119878119873119877 is calculated as follows

PSNR = 10 lowast log10 (2552MSE

) MSE = 13 (mse119903 +mse119892 +mse119887) mse119896 = 1119898 lowast 119899

119898sum119894=1

119899sum119895=1

(119868 (119894 119895) minus 119902 (119894 119895))2 119896 = 119903 119892 119887

(18)

where the input image is 119868 and the output image is119902 enhanced The mean square error (119872119878119864) is the averagemean square error of the three channels (119903 119892 119887) in the colorimage

Wells [22] proposed a quality factor to evaluate theedges of an image after denoising This quality factor (Prattrsquosfigure of merit) takes into account three kinds of error theloss of the effective edge the edge of the positioning errorand noise misjudged as the edge Prattrsquos figure of meritprovides a quantitative evaluation of image edges and can beused to compare the edges in the denoised image and theoriginal image From Figures 13 and 14 it is obvious thatthere are differences between the texture parts Prattrsquos figureofmerit wasmeasured in four imagesThe results in Figure 15confirm that the edge quality factor (red curve) of the pro-posed method is higher than that of the other four methodsfor different degrees of noise variance Thus our methodachieves better edge effects

From a subjective point of view we find that not onlycan the proposedmethod preserve edge better it also reducesnoisewell when comparedwith the other fourmethods FromFigures 5ndash12 the result images (f) using proposed methodlook clearer than the others because we use a guided filterto filter the image and eliminate noise Moreover in Figures13 and 14 the edge of the result image that uses the pro-posed method is smooth and coherent which greatly helpsto enhance edge

Applied Computational Intelligence and Soft Computing 7

Figure 4 Test image Images 1ndash12 (from left to right top to bottom)

(a) 1205902 = 001 (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 5 Image 1 comparison of various experimental results under noise variance 1205902 = 001

To objectively evaluate the results we use the Prattrsquos figureof merit and PSNR for image quality evaluation Prattrsquos figureofmerit results are listed in Figure 15 119910-axis is the Pratt factorresults and 119909-axis is noise variance The curves showed thatPratt factor decreases when the noise variance increases butproposed method (red curves) is much higher than othersCurves results suggested that edge of image using proposedmethod is effective and abundant Table 1 is result of 119875119878119873119877The proposed method is superior to the other four methodswith respect to image processing

From the data in Table 1 and the quality factor curvesin Figure 15 we can conclude that the proposed method issuperior to bilateral filtering the adaptive wavelet thresholddenoising algorithm nonlocal means algorithm and BM3Dalgorithm on color image denoising From a visual point ofview the proposed method not only gives a good denoisingeffect but also achieves better edge retention

5 Conclusion

In this paper a new denoising method based on the adaptivewavelet threshold denoising algorithm and edge-guided fil-tering has been proposed The image denoising is performedaccording to the local structure of the image In comparativeexperiments against bilateral filtering the adaptive waveletdenoising method nonlocal means algorithm and BM3Dalgorithm the proposedmethod exhibited the best denoisingand edge preservation performance The proposed approachremoves Gaussian noise in the frequency domain and thenuses linear guided filtering to further enhance the imagerecovery resulting in better denoising and edge effects Ascolor images display more detailed textures this filteringovercomes the gradient inversion effect in the edge regionsAs the linearmodel (see (8)) is a block-unsupervised learningmethod it can be combined with other models to obtain new

8 Applied Computational Intelligence and Soft Computing

(a) 1205902 = 003 (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 6 Image 1 comparison of various experimental results under noise variance 1205902 = 003

(a) 1205902 = 001 (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 7 Image 5 comparison of various experimental results under noise variance 1205902 = 001

(a) 1205902 = 003 (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 8 Image 5 comparison of various experimental results under noise variance 1205902 = 003

(a) 1205902 = 001 (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 9 Image 9 comparison of various experimental results under noise variance 1205902 = 001

(a) 1205902 = 003 (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 10 Image 9 comparison of various experimental results under noise variance 1205902 = 003

Applied Computational Intelligence and Soft Computing 9

Table 1 PSNR of the proposed method bilateral filtering and adaptive wavelet

Noise variance 001 003 001 003 001 003Image 1 (256 lowast 256) Image 2 (512 lowast 512) Image 3 (256 lowast 256)

Adaptive wavelet 267048 254507 280801 264821 277967 261699Bilateral filtering 225751 220167 231551 226118 227560 221802Nonlocal means 299765 274871 301415 276777 301910 276823BM3D 289235 269276 304215 278901 309457 280957Proposed method 395634 353129 415647 360267 408101 355930

Image 4 (256 lowast 256) Image 5 (256 lowast 256) Image 6 (512 lowast 512)Adaptive wavelet 252375 242724 234663 227332 256576 245766Bilateral filtering 226074 219415 221076 215494 223016 217254Nonlocal means 266512 253287 253588 243120 278813 262105BM3D 255157 244968 240394 232556 280621 263334Proposed method 370265 341344 338535 321364 368294 339588

Image 7 (512 lowast 512) Image 8 (512 lowast 512) Image 9 (200 lowast 150)Adaptive wavelet 275706 259130 290039 269908 214746 208466Bilateral filtering 232116 224080 231373 224268 214834 210023Nonlocal means 294155 270736 313181 282534 237273 230137BM3D 291443 269120 320590 286197 217645 212712Proposed method 391414 348926 412256 357943 314041 300693

Image 10 (200 lowast 150) Image 11 (187 lowast 171) Image 12 (187 lowast 171)Adaptive wavelet 294247 275268 267443 254201 159075 169781Bilateral filtering 236728 230581 222984 217973 227751 226673Nonlocal means 303106 279794 287439 266227 174105 172673BM3D 308146 283780 318744 284922 310366 301990Proposed method 402191 359371 387096 350295 244256 257756

(a) 1205902 = 001 (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 11 Image 10 comparison of various experimental results under noise variance 1205902 = 001

(a) 1205902 = 003 (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 12 Image 10 comparison of various experimental results under noise variance 1205902 = 003

10 Applied Computational Intelligence and Soft Computing

(a) Image 1 edge (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 13 Image 1 edge comparison of various experimental results under noise variance 1205902 = 003

(a) Image 5 edge (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 14 Image 5 edge comparison of various experimental results under noise variance 1205902 = 001

Data

Data Data

Data DataAdaptive wavelet

Proposed method

Bilateral filtering

Nonlocal

BM3D

Data

Data Data

Data DataAdaptive wavelet

Proposed method

Bilateral filtering

Nonlocal

BM3DData

Data Data

Data DataAdaptive wavelet

Proposed method

Bilateral filtering

Nonlocal

BM3D

Data

Data Data

Data DataAdaptive wavelet

Proposed method

Bilateral filtering

Nonlocal

BM3D

87001 002 003 004 005 006 007

Image 1

008 009 01 011

888990919293949596

y

x

82001 002 003 004 005 006 007

Image 5

Image 10

008 009 01 011

848688909294

9896

y

x

001 002 003 004 005 006 007 008 009 01 01175

80

85

90

95

100

y

x

Image 12

001 002 003 004 005 006 007 008 009 01 01175

80

85

90

95

100

y

x

Figure 15 Prattrsquos figure of merit

Applied Computational Intelligence and Soft Computing 11

denoising techniquesThis will be the focus of future researchand exploration on color image denoising

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China (nos 61370138 61572077 andU1301251)and the Beijing Municipal Natural Science Foundation(no 4162027) the Project of Oriented Characteristic Dis-ciplines (no KYDE40201701) the Project of Constructionof Innovative Teams and Teacher Career Development forUniversities and Colleges Under Beijing Municipality (noIDHT20170511)

References

[1] C Tomasi and R Manduchi ldquoBilateral filtering for gray andcolor imagesrdquo in Proceedings of the International Conference onComputer Vision IEEE Computer Society 839 pages 1998

[2] Y Zhang X Tian and P Ren ldquoAn adaptive bilateral filter basedframework for image denoisingrdquo Neurocomputing vol 140 pp299ndash316 2014

[3] J S LimTwo-dimensional signal and image processing Prentice-Hall Inc Upper Saddle River NJ USA 1990

[4] D L Donoho and I M Johnstone ldquoAdapting to unknownsmoothness via wavelet shrinkagerdquo Journal of the AmericanStatistical Association vol 90 no 432 pp 1200ndash1224 1995

[5] D L Donoho ldquoDe-noising by soft-thresholdingrdquo Institute ofElectrical and Electronics Engineers Transactions on InformationTheory vol 41 no 3 pp 613ndash627 1995

[6] T D Bui and G Chen ldquoTranslation-invariant denoising usingmultiwaveletsrdquo IEEE Transactions on Signal Processing vol 46no 12 pp 3414ndash3420 1998

[7] C Srisailam P Sharma and S Suhane ldquoColor image denoisingusingwavelet soft thresholdingrdquo International Journal of Emerg-ing Technology and Advanced Engineering vol 4 no 7 pp 474ndash478 2014

[8] K K Gupta and R Gupta ldquoFeature adaptive wavelet shrinkagefor image denoisingrdquo in Proceedings of the 2007 InternationalConference on Signal Processing Communications and Network-ing ICSCN 2007 pp 81ndash85 ind February 2007

[9] E Ordentlich G Seroussi S Verdu M Weinberger and TWeissman ldquoA discrete universal denoiser and its application tobinary imagesrdquo in Proceedings of the International Conference onImage Processing (ICIP 2003) vol 1 pp 20ndash117 2003

[10] W Dong and H Ding ldquoFull frequency de-noising methodbased on wavelet decomposition and noise-type detectionrdquoNeurocomputing vol 214 pp 902ndash909 2016

[11] I Elyasi and S Zermchi ldquoElimination noise by adaptive waveletthresholdrdquoWorldAcademy of Science EngineeringampTechnologyvol 3 no 8 pp 1541ndash1545 2009

[12] A K Bhandari D Kumar A Kumar and G K Singh ldquoOpti-mal sub-band adaptive thresholding based edge preserved satel-lite image denoising using adaptive differential evolution algo-rithmrdquo Neurocomputing vol 174 pp 698ndash721 2016

[13] T T Cai and B W Silverman ldquoIncorporating information onneighbouring coefficients into wavelet estimation SankhyardquoThe Indian Journal of Statistics Series B (1960-2002) vol 63 no2 pp 127ndash148 2001

[14] G Y Chen T D Bui and A Krzyzak ldquoImage denoising usingneighbouring wavelet coefficientsrdquo Integrated Computer-AidedEngineering vol 12 no 1 pp 99ndash107 2005

[15] K He J Sun and X Tang ldquoGuided image filteringrdquo IEEE Tran-sactions on PatternAnalysis andMachine Intelligence vol 35 no6 pp 1397ndash1409 2013

[16] M Nasri and H Nezamabadi-pour ldquoImage denoising in thewavelet domain using a new adaptive thresholding functionrdquoNeurocomputing vol 72 no 4ndash6 pp 1012ndash1025 2009

[17] X Liu H Wan Z Shang and L Shi ldquoAutomatic extracellularspike denoising using wavelet neighbor coefficients and leveldependencyrdquo Neurocomputing vol 149 pp 1407ndash1414 2015

[18] C-C Kao J-H Lai and S-Y Chien ldquoVLSI architecture designof guided filter for 30 framess full-HD Videordquo IEEE Trans-actions on Circuits and Systems for Video Technology vol 24 no3 pp 513ndash524 2014

[19] A Gadge and S S Agrawal ldquoGuided filter for color imagerdquoIJIREEICE vol 4 no 6 pp 250ndash252 2016

[20] A Buades B Coll and J-M Morel ldquoA non-local algorithm forimage denoisingrdquo in Proceedings of the IEEE Computer SocietyConference on Computer Vision and Pattern Recognition (CVPRrsquo05) pp 60ndash65 June 2005

[21] K Dabov A Foi V Katkovnik and K Egiazarian ldquoImagedenoising by sparse 3-D transform-domain collaborative filter-ingrdquo IEEE Transactions on Image Processing vol 16 no 8 pp2080ndash2095 2007

[22] P N T Wells Digital Image Processing W K Pratt John WileyChichester UK 1991 (Medical Engineering amp Physics vol 16no 1 p 83 1994)

Submit your manuscripts athttpswwwhindawicom

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Applied Computational Intelligence and Soft Computing

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Applied Computational Intelligence and Soft Computing 3

algorithm He et al [15] proposed a new explicit local linearguided filtering model which is a fast and nonapproximatelinear time algorithm Their model senses the edges andenhances the texture detail Gadge and Agrawal [19] usedguided filtering to color images

Guided filter of image is a linear transformable filteringprocess where the guidance image 119868 needs to be presetaccording to the specific application and 119868 could be identicalto the input image 119901 The output value at pixel 119894 is calculatedas follows

119902119894 = sum119895

119882119894119895 (119868) 119901119895 (3)

where 119894 and 119895 are pixel indexes 119882119894119895 is filter kernel functionwhich defined in [15] expressed by

119882119894119895 (119868) = 1|120596|2 sum119896(119894119895)isin120596119896

(1 + (119868119894 minus 120583119896) (119868119895 minus 120583119896)1205902119896+ 120576 ) (4)

where 120596119896 is the local window that center of 119896 |120596| is count ofpixels in the local window120583119896 and1205902119896 aremean and variance ofguidance image 119868 in the window and finally 120576 is a smoothingfactor

A local linear model (3) is used in guided filter Thislinear relationship ensures that output 119902119894 has the same edgeinformation with guidance image 119868 Thus guided filter hasa better edge-preserving smoothing and avoids the gradientreverse In addition its algorithm computed efficiently andnonapproximately

3 Proposed Algorithm

In this paper we describe an adaptive wavelet transformmethod to remove noise from a color image and use theinverse discrete wavelet transform to obtain the denoisedimage The guided filter is then applied for edge and texturerecovery and enhancement producing a better color imageeffect

31 Overview of Method Structure The framework of pro-posed method contains two main stages (Figure 1) The firststep is to obtain preliminary denoised image 119901 using adaptivewavelet threshold shrinkage algorithm which is based onimage structure feature to shrinkage wavelet coefficients Thewavelet coefficients are decomposed by two-level discretewavelet transform (DWT)The second step is further denois-ing and enhancing by using guided filter to the previous result119901 In guided filter the guidance image 119868 should be presetSetting 119868 and 119901 is identical and can perverse edge and textureof image

In the ideal case the wavelet threshold shrinkage algo-rithm subtracts Gaussian noise from the image and itsdenoising effect is obvious Natural image denoising using thewavelet threshold is very effective because it can capture theenergy of the converted images

Proposed denoising algorithm has the following steps indetail

(1) Transform the noisy image into the frequency domainusing DWT

(2) Apply the adaptive wavelet threshold shrinkage algo-rithm to the local window on each subband and thenuse inverse DWT to obtain preliminary denoisingimage 119901

(3) Apply guided filter on image 119901 to obtain furtherdenoise image 119902

(4) Enhance 119902 and output image

32 Adaptive Wavelet Threshold Algorithm The discretewavelet transform (DWT) applied to image processinghas two main components decomposition and reconstruc-tion We use DWT to decompose the noisy image into asequence of images of different spatial resolutions Two-dimensional images can be decomposed in two-degreedirections resulting in different frequency bands LL (Low-Frequency) LH (Horizontal High-Frequency) HL (VerticalHigh-Frequency) and HH (Diagonal High-Frequency)

In Figure 2 using DWT to decompose the noisy imageinto a sequence of images of different frequency bands Low-Frequency (LL) is decomposed using DWT And decom-posing it produces four different frequency subbands (LL2HL2 LH2 and HH2) using two-level wavelet decompositionfunction On the basis of these frequency subbands thedifferent wavelet threshold shrinkage algorithm can be usedto denoise from the image

After the two-level wavelet decomposition of the image(Figure 2) an adaptivewavelet transform is used to extract thestructure information in the multiresolution image and thecorresponding shrinkage function is applied to the structurefeatures of the image In fact the natural image structureof the wavelet coefficients in the resolution scale exhibits acertain similarity so there is a certain degree of redundancyin the wavelet decomposition scale For example the waveletcoefficients of the edge region are usually concentratedtogether indicating that there is a certain degree of depen-dency in the adjacent wavelet coefficients corresponding tothe edge region

The structure information of the image can be obtained bycalculating the energy of the local area in the wavelet domainThe smoother the image the lower the energy A thresholdrange is determined based on the local energy calculated bythe wavelet decomposition and a different function is usedwithin the corresponding threshold The specific algorithmtakes the average of the square of each pixel value in thelocal window to calculate the energy of the center pixel of thewindowThe appropriate shrinkage factor120572 120573 is then selectedaccording to the corresponding shrink function (6)

In practice we select the local window 119877 lowast 119877 (ie 119877 = 5)using (5) to calculate the local window center pixel energyvalue 1198782119895119896 and then use (6) to calculate the local shrinkagefunction

1198782119895119896 = 11198772119898=119877sum119898=minus119877

119899=119877sum119899=minus119877

1198892119898119899 (5)

119889119895119896 = 119889119895119896(1 minus 120572 lowast 12058221198782

119895119896

) if 1198782119895119896 ge 120573 lowast 12058220 else

(6)

