research article an efficient image denoising method for...

Research ArticleAn Efficient Image Denoising Method for WirelessMultimedia Sensor Networks Based on DT-CWT

Rachid Sammouda1 Abdul Malik S Al-Salman1 Abdu Gumaei1 and Nejmeddine Tagoug2

1Department of Computer Science King Saud University Riyadh Saudi Arabia2Department of Information Systems King Saud University Riyadh Saudi Arabia

Correspondence should be addressed to Abdu Gumaei abdugumaeigmailcom

Received 23 May 2015 Revised 11 September 2015 Accepted 15 October 2015

Academic Editor Wen-Huang Cheng

Copyright copy 2015 Rachid Sammouda et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

Wireless multimedia sensor network (WMSN) is a developed technology of wireless sensor networks and includes a set of nodesequipped with cameras and other sensors to detect ambient environment and produce multimedia data content In this contextmany types of noises occur due to sensors problems change of illumination fog rain and other weather conditions These noisesusually degrade the digital images acquired by camera sensors Image denoising in spatial domain is more difficult and time-consuming for real-time processing ofWMSNs applications In this study an efficientmethod based onDual-TreeComplexWaveletTransform (DT-CWT) is developed to enhance the image denosing inWMSNsThismethod is designed to reduce the image noisesby selecting an optimal threshold value estimated from the approximation of wavelet coefficients In our experiment the proposedmethod was tested and compared with standard Discrete Wavelet Transform (DWT) and StationaryWavelet Transform (SWT) ona set of natural scene images Better results were achieved by using the DT-CWT in terms of image quality metrics and processingtime

1 Introduction

WMSN is a developed technology ofwireless sensor networkswhich contains a set of nodes connected with camera sensorsto acquire and transfer images and videos through sensornetworks [1ndash3] However digital images and videos generatedby camera sensors can be affected by noise during capturingtransmitting and retrieving processes As a result many dotscan be spotted in an image under low lighting conditionschange of illumination fog rain and other weather prob-lems In general the noisy images impose excessive limita-tions on the performance of image processing techniquessuch as detection and segmentationwhich need a clean imageto work effectively [4ndash7] Thus image denoising methods aremainly used to remove these noises from captured imageswithout affecting the images information asmuch as possible

The literature showed that there are many differentmethods of image denoising These methods can be dividedinto two groups based on the image representation domainused spatial domain-based and frequency domain-basedIn fact applying one of these techniques depends on the

domain of image processing applications and the statisticalproperty of image noises In spatial domain every pixel ofthe original image can be processed independently based onsome relations with its neighbors and correspondence valuesof their filter matrix Median filter [8] neighborhood averagemethod [9] and weighted median filter and the center-weight median filter [8 10] are some common methods thathave been applied for image denoising in spatial domainHowever these methods had some limitations such as a highcomputation load Furthermore recent methods [11ndash17] triedto combine the median filter with the impulse detection toreduce median filters limitations However the performanceof thesemethods is totally depending on the impulse detectorperformance In addition mean-based filters [18ndash20] can beused as an alternative solution in reducing the high loadcomputation Recently some methods [21ndash24] have beenproposed for image noise reduction by using some fuzzylogic approaches Unfortunately most existing methods arestill suffering from the high load computations which delaythe processing time of images and the response of WMSNsapplications as a real-time application In frequency domain

Hindawi Publishing CorporationInternational Journal of Distributed Sensor NetworksVolume 2015 Article ID 632568 13 pageshttpdxdoiorg1011552015632568