4 Applied Computational Intelligence and Soft Computing

Adaptive

Noise image Image p

waveletthreshold

Input

Guide

I = p

p

Left Right

Output

q

qi = aIi + b

ＩＨＭＮＬＣＨＮＭ qi = pi minus ni

Figure 1 Illustration of the proposed method It contains two main parts Left part is denoising by adaptive wavelet threshold algorithm toobtain denoise image 119901 Right part is using guided filter to enhance edges of image 119901

LL HL

LH HH

LL2

LH2 HH2

HL2

Figure 2 Two-level decomposition of the image Obtaining Low-Frequency image (LL) from the noise image and decomposing it resultingin subbands LL2 HL2 LH2 and HH2 The adaptive wavelet shrink algorithm is applied to each subband to denoise the image

1205902 = [Median (1003816100381610038161003816100381611988411989411989510038161003816100381610038161003816)06745 ] (119884119894119895 = subband HH) (7)

where 1205822 = (41205902 log119877) Equation (7) gives the noise variance1205902 and 119889119895119896 is the central pixel of the local window If 119889119895119896 is atthe boundary of the second wavelet coefficients a boundarycondition is required In the experiments we set 120572 = 01 120573 =03 Finally the reconstructed image is denoised

This denoising algorithm uses the DWT to calculate theenergy near the wavelet coefficients and then applies theadaptive wavelet threshold shrink function to denoise theimage In the experiments we added Gaussian noise withvariances of 1205902 = 001 and 1205902 = 003 to the images Adap-tive wavelet threshold shrink function denoising noise and

getting denoised image 119901 From the experimental results itcan be seen that when the noise variance is large the image 119901is not very clear after denoising in particular the effect of tex-ture is not obvious Therefore we need to enhance the image119901 after this processing step Thus the proposed techniqueuses the guided filter to enhance the image after denoising

33 Guided Filter to Further Processing Guided filtering is aspatial enhancement technique for the spatial domain andthe filtered output is a linear transformation of the localizedimageThefiltering algorithmuses a guiding image to processthe edges of the noisy image The guiding image can be theimage itself At this time their structures are the same thatis the edges of the original image are the same as the edges ofthe guiding image The output pixel values take into account

Applied Computational Intelligence and Soft Computing 5

the statistics of the local spatial neighborhood in the guidedimage Hence using guided filtering the output image ismore structured This can be used for image dehazing andso onThe guided filter adopts an exact linear algorithmThealgorithm is efficient and fast and is considered to be one ofthe fastest edge-preserving filters

For both grayscale and color images the guided filteringalgorithm has 119900(119873) time complexity regardless of the localwindow radius (119903)331 Algorithm of Guided Filter

Guided Filter Theguide image can be a separate image or theoriginal input image when the guiding image is the originalinput image the guided filter retains the edges for imagereconstruction

Assume that the input image is 119901 the output image is119902 and the guiding image is 119868 119902 and 119868 have a local linearrelationship in the window 120596119896 centered on pixel 119896

119902119894 = 119886119896119868119894 + 119887119896 forall119894 isin 120596119896 (8)

where 119886119896 119887119896 are linear (constant) coefficients in the localwindow and the window radius is 119903 Equation (8) calculatesthe guidance of the guiding image to be nabla119902 = 119886nabla119868 Thereforethe linear equation is only guaranteed if 119868 is in the presenceof an edge and the output image 119902 will contain edges Todetermine the coefficients we require constraints from theinput image 119901 The output 119902 is the input 119901 with a number ofnoise components 119899119894 subtracted that is

119902119894 = 119901119894 minus 119899119894 (9)

To minimize the difference between the output 119902 and theinput 119901 and ensure the linearity of (8) the function 119864(119886119896 119887119896)is minimized in the window 120596119896 where 120576 is the regularizationparameter

119864 (119886119896 119887119896) = sum119894isin120596119896

((119886119896119868119894 + 119887119896 minus 119901119894)2 + 1205761198862119896) (10)

In order to minimize the value of the model 119864(119886119896 119887119896) we canderive 119886119896 and 119887119896 respectively and (10) can be solved usinglinear regression

119886119896 = ((1 |120596|) sum119894isin120596119896 119868119894119901119894) minus 1205831198961199011198961205902119896+ 120576

119887119896 = 119901119896 minus 119886119896120583119896(11)

where 120583119896 and 1205902119896 represent the mean and variance in the localwindow 120596119896 respectively |120596| is the number of pixels in thewindow and 119901119896 represents the mean value in the window 120596119896of 119901 After obtaining 119886119896 and 119887119896 in Figure 3 the output 119902119894 is

119902119894 = 1|120596| sum119896|119894isin120596119896

(119886119896119868119894 + 119887119896) = 119886119894119868119894 + 119887119894 (12)

where 119886119894 = (1|120596|) sum119896isin120596119894 119886119896 119887119894 = (1|120596|) sum119896isin120596119896 119887119896 Convert119886119896 and 119887119896 into weights forms which is the general form offiltering

21

qi

qi

Figure 3 Illustration of (12) When the window 120596 is sliding in theimage a pixel is involved in many windows that covers pixel Forinstance windows 1205961 and 1205962 are different local windows that coverthe same pixel 119894Therefore the output 119902119894 should average all the valuesof pixel 119894 in different windows

Therefore the guide filter algorithm proceeds as followsTraverse the entire image via each local window implement-ing the following calculation where 119891 is the mean filter withlocal window radius 119903 input image is 119901 guidance image is119868 corr is the correlation coefficient var is the variance 120576 issmoothing factor and cov is the covariance

mean119868 = 119891mean (119868 119903)mean119901 = 119891mean (119901 119903)corr119868 = 119891mean (119868 lowast 119868 119903)corr119868119901 = 119891mean (119868 lowast 119901 119903)var119868 = corr119868 minusmean119868 lowastmean119868

cov119868119901 = cov119868119901 minusmean119868 lowastmean119901

119886 = cov119868119901(var119868 + 120576)119887 = mean119901 minus 119886 lowastmean119868

mean119886 = 119891mean (119886 119903)mean119887 = 119891mean (119887 119903)

119902 = mean119886 lowast 119868 +mean119887

(13)

332 Edge Preservation When 119868 = 119901 the guided filterbecomes an edge-preserving filter At this point we have

119886119896 = 1205902119896(1205902119896+ 120576)

119887119896 = (1 minus 119886119896) 120583119896(14)

Therefore when the local window variance is large thecenter pixel value remains unchanged In smoother areas theaverage value of the neighboring pixels is used as the centerpixel value

6 Applied Computational Intelligence and Soft Computing

333 Guided Filter for Color Image When the guided filter isapplied independently to the three color channels of the colorimage (8) can be rewritten as

119902119894 = 119886119879119896 119868119894 + 119887119896 forall119894 isin 120596119896 (15)

where 119868119894 is a 3 times 1 color vector 119886119896 is a 3 times 1 coefficient vectorand 119902119894 119887119896 are scalarsThus the color image of the guided filteris

119886119896 = (sum119896

+120576119880)minus1

( 1|120596| sum119894isin120596119896 119868119894119901119894 minus 120583119896119901119896) 119887119896 = 119901119896 minus 119886119896119879120583119896119902119894 = 119886119894119879119868119894 + 119887119894

(16)

where sum119896 is the 3 times 3 covariance matrix of 119868 in 120596119896 and 119880 isthe 3 times 3 identity matrix

Because the local linear model is more effective in thecolor space the edges of gray images cannot be identified butthrough the color image of the guided filter it can be well-preserved Thus the image edges have a significant effect

34 Image Enhancement For images with more texture (ieImage 5) the above denoising method may cause someregions to appear too smooth Therefore it is necessary tofurther enhance the image texture detail Using (17) thedenoised image 119902 is subtracted from the original noiselessimage to yield the details of the loss in 119902 Positive number 119888 isto control and balance the degree of its stacking

119902 enhanced = (119868 minus 119902) lowast 119888 + 119902 (17)

The proposed algorithm uses the characteristics of the imagestructure In the wavelet domain threshold shrinkage is usedto denoise the image and then the guided filter enhances theedges of the denoised image to better reflect the texture detailsof the image

4 Experimental Results and Analysis

We conducted a series of experiments using MATLABR2015b and images in Figure 4 Images in Figure 4 Image 9Image 10 Image 11 and Image 12 are rich in texture Firstvariance of 001 and 003 Gaussian noise was added to thecolor images in Figure 4 This produced the noisy imagesshown in Figures 5(a) 6(a) 7(a) 8(a) 9(a) 10(a) 11(a) and12(a) The proposed method based on image characteristicsand the adaptive wavelet threshold shrinkage algorithm wasthen applied to obtain the denoised images 119901 shown inFigures 5(c) 6(c) 7(c) 8(c) 9(c) 10(c) 11(c) and 12(c) Weused the ldquosym4rdquo two-level wavelet decomposition function todecompose the noisy images with a local window 119877 = 5 lowast 5120573 = 03 and 120572 = 01 to control the degree of shrinkage in thewavelet coefficients

The guided filter was used to denoise the image 119901 withthe guiding image 119868 set to the original image without noiseThis was intended to give the image a better edge effect after

denoising The local window radius was set to 119903 = 8 and 120576 =0022 The image 119901 was denoised after the adaptive waveletthreshold algorithm In image 119901 the 119903 119892 119887 channels wereindividually subjected to the guide filterThe texture and edgeinformation of the images were enhanced and we obtainedthe output 119902 The parameter 119888 in (17) was found to give bettertexture effects and undistorted images when 119888 = 15 Thefinal results 119902 enhanced images are presented in Figures 5(f)6(f) 7(f) 8(f) 9(f) 10(f) 11(f) and 12(f) From Figures 9(f)10(f) 11(f) and 12(f) it can be concluded that the textureand the edge of images had a good performance in proposedmethod

The peak signal-to-noise ratio (119875119878119873119877) of the proposedmethod is presented in Table 1 These 119875119878119873119877119904 indicate thatthe method proposed in this paper is superior to bilateralfiltering the adaptive wavelet threshold algorithm nonlocalmeans [20] algorithm and BM3D [21] method When thenoise level increases the denoising effect of all five methodsdecreases but the proposedmethod gives better performancethan the other four

The 119875119878119873119877 is calculated as follows

PSNR = 10 lowast log10 (2552MSE

) MSE = 13 (mse119903 +mse119892 +mse119887) mse119896 = 1119898 lowast 119899

119898sum119894=1

119899sum119895=1

(119868 (119894 119895) minus 119902 (119894 119895))2 119896 = 119903 119892 119887

(18)

where the input image is 119868 and the output image is119902 enhanced The mean square error (119872119878119864) is the averagemean square error of the three channels (119903 119892 119887) in the colorimage

Wells [22] proposed a quality factor to evaluate theedges of an image after denoising This quality factor (Prattrsquosfigure of merit) takes into account three kinds of error theloss of the effective edge the edge of the positioning errorand noise misjudged as the edge Prattrsquos figure of meritprovides a quantitative evaluation of image edges and can beused to compare the edges in the denoised image and theoriginal image From Figures 13 and 14 it is obvious thatthere are differences between the texture parts Prattrsquos figureofmerit wasmeasured in four imagesThe results in Figure 15confirm that the edge quality factor (red curve) of the pro-posed method is higher than that of the other four methodsfor different degrees of noise variance Thus our methodachieves better edge effects

From a subjective point of view we find that not onlycan the proposedmethod preserve edge better it also reducesnoisewell when comparedwith the other fourmethods FromFigures 5ndash12 the result images (f) using proposed methodlook clearer than the others because we use a guided filterto filter the image and eliminate noise Moreover in Figures13 and 14 the edge of the result image that uses the pro-posed method is smooth and coherent which greatly helpsto enhance edge

Applied Computational Intelligence and Soft Computing 7

Figure 4 Test image Images 1ndash12 (from left to right top to bottom)

(a) 1205902 = 001 (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 5 Image 1 comparison of various experimental results under noise variance 1205902 = 001

To objectively evaluate the results we use the Prattrsquos figureof merit and PSNR for image quality evaluation Prattrsquos figureofmerit results are listed in Figure 15 119910-axis is the Pratt factorresults and 119909-axis is noise variance The curves showed thatPratt factor decreases when the noise variance increases butproposed method (red curves) is much higher than othersCurves results suggested that edge of image using proposedmethod is effective and abundant Table 1 is result of 119875119878119873119877The proposed method is superior to the other four methodswith respect to image processing

From the data in Table 1 and the quality factor curvesin Figure 15 we can conclude that the proposed method issuperior to bilateral filtering the adaptive wavelet thresholddenoising algorithm nonlocal means algorithm and BM3Dalgorithm on color image denoising From a visual point ofview the proposed method not only gives a good denoisingeffect but also achieves better edge retention

5 Conclusion

In this paper a new denoising method based on the adaptivewavelet threshold denoising algorithm and edge-guided fil-tering has been proposed The image denoising is performedaccording to the local structure of the image In comparativeexperiments against bilateral filtering the adaptive waveletdenoising method nonlocal means algorithm and BM3Dalgorithm the proposedmethod exhibited the best denoisingand edge preservation performance The proposed approachremoves Gaussian noise in the frequency domain and thenuses linear guided filtering to further enhance the imagerecovery resulting in better denoising and edge effects Ascolor images display more detailed textures this filteringovercomes the gradient inversion effect in the edge regionsAs the linearmodel (see (8)) is a block-unsupervised learningmethod it can be combined with other models to obtain new

8 Applied Computational Intelligence and Soft Computing

(a) 1205902 = 003 (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 6 Image 1 comparison of various experimental results under noise variance 1205902 = 003

(a) 1205902 = 001 (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 7 Image 5 comparison of various experimental results under noise variance 1205902 = 001

(a) 1205902 = 003 (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 8 Image 5 comparison of various experimental results under noise variance 1205902 = 003

(a) 1205902 = 001 (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 9 Image 9 comparison of various experimental results under noise variance 1205902 = 001

(a) 1205902 = 003 (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 10 Image 9 comparison of various experimental results under noise variance 1205902 = 003

Applied Computational Intelligence and Soft Computing 9

Table 1 PSNR of the proposed method bilateral filtering and adaptive wavelet

Noise variance 001 003 001 003 001 003Image 1 (256 lowast 256) Image 2 (512 lowast 512) Image 3 (256 lowast 256)

Adaptive wavelet 267048 254507 280801 264821 277967 261699Bilateral filtering 225751 220167 231551 226118 227560 221802Nonlocal means 299765 274871 301415 276777 301910 276823BM3D 289235 269276 304215 278901 309457 280957Proposed method 395634 353129 415647 360267 408101 355930

Image 4 (256 lowast 256) Image 5 (256 lowast 256) Image 6 (512 lowast 512)Adaptive wavelet 252375 242724 234663 227332 256576 245766Bilateral filtering 226074 219415 221076 215494 223016 217254Nonlocal means 266512 253287 253588 243120 278813 262105BM3D 255157 244968 240394 232556 280621 263334Proposed method 370265 341344 338535 321364 368294 339588

Image 7 (512 lowast 512) Image 8 (512 lowast 512) Image 9 (200 lowast 150)Adaptive wavelet 275706 259130 290039 269908 214746 208466Bilateral filtering 232116 224080 231373 224268 214834 210023Nonlocal means 294155 270736 313181 282534 237273 230137BM3D 291443 269120 320590 286197 217645 212712Proposed method 391414 348926 412256 357943 314041 300693

Image 10 (200 lowast 150) Image 11 (187 lowast 171) Image 12 (187 lowast 171)Adaptive wavelet 294247 275268 267443 254201 159075 169781Bilateral filtering 236728 230581 222984 217973 227751 226673Nonlocal means 303106 279794 287439 266227 174105 172673BM3D 308146 283780 318744 284922 310366 301990Proposed method 402191 359371 387096 350295 244256 257756

(a) 1205902 = 001 (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 11 Image 10 comparison of various experimental results under noise variance 1205902 = 001

(a) 1205902 = 003 (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 12 Image 10 comparison of various experimental results under noise variance 1205902 = 003

10 Applied Computational Intelligence and Soft Computing

(a) Image 1 edge (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 13 Image 1 edge comparison of various experimental results under noise variance 1205902 = 003

(a) Image 5 edge (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 14 Image 5 edge comparison of various experimental results under noise variance 1205902 = 001

Data

Data Data

Data DataAdaptive wavelet

Proposed method

Bilateral filtering

Nonlocal

BM3D

Data

Data Data

Data DataAdaptive wavelet

Proposed method

Bilateral filtering

Nonlocal

BM3DData

Data Data

Data DataAdaptive wavelet

Proposed method

Bilateral filtering

Nonlocal

BM3D

Data

Data Data

Data DataAdaptive wavelet

Proposed method

Bilateral filtering

Nonlocal

BM3D

87001 002 003 004 005 006 007

Image 1

008 009 01 011

888990919293949596

y

x

82001 002 003 004 005 006 007

Image 5

Image 10

008 009 01 011

848688909294

9896

y

x

001 002 003 004 005 006 007 008 009 01 01175

80

85

90

95

100

y

x

Image 12

001 002 003 004 005 006 007 008 009 01 01175

80

85

90

95

100

y

x

Figure 15 Prattrsquos figure of merit

Applied Computational Intelligence and Soft Computing 11

denoising techniquesThis will be the focus of future researchand exploration on color image denoising

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China (nos 61370138 61572077 andU1301251)and the Beijing Municipal Natural Science Foundation(no 4162027) the Project of Oriented Characteristic Dis-ciplines (no KYDE40201701) the Project of Constructionof Innovative Teams and Teacher Career Development forUniversities and Colleges Under Beijing Municipality (noIDHT20170511)

References

[1] C Tomasi and R Manduchi ldquoBilateral filtering for gray andcolor imagesrdquo in Proceedings of the International Conference onComputer Vision IEEE Computer Society 839 pages 1998

[2] Y Zhang X Tian and P Ren ldquoAn adaptive bilateral filter basedframework for image denoisingrdquo Neurocomputing vol 140 pp299ndash316 2014

[3] J S LimTwo-dimensional signal and image processing Prentice-Hall Inc Upper Saddle River NJ USA 1990

[4] D L Donoho and I M Johnstone ldquoAdapting to unknownsmoothness via wavelet shrinkagerdquo Journal of the AmericanStatistical Association vol 90 no 432 pp 1200ndash1224 1995

[5] D L Donoho ldquoDe-noising by soft-thresholdingrdquo Institute ofElectrical and Electronics Engineers Transactions on InformationTheory vol 41 no 3 pp 613ndash627 1995

[6] T D Bui and G Chen ldquoTranslation-invariant denoising usingmultiwaveletsrdquo IEEE Transactions on Signal Processing vol 46no 12 pp 3414ndash3420 1998

[7] C Srisailam P Sharma and S Suhane ldquoColor image denoisingusingwavelet soft thresholdingrdquo International Journal of Emerg-ing Technology and Advanced Engineering vol 4 no 7 pp 474ndash478 2014

[8] K K Gupta and R Gupta ldquoFeature adaptive wavelet shrinkagefor image denoisingrdquo in Proceedings of the 2007 InternationalConference on Signal Processing Communications and Network-ing ICSCN 2007 pp 81ndash85 ind February 2007

[9] E Ordentlich G Seroussi S Verdu M Weinberger and TWeissman ldquoA discrete universal denoiser and its application tobinary imagesrdquo in Proceedings of the International Conference onImage Processing (ICIP 2003) vol 1 pp 20ndash117 2003

[10] W Dong and H Ding ldquoFull frequency de-noising methodbased on wavelet decomposition and noise-type detectionrdquoNeurocomputing vol 214 pp 902ndash909 2016

[11] I Elyasi and S Zermchi ldquoElimination noise by adaptive waveletthresholdrdquoWorldAcademy of Science EngineeringampTechnologyvol 3 no 8 pp 1541ndash1545 2009

[12] A K Bhandari D Kumar A Kumar and G K Singh ldquoOpti-mal sub-band adaptive thresholding based edge preserved satel-lite image denoising using adaptive differential evolution algo-rithmrdquo Neurocomputing vol 174 pp 698ndash721 2016

[13] T T Cai and B W Silverman ldquoIncorporating information onneighbouring coefficients into wavelet estimation SankhyardquoThe Indian Journal of Statistics Series B (1960-2002) vol 63 no2 pp 127ndash148 2001

[14] G Y Chen T D Bui and A Krzyzak ldquoImage denoising usingneighbouring wavelet coefficientsrdquo Integrated Computer-AidedEngineering vol 12 no 1 pp 99ndash107 2005

[15] K He J Sun and X Tang ldquoGuided image filteringrdquo IEEE Tran-sactions on PatternAnalysis andMachine Intelligence vol 35 no6 pp 1397ndash1409 2013

[16] M Nasri and H Nezamabadi-pour ldquoImage denoising in thewavelet domain using a new adaptive thresholding functionrdquoNeurocomputing vol 72 no 4ndash6 pp 1012ndash1025 2009

[17] X Liu H Wan Z Shang and L Shi ldquoAutomatic extracellularspike denoising using wavelet neighbor coefficients and leveldependencyrdquo Neurocomputing vol 149 pp 1407ndash1414 2015

[18] C-C Kao J-H Lai and S-Y Chien ldquoVLSI architecture designof guided filter for 30 framess full-HD Videordquo IEEE Trans-actions on Circuits and Systems for Video Technology vol 24 no3 pp 513ndash524 2014

[19] A Gadge and S S Agrawal ldquoGuided filter for color imagerdquoIJIREEICE vol 4 no 6 pp 250ndash252 2016

[20] A Buades B Coll and J-M Morel ldquoA non-local algorithm forimage denoisingrdquo in Proceedings of the IEEE Computer SocietyConference on Computer Vision and Pattern Recognition (CVPRrsquo05) pp 60ndash65 June 2005

[21] K Dabov A Foi V Katkovnik and K Egiazarian ldquoImagedenoising by sparse 3-D transform-domain collaborative filter-ingrdquo IEEE Transactions on Image Processing vol 16 no 8 pp2080ndash2095 2007

[22] P N T Wells Digital Image Processing W K Pratt John WileyChichester UK 1991 (Medical Engineering amp Physics vol 16no 1 p 83 1994)

Submit your manuscripts athttpswwwhindawicom

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Applied Computational Intelligence and Soft Computing

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Advances in

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Human-ComputerInteraction

Advances in

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4 Applied Computational Intelligence and Soft Computing

Adaptive

Noise image Image p

waveletthreshold

Input

Guide

I = p

p

Left Right

Output

q

qi = aIi + b

ＩＨＭＮＬＣＨＮＭ qi = pi minus ni

Figure 1 Illustration of the proposed method It contains two main parts Left part is denoising by adaptive wavelet threshold algorithm toobtain denoise image 119901 Right part is using guided filter to enhance edges of image 119901

LL HL

LH HH

LL2

LH2 HH2

HL2

Figure 2 Two-level decomposition of the image Obtaining Low-Frequency image (LL) from the noise image and decomposing it resultingin subbands LL2 HL2 LH2 and HH2 The adaptive wavelet shrink algorithm is applied to each subband to denoise the image

1205902 = [Median (1003816100381610038161003816100381611988411989411989510038161003816100381610038161003816)06745 ] (119884119894119895 = subband HH) (7)

where 1205822 = (41205902 log119877) Equation (7) gives the noise variance1205902 and 119889119895119896 is the central pixel of the local window If 119889119895119896 is atthe boundary of the second wavelet coefficients a boundarycondition is required In the experiments we set 120572 = 01 120573 =03 Finally the reconstructed image is denoised

This denoising algorithm uses the DWT to calculate theenergy near the wavelet coefficients and then applies theadaptive wavelet threshold shrink function to denoise theimage In the experiments we added Gaussian noise withvariances of 1205902 = 001 and 1205902 = 003 to the images Adap-tive wavelet threshold shrink function denoising noise and

getting denoised image 119901 From the experimental results itcan be seen that when the noise variance is large the image 119901is not very clear after denoising in particular the effect of tex-ture is not obvious Therefore we need to enhance the image119901 after this processing step Thus the proposed techniqueuses the guided filter to enhance the image after denoising

33 Guided Filter to Further Processing Guided filtering is aspatial enhancement technique for the spatial domain andthe filtered output is a linear transformation of the localizedimageThefiltering algorithmuses a guiding image to processthe edges of the noisy image The guiding image can be theimage itself At this time their structures are the same thatis the edges of the original image are the same as the edges ofthe guiding image The output pixel values take into account

Applied Computational Intelligence and Soft Computing 5

the statistics of the local spatial neighborhood in the guidedimage Hence using guided filtering the output image ismore structured This can be used for image dehazing andso onThe guided filter adopts an exact linear algorithmThealgorithm is efficient and fast and is considered to be one ofthe fastest edge-preserving filters

For both grayscale and color images the guided filteringalgorithm has 119900(119873) time complexity regardless of the localwindow radius (119903)331 Algorithm of Guided Filter

Guided Filter Theguide image can be a separate image or theoriginal input image when the guiding image is the originalinput image the guided filter retains the edges for imagereconstruction

Assume that the input image is 119901 the output image is119902 and the guiding image is 119868 119902 and 119868 have a local linearrelationship in the window 120596119896 centered on pixel 119896

119902119894 = 119886119896119868119894 + 119887119896 forall119894 isin 120596119896 (8)

where 119886119896 119887119896 are linear (constant) coefficients in the localwindow and the window radius is 119903 Equation (8) calculatesthe guidance of the guiding image to be nabla119902 = 119886nabla119868 Thereforethe linear equation is only guaranteed if 119868 is in the presenceof an edge and the output image 119902 will contain edges Todetermine the coefficients we require constraints from theinput image 119901 The output 119902 is the input 119901 with a number ofnoise components 119899119894 subtracted that is

119902119894 = 119901119894 minus 119899119894 (9)

To minimize the difference between the output 119902 and theinput 119901 and ensure the linearity of (8) the function 119864(119886119896 119887119896)is minimized in the window 120596119896 where 120576 is the regularizationparameter

119864 (119886119896 119887119896) = sum119894isin120596119896

((119886119896119868119894 + 119887119896 minus 119901119894)2 + 1205761198862119896) (10)

In order to minimize the value of the model 119864(119886119896 119887119896) we canderive 119886119896 and 119887119896 respectively and (10) can be solved usinglinear regression

119886119896 = ((1 |120596|) sum119894isin120596119896 119868119894119901119894) minus 1205831198961199011198961205902119896+ 120576

119887119896 = 119901119896 minus 119886119896120583119896(11)

where 120583119896 and 1205902119896 represent the mean and variance in the localwindow 120596119896 respectively |120596| is the number of pixels in thewindow and 119901119896 represents the mean value in the window 120596119896of 119901 After obtaining 119886119896 and 119887119896 in Figure 3 the output 119902119894 is

119902119894 = 1|120596| sum119896|119894isin120596119896

(119886119896119868119894 + 119887119896) = 119886119894119868119894 + 119887119894 (12)

where 119886119894 = (1|120596|) sum119896isin120596119894 119886119896 119887119894 = (1|120596|) sum119896isin120596119896 119887119896 Convert119886119896 and 119887119896 into weights forms which is the general form offiltering

21

qi

qi

Figure 3 Illustration of (12) When the window 120596 is sliding in theimage a pixel is involved in many windows that covers pixel Forinstance windows 1205961 and 1205962 are different local windows that coverthe same pixel 119894Therefore the output 119902119894 should average all the valuesof pixel 119894 in different windows

Therefore the guide filter algorithm proceeds as followsTraverse the entire image via each local window implement-ing the following calculation where 119891 is the mean filter withlocal window radius 119903 input image is 119901 guidance image is119868 corr is the correlation coefficient var is the variance 120576 issmoothing factor and cov is the covariance

mean119868 = 119891mean (119868 119903)mean119901 = 119891mean (119901 119903)corr119868 = 119891mean (119868 lowast 119868 119903)corr119868119901 = 119891mean (119868 lowast 119901 119903)var119868 = corr119868 minusmean119868 lowastmean119868

cov119868119901 = cov119868119901 minusmean119868 lowastmean119901

119886 = cov119868119901(var119868 + 120576)119887 = mean119901 minus 119886 lowastmean119868

mean119886 = 119891mean (119886 119903)mean119887 = 119891mean (119887 119903)

119902 = mean119886 lowast 119868 +mean119887

(13)

332 Edge Preservation When 119868 = 119901 the guided filterbecomes an edge-preserving filter At this point we have

119886119896 = 1205902119896(1205902119896+ 120576)

119887119896 = (1 minus 119886119896) 120583119896(14)

Therefore when the local window variance is large thecenter pixel value remains unchanged In smoother areas theaverage value of the neighboring pixels is used as the centerpixel value

6 Applied Computational Intelligence and Soft Computing

333 Guided Filter for Color Image When the guided filter isapplied independently to the three color channels of the colorimage (8) can be rewritten as

119902119894 = 119886119879119896 119868119894 + 119887119896 forall119894 isin 120596119896 (15)

where 119868119894 is a 3 times 1 color vector 119886119896 is a 3 times 1 coefficient vectorand 119902119894 119887119896 are scalarsThus the color image of the guided filteris

119886119896 = (sum119896

+120576119880)minus1

( 1|120596| sum119894isin120596119896 119868119894119901119894 minus 120583119896119901119896) 119887119896 = 119901119896 minus 119886119896119879120583119896119902119894 = 119886119894119879119868119894 + 119887119894

(16)

where sum119896 is the 3 times 3 covariance matrix of 119868 in 120596119896 and 119880 isthe 3 times 3 identity matrix

Because the local linear model is more effective in thecolor space the edges of gray images cannot be identified butthrough the color image of the guided filter it can be well-preserved Thus the image edges have a significant effect

34 Image Enhancement For images with more texture (ieImage 5) the above denoising method may cause someregions to appear too smooth Therefore it is necessary tofurther enhance the image texture detail Using (17) thedenoised image 119902 is subtracted from the original noiselessimage to yield the details of the loss in 119902 Positive number 119888 isto control and balance the degree of its stacking

119902 enhanced = (119868 minus 119902) lowast 119888 + 119902 (17)

The proposed algorithm uses the characteristics of the imagestructure In the wavelet domain threshold shrinkage is usedto denoise the image and then the guided filter enhances theedges of the denoised image to better reflect the texture detailsof the image

4 Experimental Results and Analysis

We conducted a series of experiments using MATLABR2015b and images in Figure 4 Images in Figure 4 Image 9Image 10 Image 11 and Image 12 are rich in texture Firstvariance of 001 and 003 Gaussian noise was added to thecolor images in Figure 4 This produced the noisy imagesshown in Figures 5(a) 6(a) 7(a) 8(a) 9(a) 10(a) 11(a) and12(a) The proposed method based on image characteristicsand the adaptive wavelet threshold shrinkage algorithm wasthen applied to obtain the denoised images 119901 shown inFigures 5(c) 6(c) 7(c) 8(c) 9(c) 10(c) 11(c) and 12(c) Weused the ldquosym4rdquo two-level wavelet decomposition function todecompose the noisy images with a local window 119877 = 5 lowast 5120573 = 03 and 120572 = 01 to control the degree of shrinkage in thewavelet coefficients

The guided filter was used to denoise the image 119901 withthe guiding image 119868 set to the original image without noiseThis was intended to give the image a better edge effect after

denoising The local window radius was set to 119903 = 8 and 120576 =0022 The image 119901 was denoised after the adaptive waveletthreshold algorithm In image 119901 the 119903 119892 119887 channels wereindividually subjected to the guide filterThe texture and edgeinformation of the images were enhanced and we obtainedthe output 119902 The parameter 119888 in (17) was found to give bettertexture effects and undistorted images when 119888 = 15 Thefinal results 119902 enhanced images are presented in Figures 5(f)6(f) 7(f) 8(f) 9(f) 10(f) 11(f) and 12(f) From Figures 9(f)10(f) 11(f) and 12(f) it can be concluded that the textureand the edge of images had a good performance in proposedmethod

The peak signal-to-noise ratio (119875119878119873119877) of the proposedmethod is presented in Table 1 These 119875119878119873119877119904 indicate thatthe method proposed in this paper is superior to bilateralfiltering the adaptive wavelet threshold algorithm nonlocalmeans [20] algorithm and BM3D [21] method When thenoise level increases the denoising effect of all five methodsdecreases but the proposedmethod gives better performancethan the other four

The 119875119878119873119877 is calculated as follows

PSNR = 10 lowast log10 (2552MSE

) MSE = 13 (mse119903 +mse119892 +mse119887) mse119896 = 1119898 lowast 119899

119898sum119894=1

119899sum119895=1

(119868 (119894 119895) minus 119902 (119894 119895))2 119896 = 119903 119892 119887

(18)

where the input image is 119868 and the output image is119902 enhanced The mean square error (119872119878119864) is the averagemean square error of the three channels (119903 119892 119887) in the colorimage

Wells [22] proposed a quality factor to evaluate theedges of an image after denoising This quality factor (Prattrsquosfigure of merit) takes into account three kinds of error theloss of the effective edge the edge of the positioning errorand noise misjudged as the edge Prattrsquos figure of meritprovides a quantitative evaluation of image edges and can beused to compare the edges in the denoised image and theoriginal image From Figures 13 and 14 it is obvious thatthere are differences between the texture parts Prattrsquos figureofmerit wasmeasured in four imagesThe results in Figure 15confirm that the edge quality factor (red curve) of the pro-posed method is higher than that of the other four methodsfor different degrees of noise variance Thus our methodachieves better edge effects

From a subjective point of view we find that not onlycan the proposedmethod preserve edge better it also reducesnoisewell when comparedwith the other fourmethods FromFigures 5ndash12 the result images (f) using proposed methodlook clearer than the others because we use a guided filterto filter the image and eliminate noise Moreover in Figures13 and 14 the edge of the result image that uses the pro-posed method is smooth and coherent which greatly helpsto enhance edge

Applied Computational Intelligence and Soft Computing 7

Figure 4 Test image Images 1ndash12 (from left to right top to bottom)