2 International Journal of Distributed Sensor Networks

images are transformed into another domain to performsome operations on image coefficients [25 26] Then theinverse of the transformation is calculated and returned backinto image domain Discrete Fourier Transform (DFT) is themost popular transformation that is widely used for signaland image processing applications with satisfactory accuracy[27 28] However DFT filter method loses the correct local-ization in both time and frequency domains Thus it is notsuitable to be used for nonstationary signals like images Theother common transformation method is Discrete CosineTransform (DCT) DCT is a simple and effective tool fordenoising [28] Nevertheless some drawbacks of DCT suchas high loss of information and low resolution make itunsuitable for real-time processing of critical applicationsOver the past decade Discrete Wavelet Transform (DWT)was widely used as a more accurate tool than DFT andDCT because of its excellent localization property DWTwas considered an essential signal and image processing toolfor many applications such as compression and denoising[26 29ndash33] It provides applications with a suitable basis forseparating the noise signal from the image signal by usingthe appropriate threshold valuewithout affecting informationof the original image Several researches were conductedto find the appropriate selection for the wavelet thresholdthat can be used for signal and image denoising [29 32ndash35] In most of them DWT was commonly used but ithas three major problems These problems are lack of shiftinvariant poor directionality and lack of phase informationThe problem of shift-variant can be reduced by applyingthe Stationary Wavelet Transform (SWT) as introduced in1996 as an improvement of standard DWT [36] AlthoughSWT improves the power of wavelet in image denoisingconsiderably it suffers from the cost of very high redundancywhich makes it computationally expensive [37] Recentlymany mathematical algorithms have been proposed to solvethe DWT problems by using different forms of ComplexWavelet Transforms (CWT) [38ndash43] Dual-Tree ComplexWavelet Transform (DT-CWT) is considered as one of themost efficient forms of CWT as reported in [44 45] It givestexture information oriented in six different directions withlimited redundancy Consequently in this study we proposedan efficient image denoising method by using the DT-CWTfor real-time image processing of WMSNs applications

The rest of the paper is organized as follows Section 2introduces the mathematical basics of DT-CWT Section 3presents the proposed 2D DT-CWT-based method for imagedenoising Section 4 explains the research experiment thatused to verify the reliability of the proposed method Finallya brief conclusion about this work is drawn in Section 5

2 Dual Tree-Complex WaveletTransform (DT-CWT)

Dual Tree-Complex Wavelet Transform (DT-CWT) is anenhancement extension of DWT with important propertiesof wavelet It uses analytic filter to perform the waveletanalysis instead of real-valued filter coefficients therefore itsolves problems of DWT at the cost of limited redundancy

Analysis Synthesis

Real tree

Tree a (hxhy)

Tree b (gxgy)

Tree c (hxgy)

Tree d (gxhy)

Imaginary tree

f(t)simf(t)

Tree sima (simhxsimhy)

Tree simb (simgxsimgy)

Tree simc (simhxsimhy)

Tree simd (simgxsimgy)

Figure 1 Filter bank structure for 2D DT-CWT

Kingsbury proposed the DT-CWT technique to achieve anaccurate reconstructionwhile providing the other advantagesof complex wavelets [44] It is closely shift invariant anddirectionally selective in two and higher dimensions Thiscan be achieved with redundancy factor of only 2

119889 for d-dimensional signals which is significantly lower than theStationary Wavelet Transform (SWT) [45] In fact DT-CWTgives more information about the detail of an image byproducing six directional subbands per level for each pixeloriented at angles plusmn15∘ plusmn45∘ and plusmn75∘ with 4 1 redundancy[38] While DWT produces three directional subbands perlevel for each pixel conveying image features oriented atangles 90∘ plusmn45∘ and 0∘ it decomposes a signal into real(119903) and imaginary (119894) parts in terms of mother wavelet120595(119909) and scaling function 120593(119909) The coefficients of real andimaginary parts can be used to compute amplitude and phaseinformation The real (119903) and imaginary (119894) parts of thewavelet 120595(119909) and scaling 120593(119909) functions for one-dimensionalcase can be defined as

120595119903 (119905) = radic2

119899

sum

119894=0

119867119886 (119899) 120593119903 (2119905 minus 119899) (1)

120595119894 (119905) = radic2

119899

sum

119894=0

119867119887 (119899) 120593119894 (2119905 minus 119899) (2)

120593119903 (119905) = radic2

119899

sum

119894=0

119871119886 (119899) 120595119903 (2119905 minus 119899) (3)