(a) 1205902 = 001 (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 5 Image 1 comparison of various experimental results under noise variance 1205902 = 001

To objectively evaluate the results we use the Prattrsquos figureof merit and PSNR for image quality evaluation Prattrsquos figureofmerit results are listed in Figure 15 119910-axis is the Pratt factorresults and 119909-axis is noise variance The curves showed thatPratt factor decreases when the noise variance increases butproposed method (red curves) is much higher than othersCurves results suggested that edge of image using proposedmethod is effective and abundant Table 1 is result of 119875119878119873119877The proposed method is superior to the other four methodswith respect to image processing

From the data in Table 1 and the quality factor curvesin Figure 15 we can conclude that the proposed method issuperior to bilateral filtering the adaptive wavelet thresholddenoising algorithm nonlocal means algorithm and BM3Dalgorithm on color image denoising From a visual point ofview the proposed method not only gives a good denoisingeffect but also achieves better edge retention

5 Conclusion

In this paper a new denoising method based on the adaptivewavelet threshold denoising algorithm and edge-guided fil-tering has been proposed The image denoising is performedaccording to the local structure of the image In comparativeexperiments against bilateral filtering the adaptive waveletdenoising method nonlocal means algorithm and BM3Dalgorithm the proposedmethod exhibited the best denoisingand edge preservation performance The proposed approachremoves Gaussian noise in the frequency domain and thenuses linear guided filtering to further enhance the imagerecovery resulting in better denoising and edge effects Ascolor images display more detailed textures this filteringovercomes the gradient inversion effect in the edge regionsAs the linearmodel (see (8)) is a block-unsupervised learningmethod it can be combined with other models to obtain new

8 Applied Computational Intelligence and Soft Computing

(a) 1205902 = 003 (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 6 Image 1 comparison of various experimental results under noise variance 1205902 = 003

(a) 1205902 = 001 (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 7 Image 5 comparison of various experimental results under noise variance 1205902 = 001

(a) 1205902 = 003 (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 8 Image 5 comparison of various experimental results under noise variance 1205902 = 003

(a) 1205902 = 001 (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 9 Image 9 comparison of various experimental results under noise variance 1205902 = 001

(a) 1205902 = 003 (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 10 Image 9 comparison of various experimental results under noise variance 1205902 = 003

Applied Computational Intelligence and Soft Computing 9

Table 1 PSNR of the proposed method bilateral filtering and adaptive wavelet

Noise variance 001 003 001 003 001 003Image 1 (256 lowast 256) Image 2 (512 lowast 512) Image 3 (256 lowast 256)

Adaptive wavelet 267048 254507 280801 264821 277967 261699Bilateral filtering 225751 220167 231551 226118 227560 221802Nonlocal means 299765 274871 301415 276777 301910 276823BM3D 289235 269276 304215 278901 309457 280957Proposed method 395634 353129 415647 360267 408101 355930

Image 4 (256 lowast 256) Image 5 (256 lowast 256) Image 6 (512 lowast 512)Adaptive wavelet 252375 242724 234663 227332 256576 245766Bilateral filtering 226074 219415 221076 215494 223016 217254Nonlocal means 266512 253287 253588 243120 278813 262105BM3D 255157 244968 240394 232556 280621 263334Proposed method 370265 341344 338535 321364 368294 339588

Image 7 (512 lowast 512) Image 8 (512 lowast 512) Image 9 (200 lowast 150)Adaptive wavelet 275706 259130 290039 269908 214746 208466Bilateral filtering 232116 224080 231373 224268 214834 210023Nonlocal means 294155 270736 313181 282534 237273 230137BM3D 291443 269120 320590 286197 217645 212712Proposed method 391414 348926 412256 357943 314041 300693

Image 10 (200 lowast 150) Image 11 (187 lowast 171) Image 12 (187 lowast 171)Adaptive wavelet 294247 275268 267443 254201 159075 169781Bilateral filtering 236728 230581 222984 217973 227751 226673Nonlocal means 303106 279794 287439 266227 174105 172673BM3D 308146 283780 318744 284922 310366 301990Proposed method 402191 359371 387096 350295 244256 257756

(a) 1205902 = 001 (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 11 Image 10 comparison of various experimental results under noise variance 1205902 = 001

(a) 1205902 = 003 (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 12 Image 10 comparison of various experimental results under noise variance 1205902 = 003

10 Applied Computational Intelligence and Soft Computing

(a) Image 1 edge (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 13 Image 1 edge comparison of various experimental results under noise variance 1205902 = 003

(a) Image 5 edge (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 14 Image 5 edge comparison of various experimental results under noise variance 1205902 = 001

Data

Data Data

Data DataAdaptive wavelet

Proposed method

Bilateral filtering

Nonlocal

BM3D

Data

Data Data

Data DataAdaptive wavelet

Proposed method

Bilateral filtering

Nonlocal

BM3DData

Data Data

Data DataAdaptive wavelet

Proposed method

Bilateral filtering

Nonlocal

BM3D

Data

Data Data

Data DataAdaptive wavelet

Proposed method

Bilateral filtering

Nonlocal

BM3D

87001 002 003 004 005 006 007

Image 1

008 009 01 011

888990919293949596

y

x

82001 002 003 004 005 006 007

Image 5

Image 10

008 009 01 011

848688909294

9896

y

x

001 002 003 004 005 006 007 008 009 01 01175

80

85

90

95

100

y

x

Image 12

001 002 003 004 005 006 007 008 009 01 01175

80

85

90

95

100

y

x

Figure 15 Prattrsquos figure of merit

Applied Computational Intelligence and Soft Computing 11

denoising techniquesThis will be the focus of future researchand exploration on color image denoising

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China (nos 61370138 61572077 andU1301251)and the Beijing Municipal Natural Science Foundation(no 4162027) the Project of Oriented Characteristic Dis-ciplines (no KYDE40201701) the Project of Constructionof Innovative Teams and Teacher Career Development forUniversities and Colleges Under Beijing Municipality (noIDHT20170511)

References

[1] C Tomasi and R Manduchi ldquoBilateral filtering for gray andcolor imagesrdquo in Proceedings of the International Conference onComputer Vision IEEE Computer Society 839 pages 1998

[2] Y Zhang X Tian and P Ren ldquoAn adaptive bilateral filter basedframework for image denoisingrdquo Neurocomputing vol 140 pp299ndash316 2014

[3] J S LimTwo-dimensional signal and image processing Prentice-Hall Inc Upper Saddle River NJ USA 1990

[4] D L Donoho and I M Johnstone ldquoAdapting to unknownsmoothness via wavelet shrinkagerdquo Journal of the AmericanStatistical Association vol 90 no 432 pp 1200ndash1224 1995

[5] D L Donoho ldquoDe-noising by soft-thresholdingrdquo Institute ofElectrical and Electronics Engineers Transactions on InformationTheory vol 41 no 3 pp 613ndash627 1995

[6] T D Bui and G Chen ldquoTranslation-invariant denoising usingmultiwaveletsrdquo IEEE Transactions on Signal Processing vol 46no 12 pp 3414ndash3420 1998

[7] C Srisailam P Sharma and S Suhane ldquoColor image denoisingusingwavelet soft thresholdingrdquo International Journal of Emerg-ing Technology and Advanced Engineering vol 4 no 7 pp 474ndash478 2014

[8] K K Gupta and R Gupta ldquoFeature adaptive wavelet shrinkagefor image denoisingrdquo in Proceedings of the 2007 InternationalConference on Signal Processing Communications and Network-ing ICSCN 2007 pp 81ndash85 ind February 2007

[9] E Ordentlich G Seroussi S Verdu M Weinberger and TWeissman ldquoA discrete universal denoiser and its application tobinary imagesrdquo in Proceedings of the International Conference onImage Processing (ICIP 2003) vol 1 pp 20ndash117 2003

[10] W Dong and H Ding ldquoFull frequency de-noising methodbased on wavelet decomposition and noise-type detectionrdquoNeurocomputing vol 214 pp 902ndash909 2016

[11] I Elyasi and S Zermchi ldquoElimination noise by adaptive waveletthresholdrdquoWorldAcademy of Science EngineeringampTechnologyvol 3 no 8 pp 1541ndash1545 2009

[12] A K Bhandari D Kumar A Kumar and G K Singh ldquoOpti-mal sub-band adaptive thresholding based edge preserved satel-lite image denoising using adaptive differential evolution algo-rithmrdquo Neurocomputing vol 174 pp 698ndash721 2016

[13] T T Cai and B W Silverman ldquoIncorporating information onneighbouring coefficients into wavelet estimation SankhyardquoThe Indian Journal of Statistics Series B (1960-2002) vol 63 no2 pp 127ndash148 2001

[14] G Y Chen T D Bui and A Krzyzak ldquoImage denoising usingneighbouring wavelet coefficientsrdquo Integrated Computer-AidedEngineering vol 12 no 1 pp 99ndash107 2005

[15] K He J Sun and X Tang ldquoGuided image filteringrdquo IEEE Tran-sactions on PatternAnalysis andMachine Intelligence vol 35 no6 pp 1397ndash1409 2013

[16] M Nasri and H Nezamabadi-pour ldquoImage denoising in thewavelet domain using a new adaptive thresholding functionrdquoNeurocomputing vol 72 no 4ndash6 pp 1012ndash1025 2009

[17] X Liu H Wan Z Shang and L Shi ldquoAutomatic extracellularspike denoising using wavelet neighbor coefficients and leveldependencyrdquo Neurocomputing vol 149 pp 1407ndash1414 2015

[18] C-C Kao J-H Lai and S-Y Chien ldquoVLSI architecture designof guided filter for 30 framess full-HD Videordquo IEEE Trans-actions on Circuits and Systems for Video Technology vol 24 no3 pp 513ndash524 2014

[19] A Gadge and S S Agrawal ldquoGuided filter for color imagerdquoIJIREEICE vol 4 no 6 pp 250ndash252 2016

[20] A Buades B Coll and J-M Morel ldquoA non-local algorithm forimage denoisingrdquo in Proceedings of the IEEE Computer SocietyConference on Computer Vision and Pattern Recognition (CVPRrsquo05) pp 60ndash65 June 2005

[21] K Dabov A Foi V Katkovnik and K Egiazarian ldquoImagedenoising by sparse 3-D transform-domain collaborative filter-ingrdquo IEEE Transactions on Image Processing vol 16 no 8 pp2080ndash2095 2007

[22] P N T Wells Digital Image Processing W K Pratt John WileyChichester UK 1991 (Medical Engineering amp Physics vol 16no 1 p 83 1994)

Submit your manuscripts athttpswwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing 5

the statistics of the local spatial neighborhood in the guidedimage Hence using guided filtering the output image ismore structured This can be used for image dehazing andso onThe guided filter adopts an exact linear algorithmThealgorithm is efficient and fast and is considered to be one ofthe fastest edge-preserving filters

For both grayscale and color images the guided filteringalgorithm has 119900(119873) time complexity regardless of the localwindow radius (119903)331 Algorithm of Guided Filter

Guided Filter Theguide image can be a separate image or theoriginal input image when the guiding image is the originalinput image the guided filter retains the edges for imagereconstruction

Assume that the input image is 119901 the output image is119902 and the guiding image is 119868 119902 and 119868 have a local linearrelationship in the window 120596119896 centered on pixel 119896

119902119894 = 119886119896119868119894 + 119887119896 forall119894 isin 120596119896 (8)

where 119886119896 119887119896 are linear (constant) coefficients in the localwindow and the window radius is 119903 Equation (8) calculatesthe guidance of the guiding image to be nabla119902 = 119886nabla119868 Thereforethe linear equation is only guaranteed if 119868 is in the presenceof an edge and the output image 119902 will contain edges Todetermine the coefficients we require constraints from theinput image 119901 The output 119902 is the input 119901 with a number ofnoise components 119899119894 subtracted that is

119902119894 = 119901119894 minus 119899119894 (9)

To minimize the difference between the output 119902 and theinput 119901 and ensure the linearity of (8) the function 119864(119886119896 119887119896)is minimized in the window 120596119896 where 120576 is the regularizationparameter

119864 (119886119896 119887119896) = sum119894isin120596119896

((119886119896119868119894 + 119887119896 minus 119901119894)2 + 1205761198862119896) (10)

In order to minimize the value of the model 119864(119886119896 119887119896) we canderive 119886119896 and 119887119896 respectively and (10) can be solved usinglinear regression

119886119896 = ((1 |120596|) sum119894isin120596119896 119868119894119901119894) minus 1205831198961199011198961205902119896+ 120576

119887119896 = 119901119896 minus 119886119896120583119896(11)

where 120583119896 and 1205902119896 represent the mean and variance in the localwindow 120596119896 respectively |120596| is the number of pixels in thewindow and 119901119896 represents the mean value in the window 120596119896of 119901 After obtaining 119886119896 and 119887119896 in Figure 3 the output 119902119894 is

119902119894 = 1|120596| sum119896|119894isin120596119896

(119886119896119868119894 + 119887119896) = 119886119894119868119894 + 119887119894 (12)

where 119886119894 = (1|120596|) sum119896isin120596119894 119886119896 119887119894 = (1|120596|) sum119896isin120596119896 119887119896 Convert119886119896 and 119887119896 into weights forms which is the general form offiltering

21

qi

qi

Figure 3 Illustration of (12) When the window 120596 is sliding in theimage a pixel is involved in many windows that covers pixel Forinstance windows 1205961 and 1205962 are different local windows that coverthe same pixel 119894Therefore the output 119902119894 should average all the valuesof pixel 119894 in different windows

Therefore the guide filter algorithm proceeds as followsTraverse the entire image via each local window implement-ing the following calculation where 119891 is the mean filter withlocal window radius 119903 input image is 119901 guidance image is119868 corr is the correlation coefficient var is the variance 120576 issmoothing factor and cov is the covariance

mean119868 = 119891mean (119868 119903)mean119901 = 119891mean (119901 119903)corr119868 = 119891mean (119868 lowast 119868 119903)corr119868119901 = 119891mean (119868 lowast 119901 119903)var119868 = corr119868 minusmean119868 lowastmean119868

cov119868119901 = cov119868119901 minusmean119868 lowastmean119901

119886 = cov119868119901(var119868 + 120576)119887 = mean119901 minus 119886 lowastmean119868

mean119886 = 119891mean (119886 119903)mean119887 = 119891mean (119887 119903)

119902 = mean119886 lowast 119868 +mean119887

(13)

332 Edge Preservation When 119868 = 119901 the guided filterbecomes an edge-preserving filter At this point we have

119886119896 = 1205902119896(1205902119896+ 120576)

119887119896 = (1 minus 119886119896) 120583119896(14)

Therefore when the local window variance is large thecenter pixel value remains unchanged In smoother areas theaverage value of the neighboring pixels is used as the centerpixel value

6 Applied Computational Intelligence and Soft Computing

333 Guided Filter for Color Image When the guided filter isapplied independently to the three color channels of the colorimage (8) can be rewritten as

119902119894 = 119886119879119896 119868119894 + 119887119896 forall119894 isin 120596119896 (15)

where 119868119894 is a 3 times 1 color vector 119886119896 is a 3 times 1 coefficient vectorand 119902119894 119887119896 are scalarsThus the color image of the guided filteris

119886119896 = (sum119896

+120576119880)minus1

( 1|120596| sum119894isin120596119896 119868119894119901119894 minus 120583119896119901119896) 119887119896 = 119901119896 minus 119886119896119879120583119896119902119894 = 119886119894119879119868119894 + 119887119894

(16)

where sum119896 is the 3 times 3 covariance matrix of 119868 in 120596119896 and 119880 isthe 3 times 3 identity matrix

Because the local linear model is more effective in thecolor space the edges of gray images cannot be identified butthrough the color image of the guided filter it can be well-preserved Thus the image edges have a significant effect

34 Image Enhancement For images with more texture (ieImage 5) the above denoising method may cause someregions to appear too smooth Therefore it is necessary tofurther enhance the image texture detail Using (17) thedenoised image 119902 is subtracted from the original noiselessimage to yield the details of the loss in 119902 Positive number 119888 isto control and balance the degree of its stacking

119902 enhanced = (119868 minus 119902) lowast 119888 + 119902 (17)

The proposed algorithm uses the characteristics of the imagestructure In the wavelet domain threshold shrinkage is usedto denoise the image and then the guided filter enhances theedges of the denoised image to better reflect the texture detailsof the image

4 Experimental Results and Analysis

We conducted a series of experiments using MATLABR2015b and images in Figure 4 Images in Figure 4 Image 9Image 10 Image 11 and Image 12 are rich in texture Firstvariance of 001 and 003 Gaussian noise was added to thecolor images in Figure 4 This produced the noisy imagesshown in Figures 5(a) 6(a) 7(a) 8(a) 9(a) 10(a) 11(a) and12(a) The proposed method based on image characteristicsand the adaptive wavelet threshold shrinkage algorithm wasthen applied to obtain the denoised images 119901 shown inFigures 5(c) 6(c) 7(c) 8(c) 9(c) 10(c) 11(c) and 12(c) Weused the ldquosym4rdquo two-level wavelet decomposition function todecompose the noisy images with a local window 119877 = 5 lowast 5120573 = 03 and 120572 = 01 to control the degree of shrinkage in thewavelet coefficients

The guided filter was used to denoise the image 119901 withthe guiding image 119868 set to the original image without noiseThis was intended to give the image a better edge effect after

denoising The local window radius was set to 119903 = 8 and 120576 =0022 The image 119901 was denoised after the adaptive waveletthreshold algorithm In image 119901 the 119903 119892 119887 channels wereindividually subjected to the guide filterThe texture and edgeinformation of the images were enhanced and we obtainedthe output 119902 The parameter 119888 in (17) was found to give bettertexture effects and undistorted images when 119888 = 15 Thefinal results 119902 enhanced images are presented in Figures 5(f)6(f) 7(f) 8(f) 9(f) 10(f) 11(f) and 12(f) From Figures 9(f)10(f) 11(f) and 12(f) it can be concluded that the textureand the edge of images had a good performance in proposedmethod

The peak signal-to-noise ratio (119875119878119873119877) of the proposedmethod is presented in Table 1 These 119875119878119873119877119904 indicate thatthe method proposed in this paper is superior to bilateralfiltering the adaptive wavelet threshold algorithm nonlocalmeans [20] algorithm and BM3D [21] method When thenoise level increases the denoising effect of all five methodsdecreases but the proposedmethod gives better performancethan the other four

The 119875119878119873119877 is calculated as follows

PSNR = 10 lowast log10 (2552MSE

) MSE = 13 (mse119903 +mse119892 +mse119887) mse119896 = 1119898 lowast 119899

119898sum119894=1

119899sum119895=1

(119868 (119894 119895) minus 119902 (119894 119895))2 119896 = 119903 119892 119887

(18)

where the input image is 119868 and the output image is119902 enhanced The mean square error (119872119878119864) is the averagemean square error of the three channels (119903 119892 119887) in the colorimage

Wells [22] proposed a quality factor to evaluate theedges of an image after denoising This quality factor (Prattrsquosfigure of merit) takes into account three kinds of error theloss of the effective edge the edge of the positioning errorand noise misjudged as the edge Prattrsquos figure of meritprovides a quantitative evaluation of image edges and can beused to compare the edges in the denoised image and theoriginal image From Figures 13 and 14 it is obvious thatthere are differences between the texture parts Prattrsquos figureofmerit wasmeasured in four imagesThe results in Figure 15confirm that the edge quality factor (red curve) of the pro-posed method is higher than that of the other four methodsfor different degrees of noise variance Thus our methodachieves better edge effects

From a subjective point of view we find that not onlycan the proposedmethod preserve edge better it also reducesnoisewell when comparedwith the other fourmethods FromFigures 5ndash12 the result images (f) using proposed methodlook clearer than the others because we use a guided filterto filter the image and eliminate noise Moreover in Figures13 and 14 the edge of the result image that uses the pro-posed method is smooth and coherent which greatly helpsto enhance edge

Applied Computational Intelligence and Soft Computing 7

Figure 4 Test image Images 1ndash12 (from left to right top to bottom)

(a) 1205902 = 001 (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 5 Image 1 comparison of various experimental results under noise variance 1205902 = 001

To objectively evaluate the results we use the Prattrsquos figureof merit and PSNR for image quality evaluation Prattrsquos figureofmerit results are listed in Figure 15 119910-axis is the Pratt factorresults and 119909-axis is noise variance The curves showed thatPratt factor decreases when the noise variance increases butproposed method (red curves) is much higher than othersCurves results suggested that edge of image using proposedmethod is effective and abundant Table 1 is result of 119875119878119873119877The proposed method is superior to the other four methodswith respect to image processing

From the data in Table 1 and the quality factor curvesin Figure 15 we can conclude that the proposed method issuperior to bilateral filtering the adaptive wavelet thresholddenoising algorithm nonlocal means algorithm and BM3Dalgorithm on color image denoising From a visual point ofview the proposed method not only gives a good denoisingeffect but also achieves better edge retention

5 Conclusion

In this paper a new denoising method based on the adaptivewavelet threshold denoising algorithm and edge-guided fil-tering has been proposed The image denoising is performedaccording to the local structure of the image In comparativeexperiments against bilateral filtering the adaptive waveletdenoising method nonlocal means algorithm and BM3Dalgorithm the proposedmethod exhibited the best denoisingand edge preservation performance The proposed approachremoves Gaussian noise in the frequency domain and thenuses linear guided filtering to further enhance the imagerecovery resulting in better denoising and edge effects Ascolor images display more detailed textures this filteringovercomes the gradient inversion effect in the edge regionsAs the linearmodel (see (8)) is a block-unsupervised learningmethod it can be combined with other models to obtain new

8 Applied Computational Intelligence and Soft Computing

(a) 1205902 = 003 (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 6 Image 1 comparison of various experimental results under noise variance 1205902 = 003

(a) 1205902 = 001 (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 7 Image 5 comparison of various experimental results under noise variance 1205902 = 001

(a) 1205902 = 003 (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 8 Image 5 comparison of various experimental results under noise variance 1205902 = 003

(a) 1205902 = 001 (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 9 Image 9 comparison of various experimental results under noise variance 1205902 = 001

(a) 1205902 = 003 (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 10 Image 9 comparison of various experimental results under noise variance 1205902 = 003

Applied Computational Intelligence and Soft Computing 9

Table 1 PSNR of the proposed method bilateral filtering and adaptive wavelet

Noise variance 001 003 001 003 001 003Image 1 (256 lowast 256) Image 2 (512 lowast 512) Image 3 (256 lowast 256)

Adaptive wavelet 267048 254507 280801 264821 277967 261699Bilateral filtering 225751 220167 231551 226118 227560 221802Nonlocal means 299765 274871 301415 276777 301910 276823BM3D 289235 269276 304215 278901 309457 280957Proposed method 395634 353129 415647 360267 408101 355930

Image 4 (256 lowast 256) Image 5 (256 lowast 256) Image 6 (512 lowast 512)Adaptive wavelet 252375 242724 234663 227332 256576 245766Bilateral filtering 226074 219415 221076 215494 223016 217254Nonlocal means 266512 253287 253588 243120 278813 262105BM3D 255157 244968 240394 232556 280621 263334Proposed method 370265 341344 338535 321364 368294 339588

Image 7 (512 lowast 512) Image 8 (512 lowast 512) Image 9 (200 lowast 150)Adaptive wavelet 275706 259130 290039 269908 214746 208466Bilateral filtering 232116 224080 231373 224268 214834 210023Nonlocal means 294155 270736 313181 282534 237273 230137BM3D 291443 269120 320590 286197 217645 212712Proposed method 391414 348926 412256 357943 314041 300693

Image 10 (200 lowast 150) Image 11 (187 lowast 171) Image 12 (187 lowast 171)Adaptive wavelet 294247 275268 267443 254201 159075 169781Bilateral filtering 236728 230581 222984 217973 227751 226673Nonlocal means 303106 279794 287439 266227 174105 172673BM3D 308146 283780 318744 284922 310366 301990Proposed method 402191 359371 387096 350295 244256 257756

(a) 1205902 = 001 (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 11 Image 10 comparison of various experimental results under noise variance 1205902 = 001

(a) 1205902 = 003 (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 12 Image 10 comparison of various experimental results under noise variance 1205902 = 003

10 Applied Computational Intelligence and Soft Computing

(a) Image 1 edge (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 13 Image 1 edge comparison of various experimental results under noise variance 1205902 = 003

(a) Image 5 edge (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 14 Image 5 edge comparison of various experimental results under noise variance 1205902 = 001

Data

Data Data

Data DataAdaptive wavelet

Proposed method

Bilateral filtering

Nonlocal

BM3D

Data

Data Data

Data DataAdaptive wavelet

Proposed method

Bilateral filtering

Nonlocal

BM3DData

Data Data

Data DataAdaptive wavelet

Proposed method

Bilateral filtering

Nonlocal

BM3D

Data

Data Data

Data DataAdaptive wavelet

Proposed method

Bilateral filtering

Nonlocal

BM3D

87001 002 003 004 005 006 007

Image 1

008 009 01 011

888990919293949596

y

x

82001 002 003 004 005 006 007

Image 5

Image 10

008 009 01 011

848688909294

9896

y

x

001 002 003 004 005 006 007 008 009 01 01175

80

85

90

95

100

y

x

Image 12

001 002 003 004 005 006 007 008 009 01 01175

80

85

90

95

100

y

x

Figure 15 Prattrsquos figure of merit

Applied Computational Intelligence and Soft Computing 11

denoising techniquesThis will be the focus of future researchand exploration on color image denoising

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China (nos 61370138 61572077 andU1301251)and the Beijing Municipal Natural Science Foundation(no 4162027) the Project of Oriented Characteristic Dis-ciplines (no KYDE40201701) the Project of Constructionof Innovative Teams and Teacher Career Development forUniversities and Colleges Under Beijing Municipality (noIDHT20170511)

References

[1] C Tomasi and R Manduchi ldquoBilateral filtering for gray andcolor imagesrdquo in Proceedings of the International Conference onComputer Vision IEEE Computer Society 839 pages 1998

[2] Y Zhang X Tian and P Ren ldquoAn adaptive bilateral filter basedframework for image denoisingrdquo Neurocomputing vol 140 pp299ndash316 2014

[3] J S LimTwo-dimensional signal and image processing Prentice-Hall Inc Upper Saddle River NJ USA 1990

[4] D L Donoho and I M Johnstone ldquoAdapting to unknownsmoothness via wavelet shrinkagerdquo Journal of the AmericanStatistical Association vol 90 no 432 pp 1200ndash1224 1995

[5] D L Donoho ldquoDe-noising by soft-thresholdingrdquo Institute ofElectrical and Electronics Engineers Transactions on InformationTheory vol 41 no 3 pp 613ndash627 1995

[6] T D Bui and G Chen ldquoTranslation-invariant denoising usingmultiwaveletsrdquo IEEE Transactions on Signal Processing vol 46no 12 pp 3414ndash3420 1998

[7] C Srisailam P Sharma and S Suhane ldquoColor image denoisingusingwavelet soft thresholdingrdquo International Journal of Emerg-ing Technology and Advanced Engineering vol 4 no 7 pp 474ndash478 2014

[8] K K Gupta and R Gupta ldquoFeature adaptive wavelet shrinkagefor image denoisingrdquo in Proceedings of the 2007 InternationalConference on Signal Processing Communications and Network-ing ICSCN 2007 pp 81ndash85 ind February 2007

[9] E Ordentlich G Seroussi S Verdu M Weinberger and TWeissman ldquoA discrete universal denoiser and its application tobinary imagesrdquo in Proceedings of the International Conference onImage Processing (ICIP 2003) vol 1 pp 20ndash117 2003

[10] W Dong and H Ding ldquoFull frequency de-noising methodbased on wavelet decomposition and noise-type detectionrdquoNeurocomputing vol 214 pp 902ndash909 2016

[11] I Elyasi and S Zermchi ldquoElimination noise by adaptive waveletthresholdrdquoWorldAcademy of Science EngineeringampTechnologyvol 3 no 8 pp 1541ndash1545 2009

[12] A K Bhandari D Kumar A Kumar and G K Singh ldquoOpti-mal sub-band adaptive thresholding based edge preserved satel-lite image denoising using adaptive differential evolution algo-rithmrdquo Neurocomputing vol 174 pp 698ndash721 2016

[13] T T Cai and B W Silverman ldquoIncorporating information onneighbouring coefficients into wavelet estimation SankhyardquoThe Indian Journal of Statistics Series B (1960-2002) vol 63 no2 pp 127ndash148 2001

[14] G Y Chen T D Bui and A Krzyzak ldquoImage denoising usingneighbouring wavelet coefficientsrdquo Integrated Computer-AidedEngineering vol 12 no 1 pp 99ndash107 2005

[15] K He J Sun and X Tang ldquoGuided image filteringrdquo IEEE Tran-sactions on PatternAnalysis andMachine Intelligence vol 35 no6 pp 1397ndash1409 2013

[16] M Nasri and H Nezamabadi-pour ldquoImage denoising in thewavelet domain using a new adaptive thresholding functionrdquoNeurocomputing vol 72 no 4ndash6 pp 1012ndash1025 2009

[17] X Liu H Wan Z Shang and L Shi ldquoAutomatic extracellularspike denoising using wavelet neighbor coefficients and leveldependencyrdquo Neurocomputing vol 149 pp 1407ndash1414 2015

[18] C-C Kao J-H Lai and S-Y Chien ldquoVLSI architecture designof guided filter for 30 framess full-HD Videordquo IEEE Trans-actions on Circuits and Systems for Video Technology vol 24 no3 pp 513ndash524 2014

[19] A Gadge and S S Agrawal ldquoGuided filter for color imagerdquoIJIREEICE vol 4 no 6 pp 250ndash252 2016

[20] A Buades B Coll and J-M Morel ldquoA non-local algorithm forimage denoisingrdquo in Proceedings of the IEEE Computer SocietyConference on Computer Vision and Pattern Recognition (CVPRrsquo05) pp 60ndash65 June 2005

[21] K Dabov A Foi V Katkovnik and K Egiazarian ldquoImagedenoising by sparse 3-D transform-domain collaborative filter-ingrdquo IEEE Transactions on Image Processing vol 16 no 8 pp2080ndash2095 2007

[22] P N T Wells Digital Image Processing W K Pratt John WileyChichester UK 1991 (Medical Engineering amp Physics vol 16no 1 p 83 1994)

Submit your manuscripts athttpswwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

6 Applied Computational Intelligence and Soft Computing

333 Guided Filter for Color Image When the guided filter isapplied independently to the three color channels of the colorimage (8) can be rewritten as

119902119894 = 119886119879119896 119868119894 + 119887119896 forall119894 isin 120596119896 (15)

where 119868119894 is a 3 times 1 color vector 119886119896 is a 3 times 1 coefficient vectorand 119902119894 119887119896 are scalarsThus the color image of the guided filteris

119886119896 = (sum119896

+120576119880)minus1

( 1|120596| sum119894isin120596119896 119868119894119901119894 minus 120583119896119901119896) 119887119896 = 119901119896 minus 119886119896119879120583119896119902119894 = 119886119894119879119868119894 + 119887119894

(16)

where sum119896 is the 3 times 3 covariance matrix of 119868 in 120596119896 and 119880 isthe 3 times 3 identity matrix

Because the local linear model is more effective in thecolor space the edges of gray images cannot be identified butthrough the color image of the guided filter it can be well-preserved Thus the image edges have a significant effect

34 Image Enhancement For images with more texture (ieImage 5) the above denoising method may cause someregions to appear too smooth Therefore it is necessary tofurther enhance the image texture detail Using (17) thedenoised image 119902 is subtracted from the original noiselessimage to yield the details of the loss in 119902 Positive number 119888 isto control and balance the degree of its stacking

119902 enhanced = (119868 minus 119902) lowast 119888 + 119902 (17)

The proposed algorithm uses the characteristics of the imagestructure In the wavelet domain threshold shrinkage is usedto denoise the image and then the guided filter enhances theedges of the denoised image to better reflect the texture detailsof the image

4 Experimental Results and Analysis

We conducted a series of experiments using MATLABR2015b and images in Figure 4 Images in Figure 4 Image 9Image 10 Image 11 and Image 12 are rich in texture Firstvariance of 001 and 003 Gaussian noise was added to thecolor images in Figure 4 This produced the noisy imagesshown in Figures 5(a) 6(a) 7(a) 8(a) 9(a) 10(a) 11(a) and12(a) The proposed method based on image characteristicsand the adaptive wavelet threshold shrinkage algorithm wasthen applied to obtain the denoised images 119901 shown inFigures 5(c) 6(c) 7(c) 8(c) 9(c) 10(c) 11(c) and 12(c) Weused the ldquosym4rdquo two-level wavelet decomposition function todecompose the noisy images with a local window 119877 = 5 lowast 5120573 = 03 and 120572 = 01 to control the degree of shrinkage in thewavelet coefficients

The guided filter was used to denoise the image 119901 withthe guiding image 119868 set to the original image without noiseThis was intended to give the image a better edge effect after

denoising The local window radius was set to 119903 = 8 and 120576 =0022 The image 119901 was denoised after the adaptive waveletthreshold algorithm In image 119901 the 119903 119892 119887 channels wereindividually subjected to the guide filterThe texture and edgeinformation of the images were enhanced and we obtainedthe output 119902 The parameter 119888 in (17) was found to give bettertexture effects and undistorted images when 119888 = 15 Thefinal results 119902 enhanced images are presented in Figures 5(f)6(f) 7(f) 8(f) 9(f) 10(f) 11(f) and 12(f) From Figures 9(f)10(f) 11(f) and 12(f) it can be concluded that the textureand the edge of images had a good performance in proposedmethod

The peak signal-to-noise ratio (119875119878119873119877) of the proposedmethod is presented in Table 1 These 119875119878119873119877119904 indicate thatthe method proposed in this paper is superior to bilateralfiltering the adaptive wavelet threshold algorithm nonlocalmeans [20] algorithm and BM3D [21] method When thenoise level increases the denoising effect of all five methodsdecreases but the proposedmethod gives better performancethan the other four

The 119875119878119873119877 is calculated as follows

PSNR = 10 lowast log10 (2552MSE

) MSE = 13 (mse119903 +mse119892 +mse119887) mse119896 = 1119898 lowast 119899

119898sum119894=1

119899sum119895=1

(119868 (119894 119895) minus 119902 (119894 119895))2 119896 = 119903 119892 119887

(18)

where the input image is 119868 and the output image is119902 enhanced The mean square error (119872119878119864) is the averagemean square error of the three channels (119903 119892 119887) in the colorimage

Wells [22] proposed a quality factor to evaluate theedges of an image after denoising This quality factor (Prattrsquosfigure of merit) takes into account three kinds of error theloss of the effective edge the edge of the positioning errorand noise misjudged as the edge Prattrsquos figure of meritprovides a quantitative evaluation of image edges and can beused to compare the edges in the denoised image and theoriginal image From Figures 13 and 14 it is obvious thatthere are differences between the texture parts Prattrsquos figureofmerit wasmeasured in four imagesThe results in Figure 15confirm that the edge quality factor (red curve) of the pro-posed method is higher than that of the other four methodsfor different degrees of noise variance Thus our methodachieves better edge effects

From a subjective point of view we find that not onlycan the proposedmethod preserve edge better it also reducesnoisewell when comparedwith the other fourmethods FromFigures 5ndash12 the result images (f) using proposed methodlook clearer than the others because we use a guided filterto filter the image and eliminate noise Moreover in Figures13 and 14 the edge of the result image that uses the pro-posed method is smooth and coherent which greatly helpsto enhance edge

Applied Computational Intelligence and Soft Computing 7

Figure 4 Test image Images 1ndash12 (from left to right top to bottom)

(a) 1205902 = 001 (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 5 Image 1 comparison of various experimental results under noise variance 1205902 = 001

To objectively evaluate the results we use the Prattrsquos figureof merit and PSNR for image quality evaluation Prattrsquos figureofmerit results are listed in Figure 15 119910-axis is the Pratt factorresults and 119909-axis is noise variance The curves showed thatPratt factor decreases when the noise variance increases butproposed method (red curves) is much higher than othersCurves results suggested that edge of image using proposedmethod is effective and abundant Table 1 is result of 119875119878119873119877The proposed method is superior to the other four methodswith respect to image processing

From the data in Table 1 and the quality factor curvesin Figure 15 we can conclude that the proposed method issuperior to bilateral filtering the adaptive wavelet thresholddenoising algorithm nonlocal means algorithm and BM3Dalgorithm on color image denoising From a visual point ofview the proposed method not only gives a good denoisingeffect but also achieves better edge retention

5 Conclusion

In this paper a new denoising method based on the adaptivewavelet threshold denoising algorithm and edge-guided fil-tering has been proposed The image denoising is performedaccording to the local structure of the image In comparativeexperiments against bilateral filtering the adaptive waveletdenoising method nonlocal means algorithm and BM3Dalgorithm the proposedmethod exhibited the best denoisingand edge preservation performance The proposed approachremoves Gaussian noise in the frequency domain and thenuses linear guided filtering to further enhance the imagerecovery resulting in better denoising and edge effects Ascolor images display more detailed textures this filteringovercomes the gradient inversion effect in the edge regionsAs the linearmodel (see (8)) is a block-unsupervised learningmethod it can be combined with other models to obtain new

8 Applied Computational Intelligence and Soft Computing

(a) 1205902 = 003 (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 6 Image 1 comparison of various experimental results under noise variance 1205902 = 003

(a) 1205902 = 001 (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 7 Image 5 comparison of various experimental results under noise variance 1205902 = 001

(a) 1205902 = 003 (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 8 Image 5 comparison of various experimental results under noise variance 1205902 = 003

(a) 1205902 = 001 (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 9 Image 9 comparison of various experimental results under noise variance 1205902 = 001

(a) 1205902 = 003 (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 10 Image 9 comparison of various experimental results under noise variance 1205902 = 003

Applied Computational Intelligence and Soft Computing 9

Table 1 PSNR of the proposed method bilateral filtering and adaptive wavelet

Noise variance 001 003 001 003 001 003Image 1 (256 lowast 256) Image 2 (512 lowast 512) Image 3 (256 lowast 256)

Adaptive wavelet 267048 254507 280801 264821 277967 261699Bilateral filtering 225751 220167 231551 226118 227560 221802Nonlocal means 299765 274871 301415 276777 301910 276823BM3D 289235 269276 304215 278901 309457 280957Proposed method 395634 353129 415647 360267 408101 355930

Image 4 (256 lowast 256) Image 5 (256 lowast 256) Image 6 (512 lowast 512)Adaptive wavelet 252375 242724 234663 227332 256576 245766Bilateral filtering 226074 219415 221076 215494 223016 217254Nonlocal means 266512 253287 253588 243120 278813 262105BM3D 255157 244968 240394 232556 280621 263334Proposed method 370265 341344 338535 321364 368294 339588

Image 7 (512 lowast 512) Image 8 (512 lowast 512) Image 9 (200 lowast 150)Adaptive wavelet 275706 259130 290039 269908 214746 208466Bilateral filtering 232116 224080 231373 224268 214834 210023Nonlocal means 294155 270736 313181 282534 237273 230137BM3D 291443 269120 320590 286197 217645 212712Proposed method 391414 348926 412256 357943 314041 300693

Image 10 (200 lowast 150) Image 11 (187 lowast 171) Image 12 (187 lowast 171)Adaptive wavelet 294247 275268 267443 254201 159075 169781Bilateral filtering 236728 230581 222984 217973 227751 226673Nonlocal means 303106 279794 287439 266227 174105 172673BM3D 308146 283780 318744 284922 310366 301990Proposed method 402191 359371 387096 350295 244256 257756

(a) 1205902 = 001 (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 11 Image 10 comparison of various experimental results under noise variance 1205902 = 001

(a) 1205902 = 003 (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 12 Image 10 comparison of various experimental results under noise variance 1205902 = 003

10 Applied Computational Intelligence and Soft Computing

(a) Image 1 edge (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 13 Image 1 edge comparison of various experimental results under noise variance 1205902 = 003

(a) Image 5 edge (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 14 Image 5 edge comparison of various experimental results under noise variance 1205902 = 001

Data

Data Data

Data DataAdaptive wavelet

Proposed method

Bilateral filtering

Nonlocal

BM3D

Data

Data Data

Data DataAdaptive wavelet

Proposed method

Bilateral filtering

Nonlocal

BM3DData

Data Data

Data DataAdaptive wavelet

Proposed method

Bilateral filtering

Nonlocal

BM3D

Data

Data Data

Data DataAdaptive wavelet

Proposed method

Bilateral filtering

Nonlocal

BM3D

87001 002 003 004 005 006 007

Image 1

008 009 01 011

888990919293949596

y

x

82001 002 003 004 005 006 007

Image 5

Image 10

008 009 01 011

848688909294

9896

y

x

001 002 003 004 005 006 007 008 009 01 01175

80

85

90

95

100

y

x

Image 12

001 002 003 004 005 006 007 008 009 01 01175

80

85

90

95

100

y

x

Figure 15 Prattrsquos figure of merit

Applied Computational Intelligence and Soft Computing 11

denoising techniquesThis will be the focus of future researchand exploration on color image denoising

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China (nos 61370138 61572077 andU1301251)and the Beijing Municipal Natural Science Foundation(no 4162027) the Project of Oriented Characteristic Dis-ciplines (no KYDE40201701) the Project of Constructionof Innovative Teams and Teacher Career Development forUniversities and Colleges Under Beijing Municipality (noIDHT20170511)

References

[1] C Tomasi and R Manduchi ldquoBilateral filtering for gray andcolor imagesrdquo in Proceedings of the International Conference onComputer Vision IEEE Computer Society 839 pages 1998

[2] Y Zhang X Tian and P Ren ldquoAn adaptive bilateral filter basedframework for image denoisingrdquo Neurocomputing vol 140 pp299ndash316 2014

[3] J S LimTwo-dimensional signal and image processing Prentice-Hall Inc Upper Saddle River NJ USA 1990

[4] D L Donoho and I M Johnstone ldquoAdapting to unknownsmoothness via wavelet shrinkagerdquo Journal of the AmericanStatistical Association vol 90 no 432 pp 1200ndash1224 1995

[5] D L Donoho ldquoDe-noising by soft-thresholdingrdquo Institute ofElectrical and Electronics Engineers Transactions on InformationTheory vol 41 no 3 pp 613ndash627 1995

[6] T D Bui and G Chen ldquoTranslation-invariant denoising usingmultiwaveletsrdquo IEEE Transactions on Signal Processing vol 46no 12 pp 3414ndash3420 1998

[7] C Srisailam P Sharma and S Suhane ldquoColor image denoisingusingwavelet soft thresholdingrdquo International Journal of Emerg-ing Technology and Advanced Engineering vol 4 no 7 pp 474ndash478 2014

[8] K K Gupta and R Gupta ldquoFeature adaptive wavelet shrinkagefor image denoisingrdquo in Proceedings of the 2007 InternationalConference on Signal Processing Communications and Network-ing ICSCN 2007 pp 81ndash85 ind February 2007

[9] E Ordentlich G Seroussi S Verdu M Weinberger and TWeissman ldquoA discrete universal denoiser and its application tobinary imagesrdquo in Proceedings of the International Conference onImage Processing (ICIP 2003) vol 1 pp 20ndash117 2003

[10] W Dong and H Ding ldquoFull frequency de-noising methodbased on wavelet decomposition and noise-type detectionrdquoNeurocomputing vol 214 pp 902ndash909 2016

[11] I Elyasi and S Zermchi ldquoElimination noise by adaptive waveletthresholdrdquoWorldAcademy of Science EngineeringampTechnologyvol 3 no 8 pp 1541ndash1545 2009

[12] A K Bhandari D Kumar A Kumar and G K Singh ldquoOpti-mal sub-band adaptive thresholding based edge preserved satel-lite image denoising using adaptive differential evolution algo-rithmrdquo Neurocomputing vol 174 pp 698ndash721 2016

[13] T T Cai and B W Silverman ldquoIncorporating information onneighbouring coefficients into wavelet estimation SankhyardquoThe Indian Journal of Statistics Series B (1960-2002) vol 63 no2 pp 127ndash148 2001

[14] G Y Chen T D Bui and A Krzyzak ldquoImage denoising usingneighbouring wavelet coefficientsrdquo Integrated Computer-AidedEngineering vol 12 no 1 pp 99ndash107 2005

[15] K He J Sun and X Tang ldquoGuided image filteringrdquo IEEE Tran-sactions on PatternAnalysis andMachine Intelligence vol 35 no6 pp 1397ndash1409 2013

[16] M Nasri and H Nezamabadi-pour ldquoImage denoising in thewavelet domain using a new adaptive thresholding functionrdquoNeurocomputing vol 72 no 4ndash6 pp 1012ndash1025 2009

[17] X Liu H Wan Z Shang and L Shi ldquoAutomatic extracellularspike denoising using wavelet neighbor coefficients and leveldependencyrdquo Neurocomputing vol 149 pp 1407ndash1414 2015

[18] C-C Kao J-H Lai and S-Y Chien ldquoVLSI architecture designof guided filter for 30 framess full-HD Videordquo IEEE Trans-actions on Circuits and Systems for Video Technology vol 24 no3 pp 513ndash524 2014

[19] A Gadge and S S Agrawal ldquoGuided filter for color imagerdquoIJIREEICE vol 4 no 6 pp 250ndash252 2016

[20] A Buades B Coll and J-M Morel ldquoA non-local algorithm forimage denoisingrdquo in Proceedings of the IEEE Computer SocietyConference on Computer Vision and Pattern Recognition (CVPRrsquo05) pp 60ndash65 June 2005

[21] K Dabov A Foi V Katkovnik and K Egiazarian ldquoImagedenoising by sparse 3-D transform-domain collaborative filter-ingrdquo IEEE Transactions on Image Processing vol 16 no 8 pp2080ndash2095 2007

[22] P N T Wells Digital Image Processing W K Pratt John WileyChichester UK 1991 (Medical Engineering amp Physics vol 16no 1 p 83 1994)

Submit your manuscripts athttpswwwhindawicom

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International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing 7

Figure 4 Test image Images 1ndash12 (from left to right top to bottom)

(a) 1205902 = 001 (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 5 Image 1 comparison of various experimental results under noise variance 1205902 = 001

To objectively evaluate the results we use the Prattrsquos figureof merit and PSNR for image quality evaluation Prattrsquos figureofmerit results are listed in Figure 15 119910-axis is the Pratt factorresults and 119909-axis is noise variance The curves showed thatPratt factor decreases when the noise variance increases butproposed method (red curves) is much higher than othersCurves results suggested that edge of image using proposedmethod is effective and abundant Table 1 is result of 119875119878119873119877The proposed method is superior to the other four methodswith respect to image processing

From the data in Table 1 and the quality factor curvesin Figure 15 we can conclude that the proposed method issuperior to bilateral filtering the adaptive wavelet thresholddenoising algorithm nonlocal means algorithm and BM3Dalgorithm on color image denoising From a visual point ofview the proposed method not only gives a good denoisingeffect but also achieves better edge retention

5 Conclusion

In this paper a new denoising method based on the adaptivewavelet threshold denoising algorithm and edge-guided fil-tering has been proposed The image denoising is performedaccording to the local structure of the image In comparativeexperiments against bilateral filtering the adaptive waveletdenoising method nonlocal means algorithm and BM3Dalgorithm the proposedmethod exhibited the best denoisingand edge preservation performance The proposed approachremoves Gaussian noise in the frequency domain and thenuses linear guided filtering to further enhance the imagerecovery resulting in better denoising and edge effects Ascolor images display more detailed textures this filteringovercomes the gradient inversion effect in the edge regionsAs the linearmodel (see (8)) is a block-unsupervised learningmethod it can be combined with other models to obtain new

8 Applied Computational Intelligence and Soft Computing

(a) 1205902 = 003 (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 6 Image 1 comparison of various experimental results under noise variance 1205902 = 003

(a) 1205902 = 001 (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 7 Image 5 comparison of various experimental results under noise variance 1205902 = 001

(a) 1205902 = 003 (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 8 Image 5 comparison of various experimental results under noise variance 1205902 = 003

(a) 1205902 = 001 (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 9 Image 9 comparison of various experimental results under noise variance 1205902 = 001

(a) 1205902 = 003 (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 10 Image 9 comparison of various experimental results under noise variance 1205902 = 003

Applied Computational Intelligence and Soft Computing 9

Table 1 PSNR of the proposed method bilateral filtering and adaptive wavelet

Noise variance 001 003 001 003 001 003Image 1 (256 lowast 256) Image 2 (512 lowast 512) Image 3 (256 lowast 256)

Adaptive wavelet 267048 254507 280801 264821 277967 261699Bilateral filtering 225751 220167 231551 226118 227560 221802Nonlocal means 299765 274871 301415 276777 301910 276823BM3D 289235 269276 304215 278901 309457 280957Proposed method 395634 353129 415647 360267 408101 355930

Image 4 (256 lowast 256) Image 5 (256 lowast 256) Image 6 (512 lowast 512)Adaptive wavelet 252375 242724 234663 227332 256576 245766Bilateral filtering 226074 219415 221076 215494 223016 217254Nonlocal means 266512 253287 253588 243120 278813 262105BM3D 255157 244968 240394 232556 280621 263334Proposed method 370265 341344 338535 321364 368294 339588

Image 7 (512 lowast 512) Image 8 (512 lowast 512) Image 9 (200 lowast 150)Adaptive wavelet 275706 259130 290039 269908 214746 208466Bilateral filtering 232116 224080 231373 224268 214834 210023Nonlocal means 294155 270736 313181 282534 237273 230137BM3D 291443 269120 320590 286197 217645 212712Proposed method 391414 348926 412256 357943 314041 300693

Image 10 (200 lowast 150) Image 11 (187 lowast 171) Image 12 (187 lowast 171)Adaptive wavelet 294247 275268 267443 254201 159075 169781Bilateral filtering 236728 230581 222984 217973 227751 226673Nonlocal means 303106 279794 287439 266227 174105 172673BM3D 308146 283780 318744 284922 310366 301990Proposed method 402191 359371 387096 350295 244256 257756

(a) 1205902 = 001 (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 11 Image 10 comparison of various experimental results under noise variance 1205902 = 001

(a) 1205902 = 003 (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 12 Image 10 comparison of various experimental results under noise variance 1205902 = 003

10 Applied Computational Intelligence and Soft Computing

(a) Image 1 edge (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 13 Image 1 edge comparison of various experimental results under noise variance 1205902 = 003

(a) Image 5 edge (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 14 Image 5 edge comparison of various experimental results under noise variance 1205902 = 001

Data

Data Data

Data DataAdaptive wavelet

Proposed method

Bilateral filtering

Nonlocal

BM3D

Data

Data Data

Data DataAdaptive wavelet

Proposed method

Bilateral filtering

Nonlocal

BM3DData

Data Data

Data DataAdaptive wavelet

Proposed method

Bilateral filtering

Nonlocal

BM3D

Data

Data Data

Data DataAdaptive wavelet

Proposed method

Bilateral filtering

Nonlocal

BM3D

87001 002 003 004 005 006 007

Image 1

008 009 01 011

888990919293949596

y

x

82001 002 003 004 005 006 007

Image 5

Image 10

008 009 01 011

848688909294

9896

y

x

001 002 003 004 005 006 007 008 009 01 01175

80

85

90

95

100

y

x

Image 12

001 002 003 004 005 006 007 008 009 01 01175

80

85

90

95

100

y

x

Figure 15 Prattrsquos figure of merit

Applied Computational Intelligence and Soft Computing 11

denoising techniquesThis will be the focus of future researchand exploration on color image denoising

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China (nos 61370138 61572077 andU1301251)and the Beijing Municipal Natural Science Foundation(no 4162027) the Project of Oriented Characteristic Dis-ciplines (no KYDE40201701) the Project of Constructionof Innovative Teams and Teacher Career Development forUniversities and Colleges Under Beijing Municipality (noIDHT20170511)

References

[1] C Tomasi and R Manduchi ldquoBilateral filtering for gray andcolor imagesrdquo in Proceedings of the International Conference onComputer Vision IEEE Computer Society 839 pages 1998

[2] Y Zhang X Tian and P Ren ldquoAn adaptive bilateral filter basedframework for image denoisingrdquo Neurocomputing vol 140 pp299ndash316 2014

[3] J S LimTwo-dimensional signal and image processing Prentice-Hall Inc Upper Saddle River NJ USA 1990

[4] D L Donoho and I M Johnstone ldquoAdapting to unknownsmoothness via wavelet shrinkagerdquo Journal of the AmericanStatistical Association vol 90 no 432 pp 1200ndash1224 1995

[5] D L Donoho ldquoDe-noising by soft-thresholdingrdquo Institute ofElectrical and Electronics Engineers Transactions on InformationTheory vol 41 no 3 pp 613ndash627 1995

[6] T D Bui and G Chen ldquoTranslation-invariant denoising usingmultiwaveletsrdquo IEEE Transactions on Signal Processing vol 46no 12 pp 3414ndash3420 1998

[7] C Srisailam P Sharma and S Suhane ldquoColor image denoisingusingwavelet soft thresholdingrdquo International Journal of Emerg-ing Technology and Advanced Engineering vol 4 no 7 pp 474ndash478 2014

[8] K K Gupta and R Gupta ldquoFeature adaptive wavelet shrinkagefor image denoisingrdquo in Proceedings of the 2007 InternationalConference on Signal Processing Communications and Network-ing ICSCN 2007 pp 81ndash85 ind February 2007

[9] E Ordentlich G Seroussi S Verdu M Weinberger and TWeissman ldquoA discrete universal denoiser and its application tobinary imagesrdquo in Proceedings of the International Conference onImage Processing (ICIP 2003) vol 1 pp 20ndash117 2003

[10] W Dong and H Ding ldquoFull frequency de-noising methodbased on wavelet decomposition and noise-type detectionrdquoNeurocomputing vol 214 pp 902ndash909 2016

[11] I Elyasi and S Zermchi ldquoElimination noise by adaptive waveletthresholdrdquoWorldAcademy of Science EngineeringampTechnologyvol 3 no 8 pp 1541ndash1545 2009

[12] A K Bhandari D Kumar A Kumar and G K Singh ldquoOpti-mal sub-band adaptive thresholding based edge preserved satel-lite image denoising using adaptive differential evolution algo-rithmrdquo Neurocomputing vol 174 pp 698ndash721 2016

[13] T T Cai and B W Silverman ldquoIncorporating information onneighbouring coefficients into wavelet estimation SankhyardquoThe Indian Journal of Statistics Series B (1960-2002) vol 63 no2 pp 127ndash148 2001

[14] G Y Chen T D Bui and A Krzyzak ldquoImage denoising usingneighbouring wavelet coefficientsrdquo Integrated Computer-AidedEngineering vol 12 no 1 pp 99ndash107 2005

[15] K He J Sun and X Tang ldquoGuided image filteringrdquo IEEE Tran-sactions on PatternAnalysis andMachine Intelligence vol 35 no6 pp 1397ndash1409 2013

[16] M Nasri and H Nezamabadi-pour ldquoImage denoising in thewavelet domain using a new adaptive thresholding functionrdquoNeurocomputing vol 72 no 4ndash6 pp 1012ndash1025 2009

[17] X Liu H Wan Z Shang and L Shi ldquoAutomatic extracellularspike denoising using wavelet neighbor coefficients and leveldependencyrdquo Neurocomputing vol 149 pp 1407ndash1414 2015

[18] C-C Kao J-H Lai and S-Y Chien ldquoVLSI architecture designof guided filter for 30 framess full-HD Videordquo IEEE Trans-actions on Circuits and Systems for Video Technology vol 24 no3 pp 513ndash524 2014

[19] A Gadge and S S Agrawal ldquoGuided filter for color imagerdquoIJIREEICE vol 4 no 6 pp 250ndash252 2016

[20] A Buades B Coll and J-M Morel ldquoA non-local algorithm forimage denoisingrdquo in Proceedings of the IEEE Computer SocietyConference on Computer Vision and Pattern Recognition (CVPRrsquo05) pp 60ndash65 June 2005

[21] K Dabov A Foi V Katkovnik and K Egiazarian ldquoImagedenoising by sparse 3-D transform-domain collaborative filter-ingrdquo IEEE Transactions on Image Processing vol 16 no 8 pp2080ndash2095 2007

[22] P N T Wells Digital Image Processing W K Pratt John WileyChichester UK 1991 (Medical Engineering amp Physics vol 16no 1 p 83 1994)

Submit your manuscripts athttpswwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

8 Applied Computational Intelligence and Soft Computing

(a) 1205902 = 003 (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 6 Image 1 comparison of various experimental results under noise variance 1205902 = 003

(a) 1205902 = 001 (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 7 Image 5 comparison of various experimental results under noise variance 1205902 = 001

(a) 1205902 = 003 (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 8 Image 5 comparison of various experimental results under noise variance 1205902 = 003

(a) 1205902 = 001 (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 9 Image 9 comparison of various experimental results under noise variance 1205902 = 001

(a) 1205902 = 003 (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 10 Image 9 comparison of various experimental results under noise variance 1205902 = 003

Applied Computational Intelligence and Soft Computing 9

Table 1 PSNR of the proposed method bilateral filtering and adaptive wavelet

Noise variance 001 003 001 003 001 003Image 1 (256 lowast 256) Image 2 (512 lowast 512) Image 3 (256 lowast 256)

Adaptive wavelet 267048 254507 280801 264821 277967 261699Bilateral filtering 225751 220167 231551 226118 227560 221802Nonlocal means 299765 274871 301415 276777 301910 276823BM3D 289235 269276 304215 278901 309457 280957Proposed method 395634 353129 415647 360267 408101 355930

Image 4 (256 lowast 256) Image 5 (256 lowast 256) Image 6 (512 lowast 512)Adaptive wavelet 252375 242724 234663 227332 256576 245766Bilateral filtering 226074 219415 221076 215494 223016 217254Nonlocal means 266512 253287 253588 243120 278813 262105BM3D 255157 244968 240394 232556 280621 263334Proposed method 370265 341344 338535 321364 368294 339588

Image 7 (512 lowast 512) Image 8 (512 lowast 512) Image 9 (200 lowast 150)Adaptive wavelet 275706 259130 290039 269908 214746 208466Bilateral filtering 232116 224080 231373 224268 214834 210023Nonlocal means 294155 270736 313181 282534 237273 230137BM3D 291443 269120 320590 286197 217645 212712Proposed method 391414 348926 412256 357943 314041 300693

Image 10 (200 lowast 150) Image 11 (187 lowast 171) Image 12 (187 lowast 171)Adaptive wavelet 294247 275268 267443 254201 159075 169781Bilateral filtering 236728 230581 222984 217973 227751 226673Nonlocal means 303106 279794 287439 266227 174105 172673BM3D 308146 283780 318744 284922 310366 301990Proposed method 402191 359371 387096 350295 244256 257756

(a) 1205902 = 001 (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 11 Image 10 comparison of various experimental results under noise variance 1205902 = 001

(a) 1205902 = 003 (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 12 Image 10 comparison of various experimental results under noise variance 1205902 = 003

10 Applied Computational Intelligence and Soft Computing

(a) Image 1 edge (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 13 Image 1 edge comparison of various experimental results under noise variance 1205902 = 003

(a) Image 5 edge (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 14 Image 5 edge comparison of various experimental results under noise variance 1205902 = 001

Data

Data Data

Data DataAdaptive wavelet

Proposed method

Bilateral filtering

Nonlocal

BM3D

Data

Data Data

Data DataAdaptive wavelet

Proposed method

Bilateral filtering

Nonlocal

BM3DData

Data Data

Data DataAdaptive wavelet

Proposed method

Bilateral filtering

Nonlocal

BM3D

Data

Data Data

Data DataAdaptive wavelet

Proposed method

Bilateral filtering

Nonlocal

BM3D

87001 002 003 004 005 006 007

Image 1

008 009 01 011

888990919293949596

y

x

82001 002 003 004 005 006 007

Image 5

Image 10

008 009 01 011

848688909294

9896

y

x

001 002 003 004 005 006 007 008 009 01 01175

80

85

90

95

100

y

x

Image 12

001 002 003 004 005 006 007 008 009 01 01175

80

85

90

95

100

y

x

Figure 15 Prattrsquos figure of merit

Applied Computational Intelligence and Soft Computing 11

denoising techniquesThis will be the focus of future researchand exploration on color image denoising

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China (nos 61370138 61572077 andU1301251)and the Beijing Municipal Natural Science Foundation(no 4162027) the Project of Oriented Characteristic Dis-ciplines (no KYDE40201701) the Project of Constructionof Innovative Teams and Teacher Career Development forUniversities and Colleges Under Beijing Municipality (noIDHT20170511)

References

[1] C Tomasi and R Manduchi ldquoBilateral filtering for gray andcolor imagesrdquo in Proceedings of the International Conference onComputer Vision IEEE Computer Society 839 pages 1998

[2] Y Zhang X Tian and P Ren ldquoAn adaptive bilateral filter basedframework for image denoisingrdquo Neurocomputing vol 140 pp299ndash316 2014

[3] J S LimTwo-dimensional signal and image processing Prentice-Hall Inc Upper Saddle River NJ USA 1990

[4] D L Donoho and I M Johnstone ldquoAdapting to unknownsmoothness via wavelet shrinkagerdquo Journal of the AmericanStatistical Association vol 90 no 432 pp 1200ndash1224 1995

[5] D L Donoho ldquoDe-noising by soft-thresholdingrdquo Institute ofElectrical and Electronics Engineers Transactions on InformationTheory vol 41 no 3 pp 613ndash627 1995

[6] T D Bui and G Chen ldquoTranslation-invariant denoising usingmultiwaveletsrdquo IEEE Transactions on Signal Processing vol 46no 12 pp 3414ndash3420 1998

[7] C Srisailam P Sharma and S Suhane ldquoColor image denoisingusingwavelet soft thresholdingrdquo International Journal of Emerg-ing Technology and Advanced Engineering vol 4 no 7 pp 474ndash478 2014

[8] K K Gupta and R Gupta ldquoFeature adaptive wavelet shrinkagefor image denoisingrdquo in Proceedings of the 2007 InternationalConference on Signal Processing Communications and Network-ing ICSCN 2007 pp 81ndash85 ind February 2007

[9] E Ordentlich G Seroussi S Verdu M Weinberger and TWeissman ldquoA discrete universal denoiser and its application tobinary imagesrdquo in Proceedings of the International Conference onImage Processing (ICIP 2003) vol 1 pp 20ndash117 2003

[10] W Dong and H Ding ldquoFull frequency de-noising methodbased on wavelet decomposition and noise-type detectionrdquoNeurocomputing vol 214 pp 902ndash909 2016

[11] I Elyasi and S Zermchi ldquoElimination noise by adaptive waveletthresholdrdquoWorldAcademy of Science EngineeringampTechnologyvol 3 no 8 pp 1541ndash1545 2009

[12] A K Bhandari D Kumar A Kumar and G K Singh ldquoOpti-mal sub-band adaptive thresholding based edge preserved satel-lite image denoising using adaptive differential evolution algo-rithmrdquo Neurocomputing vol 174 pp 698ndash721 2016

[13] T T Cai and B W Silverman ldquoIncorporating information onneighbouring coefficients into wavelet estimation SankhyardquoThe Indian Journal of Statistics Series B (1960-2002) vol 63 no2 pp 127ndash148 2001

[14] G Y Chen T D Bui and A Krzyzak ldquoImage denoising usingneighbouring wavelet coefficientsrdquo Integrated Computer-AidedEngineering vol 12 no 1 pp 99ndash107 2005

[15] K He J Sun and X Tang ldquoGuided image filteringrdquo IEEE Tran-sactions on PatternAnalysis andMachine Intelligence vol 35 no6 pp 1397ndash1409 2013

[16] M Nasri and H Nezamabadi-pour ldquoImage denoising in thewavelet domain using a new adaptive thresholding functionrdquoNeurocomputing vol 72 no 4ndash6 pp 1012ndash1025 2009

[17] X Liu H Wan Z Shang and L Shi ldquoAutomatic extracellularspike denoising using wavelet neighbor coefficients and leveldependencyrdquo Neurocomputing vol 149 pp 1407ndash1414 2015

[18] C-C Kao J-H Lai and S-Y Chien ldquoVLSI architecture designof guided filter for 30 framess full-HD Videordquo IEEE Trans-actions on Circuits and Systems for Video Technology vol 24 no3 pp 513ndash524 2014

[19] A Gadge and S S Agrawal ldquoGuided filter for color imagerdquoIJIREEICE vol 4 no 6 pp 250ndash252 2016

[20] A Buades B Coll and J-M Morel ldquoA non-local algorithm forimage denoisingrdquo in Proceedings of the IEEE Computer SocietyConference on Computer Vision and Pattern Recognition (CVPRrsquo05) pp 60ndash65 June 2005

[21] K Dabov A Foi V Katkovnik and K Egiazarian ldquoImagedenoising by sparse 3-D transform-domain collaborative filter-ingrdquo IEEE Transactions on Image Processing vol 16 no 8 pp2080ndash2095 2007

[22] P N T Wells Digital Image Processing W K Pratt John WileyChichester UK 1991 (Medical Engineering amp Physics vol 16no 1 p 83 1994)

Submit your manuscripts athttpswwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing 9

Table 1 PSNR of the proposed method bilateral filtering and adaptive wavelet

Noise variance 001 003 001 003 001 003Image 1 (256 lowast 256) Image 2 (512 lowast 512) Image 3 (256 lowast 256)

Adaptive wavelet 267048 254507 280801 264821 277967 261699Bilateral filtering 225751 220167 231551 226118 227560 221802Nonlocal means 299765 274871 301415 276777 301910 276823BM3D 289235 269276 304215 278901 309457 280957Proposed method 395634 353129 415647 360267 408101 355930

Image 4 (256 lowast 256) Image 5 (256 lowast 256) Image 6 (512 lowast 512)Adaptive wavelet 252375 242724 234663 227332 256576 245766Bilateral filtering 226074 219415 221076 215494 223016 217254Nonlocal means 266512 253287 253588 243120 278813 262105BM3D 255157 244968 240394 232556 280621 263334Proposed method 370265 341344 338535 321364 368294 339588

Image 7 (512 lowast 512) Image 8 (512 lowast 512) Image 9 (200 lowast 150)Adaptive wavelet 275706 259130 290039 269908 214746 208466Bilateral filtering 232116 224080 231373 224268 214834 210023Nonlocal means 294155 270736 313181 282534 237273 230137BM3D 291443 269120 320590 286197 217645 212712Proposed method 391414 348926 412256 357943 314041 300693

Image 10 (200 lowast 150) Image 11 (187 lowast 171) Image 12 (187 lowast 171)Adaptive wavelet 294247 275268 267443 254201 159075 169781Bilateral filtering 236728 230581 222984 217973 227751 226673Nonlocal means 303106 279794 287439 266227 174105 172673BM3D 308146 283780 318744 284922 310366 301990Proposed method 402191 359371 387096 350295 244256 257756

(a) 1205902 = 001 (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 11 Image 10 comparison of various experimental results under noise variance 1205902 = 001

(a) 1205902 = 003 (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 12 Image 10 comparison of various experimental results under noise variance 1205902 = 003

10 Applied Computational Intelligence and Soft Computing

(a) Image 1 edge (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 13 Image 1 edge comparison of various experimental results under noise variance 1205902 = 003

(a) Image 5 edge (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 14 Image 5 edge comparison of various experimental results under noise variance 1205902 = 001

Data

Data Data

Data DataAdaptive wavelet

Proposed method

Bilateral filtering

Nonlocal

BM3D

Data

Data Data

Data DataAdaptive wavelet

Proposed method

Bilateral filtering

Nonlocal

BM3DData

Data Data

Data DataAdaptive wavelet

Proposed method

Bilateral filtering

Nonlocal

BM3D

Data

Data Data

Data DataAdaptive wavelet

Proposed method

Bilateral filtering

Nonlocal

BM3D

87001 002 003 004 005 006 007

Image 1

008 009 01 011

888990919293949596

y

x

82001 002 003 004 005 006 007

Image 5

Image 10

008 009 01 011

848688909294

9896

y

x

001 002 003 004 005 006 007 008 009 01 01175

80

85

90

95

100

y

x

Image 12

001 002 003 004 005 006 007 008 009 01 01175

80

85

90

95

100

y

x

Figure 15 Prattrsquos figure of merit

Applied Computational Intelligence and Soft Computing 11

denoising techniquesThis will be the focus of future researchand exploration on color image denoising

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China (nos 61370138 61572077 andU1301251)and the Beijing Municipal Natural Science Foundation(no 4162027) the Project of Oriented Characteristic Dis-ciplines (no KYDE40201701) the Project of Constructionof Innovative Teams and Teacher Career Development forUniversities and Colleges Under Beijing Municipality (noIDHT20170511)

References

[1] C Tomasi and R Manduchi ldquoBilateral filtering for gray andcolor imagesrdquo in Proceedings of the International Conference onComputer Vision IEEE Computer Society 839 pages 1998

[2] Y Zhang X Tian and P Ren ldquoAn adaptive bilateral filter basedframework for image denoisingrdquo Neurocomputing vol 140 pp299ndash316 2014

[3] J S LimTwo-dimensional signal and image processing Prentice-Hall Inc Upper Saddle River NJ USA 1990

[4] D L Donoho and I M Johnstone ldquoAdapting to unknownsmoothness via wavelet shrinkagerdquo Journal of the AmericanStatistical Association vol 90 no 432 pp 1200ndash1224 1995

[5] D L Donoho ldquoDe-noising by soft-thresholdingrdquo Institute ofElectrical and Electronics Engineers Transactions on InformationTheory vol 41 no 3 pp 613ndash627 1995

[6] T D Bui and G Chen ldquoTranslation-invariant denoising usingmultiwaveletsrdquo IEEE Transactions on Signal Processing vol 46no 12 pp 3414ndash3420 1998

[7] C Srisailam P Sharma and S Suhane ldquoColor image denoisingusingwavelet soft thresholdingrdquo International Journal of Emerg-ing Technology and Advanced Engineering vol 4 no 7 pp 474ndash478 2014

[8] K K Gupta and R Gupta ldquoFeature adaptive wavelet shrinkagefor image denoisingrdquo in Proceedings of the 2007 InternationalConference on Signal Processing Communications and Network-ing ICSCN 2007 pp 81ndash85 ind February 2007

[9] E Ordentlich G Seroussi S Verdu M Weinberger and TWeissman ldquoA discrete universal denoiser and its application tobinary imagesrdquo in Proceedings of the International Conference onImage Processing (ICIP 2003) vol 1 pp 20ndash117 2003

[10] W Dong and H Ding ldquoFull frequency de-noising methodbased on wavelet decomposition and noise-type detectionrdquoNeurocomputing vol 214 pp 902ndash909 2016

[11] I Elyasi and S Zermchi ldquoElimination noise by adaptive waveletthresholdrdquoWorldAcademy of Science EngineeringampTechnologyvol 3 no 8 pp 1541ndash1545 2009

[12] A K Bhandari D Kumar A Kumar and G K Singh ldquoOpti-mal sub-band adaptive thresholding based edge preserved satel-lite image denoising using adaptive differential evolution algo-rithmrdquo Neurocomputing vol 174 pp 698ndash721 2016

[13] T T Cai and B W Silverman ldquoIncorporating information onneighbouring coefficients into wavelet estimation SankhyardquoThe Indian Journal of Statistics Series B (1960-2002) vol 63 no2 pp 127ndash148 2001

[14] G Y Chen T D Bui and A Krzyzak ldquoImage denoising usingneighbouring wavelet coefficientsrdquo Integrated Computer-AidedEngineering vol 12 no 1 pp 99ndash107 2005

[15] K He J Sun and X Tang ldquoGuided image filteringrdquo IEEE Tran-sactions on PatternAnalysis andMachine Intelligence vol 35 no6 pp 1397ndash1409 2013

[16] M Nasri and H Nezamabadi-pour ldquoImage denoising in thewavelet domain using a new adaptive thresholding functionrdquoNeurocomputing vol 72 no 4ndash6 pp 1012ndash1025 2009

[17] X Liu H Wan Z Shang and L Shi ldquoAutomatic extracellularspike denoising using wavelet neighbor coefficients and leveldependencyrdquo Neurocomputing vol 149 pp 1407ndash1414 2015

[18] C-C Kao J-H Lai and S-Y Chien ldquoVLSI architecture designof guided filter for 30 framess full-HD Videordquo IEEE Trans-actions on Circuits and Systems for Video Technology vol 24 no3 pp 513ndash524 2014

[19] A Gadge and S S Agrawal ldquoGuided filter for color imagerdquoIJIREEICE vol 4 no 6 pp 250ndash252 2016

[20] A Buades B Coll and J-M Morel ldquoA non-local algorithm forimage denoisingrdquo in Proceedings of the IEEE Computer SocietyConference on Computer Vision and Pattern Recognition (CVPRrsquo05) pp 60ndash65 June 2005

[21] K Dabov A Foi V Katkovnik and K Egiazarian ldquoImagedenoising by sparse 3-D transform-domain collaborative filter-ingrdquo IEEE Transactions on Image Processing vol 16 no 8 pp2080ndash2095 2007

[22] P N T Wells Digital Image Processing W K Pratt John WileyChichester UK 1991 (Medical Engineering amp Physics vol 16no 1 p 83 1994)

Submit your manuscripts athttpswwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

10 Applied Computational Intelligence and Soft Computing

(a) Image 1 edge (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 13 Image 1 edge comparison of various experimental results under noise variance 1205902 = 003

(a) Image 5 edge (b) Bilateral filtering (c) Adaptive wavelet (d) Nonlocal means (e) BM3D (f) Proposed method

Figure 14 Image 5 edge comparison of various experimental results under noise variance 1205902 = 001

Data

Data Data

Data DataAdaptive wavelet

Proposed method

Bilateral filtering

Nonlocal

BM3D

Data

Data Data

Data DataAdaptive wavelet

Proposed method

Bilateral filtering

Nonlocal

BM3DData

Data Data

Data DataAdaptive wavelet

Proposed method

Bilateral filtering

Nonlocal

BM3D

Data

Data Data

Data DataAdaptive wavelet

Proposed method

Bilateral filtering

Nonlocal

BM3D

87001 002 003 004 005 006 007

Image 1

008 009 01 011

888990919293949596

y

x

82001 002 003 004 005 006 007

Image 5

Image 10

008 009 01 011

848688909294

9896

y

x

001 002 003 004 005 006 007 008 009 01 01175

80

85

90

95

100

y

x

Image 12

001 002 003 004 005 006 007 008 009 01 01175

80

85

90

95

100

y

x

Figure 15 Prattrsquos figure of merit

Applied Computational Intelligence and Soft Computing 11

denoising techniquesThis will be the focus of future researchand exploration on color image denoising

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China (nos 61370138 61572077 andU1301251)and the Beijing Municipal Natural Science Foundation(no 4162027) the Project of Oriented Characteristic Dis-ciplines (no KYDE40201701) the Project of Constructionof Innovative Teams and Teacher Career Development forUniversities and Colleges Under Beijing Municipality (noIDHT20170511)

References

[1] C Tomasi and R Manduchi ldquoBilateral filtering for gray andcolor imagesrdquo in Proceedings of the International Conference onComputer Vision IEEE Computer Society 839 pages 1998

[2] Y Zhang X Tian and P Ren ldquoAn adaptive bilateral filter basedframework for image denoisingrdquo Neurocomputing vol 140 pp299ndash316 2014

[3] J S LimTwo-dimensional signal and image processing Prentice-Hall Inc Upper Saddle River NJ USA 1990

[4] D L Donoho and I M Johnstone ldquoAdapting to unknownsmoothness via wavelet shrinkagerdquo Journal of the AmericanStatistical Association vol 90 no 432 pp 1200ndash1224 1995

[5] D L Donoho ldquoDe-noising by soft-thresholdingrdquo Institute ofElectrical and Electronics Engineers Transactions on InformationTheory vol 41 no 3 pp 613ndash627 1995

[6] T D Bui and G Chen ldquoTranslation-invariant denoising usingmultiwaveletsrdquo IEEE Transactions on Signal Processing vol 46no 12 pp 3414ndash3420 1998

[7] C Srisailam P Sharma and S Suhane ldquoColor image denoisingusingwavelet soft thresholdingrdquo International Journal of Emerg-ing Technology and Advanced Engineering vol 4 no 7 pp 474ndash478 2014

[8] K K Gupta and R Gupta ldquoFeature adaptive wavelet shrinkagefor image denoisingrdquo in Proceedings of the 2007 InternationalConference on Signal Processing Communications and Network-ing ICSCN 2007 pp 81ndash85 ind February 2007

[9] E Ordentlich G Seroussi S Verdu M Weinberger and TWeissman ldquoA discrete universal denoiser and its application tobinary imagesrdquo in Proceedings of the International Conference onImage Processing (ICIP 2003) vol 1 pp 20ndash117 2003

[10] W Dong and H Ding ldquoFull frequency de-noising methodbased on wavelet decomposition and noise-type detectionrdquoNeurocomputing vol 214 pp 902ndash909 2016

[11] I Elyasi and S Zermchi ldquoElimination noise by adaptive waveletthresholdrdquoWorldAcademy of Science EngineeringampTechnologyvol 3 no 8 pp 1541ndash1545 2009

[12] A K Bhandari D Kumar A Kumar and G K Singh ldquoOpti-mal sub-band adaptive thresholding based edge preserved satel-lite image denoising using adaptive differential evolution algo-rithmrdquo Neurocomputing vol 174 pp 698ndash721 2016

[13] T T Cai and B W Silverman ldquoIncorporating information onneighbouring coefficients into wavelet estimation SankhyardquoThe Indian Journal of Statistics Series B (1960-2002) vol 63 no2 pp 127ndash148 2001

[14] G Y Chen T D Bui and A Krzyzak ldquoImage denoising usingneighbouring wavelet coefficientsrdquo Integrated Computer-AidedEngineering vol 12 no 1 pp 99ndash107 2005

[15] K He J Sun and X Tang ldquoGuided image filteringrdquo IEEE Tran-sactions on PatternAnalysis andMachine Intelligence vol 35 no6 pp 1397ndash1409 2013

[16] M Nasri and H Nezamabadi-pour ldquoImage denoising in thewavelet domain using a new adaptive thresholding functionrdquoNeurocomputing vol 72 no 4ndash6 pp 1012ndash1025 2009

[17] X Liu H Wan Z Shang and L Shi ldquoAutomatic extracellularspike denoising using wavelet neighbor coefficients and leveldependencyrdquo Neurocomputing vol 149 pp 1407ndash1414 2015

[18] C-C Kao J-H Lai and S-Y Chien ldquoVLSI architecture designof guided filter for 30 framess full-HD Videordquo IEEE Trans-actions on Circuits and Systems for Video Technology vol 24 no3 pp 513ndash524 2014

[19] A Gadge and S S Agrawal ldquoGuided filter for color imagerdquoIJIREEICE vol 4 no 6 pp 250ndash252 2016

[20] A Buades B Coll and J-M Morel ldquoA non-local algorithm forimage denoisingrdquo in Proceedings of the IEEE Computer SocietyConference on Computer Vision and Pattern Recognition (CVPRrsquo05) pp 60ndash65 June 2005

[21] K Dabov A Foi V Katkovnik and K Egiazarian ldquoImagedenoising by sparse 3-D transform-domain collaborative filter-ingrdquo IEEE Transactions on Image Processing vol 16 no 8 pp2080ndash2095 2007

[22] P N T Wells Digital Image Processing W K Pratt John WileyChichester UK 1991 (Medical Engineering amp Physics vol 16no 1 p 83 1994)

Submit your manuscripts athttpswwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing 11

denoising techniquesThis will be the focus of future researchand exploration on color image denoising

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China (nos 61370138 61572077 andU1301251)and the Beijing Municipal Natural Science Foundation(no 4162027) the Project of Oriented Characteristic Dis-ciplines (no KYDE40201701) the Project of Constructionof Innovative Teams and Teacher Career Development forUniversities and Colleges Under Beijing Municipality (noIDHT20170511)

References

[1] C Tomasi and R Manduchi ldquoBilateral filtering for gray andcolor imagesrdquo in Proceedings of the International Conference onComputer Vision IEEE Computer Society 839 pages 1998

[2] Y Zhang X Tian and P Ren ldquoAn adaptive bilateral filter basedframework for image denoisingrdquo Neurocomputing vol 140 pp299ndash316 2014

[3] J S LimTwo-dimensional signal and image processing Prentice-Hall Inc Upper Saddle River NJ USA 1990

[4] D L Donoho and I M Johnstone ldquoAdapting to unknownsmoothness via wavelet shrinkagerdquo Journal of the AmericanStatistical Association vol 90 no 432 pp 1200ndash1224 1995

[5] D L Donoho ldquoDe-noising by soft-thresholdingrdquo Institute ofElectrical and Electronics Engineers Transactions on InformationTheory vol 41 no 3 pp 613ndash627 1995

[6] T D Bui and G Chen ldquoTranslation-invariant denoising usingmultiwaveletsrdquo IEEE Transactions on Signal Processing vol 46no 12 pp 3414ndash3420 1998

[7] C Srisailam P Sharma and S Suhane ldquoColor image denoisingusingwavelet soft thresholdingrdquo International Journal of Emerg-ing Technology and Advanced Engineering vol 4 no 7 pp 474ndash478 2014

[8] K K Gupta and R Gupta ldquoFeature adaptive wavelet shrinkagefor image denoisingrdquo in Proceedings of the 2007 InternationalConference on Signal Processing Communications and Network-ing ICSCN 2007 pp 81ndash85 ind February 2007

[9] E Ordentlich G Seroussi S Verdu M Weinberger and TWeissman ldquoA discrete universal denoiser and its application tobinary imagesrdquo in Proceedings of the International Conference onImage Processing (ICIP 2003) vol 1 pp 20ndash117 2003

[10] W Dong and H Ding ldquoFull frequency de-noising methodbased on wavelet decomposition and noise-type detectionrdquoNeurocomputing vol 214 pp 902ndash909 2016

[11] I Elyasi and S Zermchi ldquoElimination noise by adaptive waveletthresholdrdquoWorldAcademy of Science EngineeringampTechnologyvol 3 no 8 pp 1541ndash1545 2009

[12] A K Bhandari D Kumar A Kumar and G K Singh ldquoOpti-mal sub-band adaptive thresholding based edge preserved satel-lite image denoising using adaptive differential evolution algo-rithmrdquo Neurocomputing vol 174 pp 698ndash721 2016

[13] T T Cai and B W Silverman ldquoIncorporating information onneighbouring coefficients into wavelet estimation SankhyardquoThe Indian Journal of Statistics Series B (1960-2002) vol 63 no2 pp 127ndash148 2001

[14] G Y Chen T D Bui and A Krzyzak ldquoImage denoising usingneighbouring wavelet coefficientsrdquo Integrated Computer-AidedEngineering vol 12 no 1 pp 99ndash107 2005

[15] K He J Sun and X Tang ldquoGuided image filteringrdquo IEEE Tran-sactions on PatternAnalysis andMachine Intelligence vol 35 no6 pp 1397ndash1409 2013

[16] M Nasri and H Nezamabadi-pour ldquoImage denoising in thewavelet domain using a new adaptive thresholding functionrdquoNeurocomputing vol 72 no 4ndash6 pp 1012ndash1025 2009

[17] X Liu H Wan Z Shang and L Shi ldquoAutomatic extracellularspike denoising using wavelet neighbor coefficients and leveldependencyrdquo Neurocomputing vol 149 pp 1407ndash1414 2015

[18] C-C Kao J-H Lai and S-Y Chien ldquoVLSI architecture designof guided filter for 30 framess full-HD Videordquo IEEE Trans-actions on Circuits and Systems for Video Technology vol 24 no3 pp 513ndash524 2014

[19] A Gadge and S S Agrawal ldquoGuided filter for color imagerdquoIJIREEICE vol 4 no 6 pp 250ndash252 2016

[20] A Buades B Coll and J-M Morel ldquoA non-local algorithm forimage denoisingrdquo in Proceedings of the IEEE Computer SocietyConference on Computer Vision and Pattern Recognition (CVPRrsquo05) pp 60ndash65 June 2005

[21] K Dabov A Foi V Katkovnik and K Egiazarian ldquoImagedenoising by sparse 3-D transform-domain collaborative filter-ingrdquo IEEE Transactions on Image Processing vol 16 no 8 pp2080ndash2095 2007

[22] P N T Wells Digital Image Processing W K Pratt John WileyChichester UK 1991 (Medical Engineering amp Physics vol 16no 1 p 83 1994)

Submit your manuscripts athttpswwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Submit your manuscripts athttpswwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014