120593119894 (119905) = radic2

119899

sum

119894=0

119871119887 (119899) 120595119894 (2119905 minus 119899) (4)

120595119888 (119905) = 120595119903 (119905) + 119895120595119894 (119905) (5)

where 120595119903 and 120595119894 represent the wavelet functions 119871 representsthe low-pass filters and 119867 represents the high-pass filtersThe wavelet functions 120595119903 and 120595119894 yield the complex waveletfunction 120595119888 which is given by (5)

To compute DT-CWT of an image it can be extendedto two-dimensional case by applying its filter bank in alldimensions separately 2D structure of DT-CWT needs fourtrees (eg trees a b c and d) for analysis and also forsynthesis (see Figure 1)

International Journal of Distributed Sensor Networks 3

Applying threshold function

Camera sensor

Capturing image

Converting color image to grayscale image

Input image Y

Performing 2D DT-CWT decomposition

Performing 2D DT-CWT inverse transform

Output image Z

Figure 2 Flow chart of 2D DT-CWT-based method for imagedenoising

The signal of the input image is decomposed up to adesired level by two separable 2D DWT branches (119886) and (119887)in parallel to the same data Each filtering process is followedby a downsampling by two and the pairs of DT-CWT treesare applied to rows (119909) and then to columns (119910) of the imagewhich can be represented as

(ℎ119909 + 119895119892119909) (ℎ119910 + 119895119892119910)

= (ℎ119909ℎ119910 + 119892119909119892119910) + 119895 (ℎ119909119892119910 + 119892119909ℎ119910)

(6)

3 Proposed Method

The proposed denoising method assumes that the signal ofimage is corrupted by different types of noise However thepower of these types of noise is still much lower than thepower of the original image signal In this work we focus ona zero mean additive white Gaussian noise (AWGN) which isgenerally more difficult to remove Based on this assumptionthe problem of image denoising can be mathematicallyexpressed as follows

119884 = 119883 + 120590119873 (7)

where 119884 is the observed noisy image 119883 is the original imageand 120590119873 is the AWGN noise with standard deviation 120590 andzero mean Both 119884 and 119883 are of the same sizes The blockdiagram that is shown in Figure 2 represents the main stepsof the proposed method The method starts with convertingthe input color image to a gray scale image where 2DDT-CWT is applied to decompose image into four levelsthen filter bank is applied for each level of image rows andcolumns A hard threshold function with optimal thresholdvalue is used for each subband coefficient except the lowestsubband Therefore all high frequency subband coefficientswhich are less than the optimal threshold are set to zeros

Finally coefficients yielded from previous step are used as aninverse of 2DDT-CWT to reconstruct the original image afterreducing image noises

In general there are mainly two methods soft thresholdfunction and hard threshold function the hard thresholdfunction has been adopted and defined by the following

Hard threshold

120596119894119895119885 =

120596119894119895119884 if 10038161003816100381610038161003816120596119894119895119884

10038161003816100381610038161003816gt 119879

0 if 10038161003816100381610038161003816120596119894119895119884

10038161003816100381610038161003816le 119879

(8)

where 120596119894119895119884 is the signal wavelet coefficients of input imagebefore threshold120596119894119895119885 is the generic wavelet coefficients afterthreshold and 119879 is the threshold value Our method adjuststhe coefficients of 2D DT-CWT by optimal or near-optimaluniversal threshold values They are computed based on theMedian Absolute Deviation (MAD) and the length of waveletcoefficients at each decomposition level as follows

119879119895 = MAD119895 lowast radic2 lowast log119873119895 (9)

where 119873119895 is the length of detail coefficients at 119895th decompo-sition level and MAD119895 is the median absolute deviation ofempirical wavelet coefficients which can be given as follows[25]

MAD119895 =

median (10038161003816100381610038161003816120596119871minus1119895

10038161003816100381610038161003816)

06745 119895 = 0 1 2

119871minus1minus 1 (10)

where 119871 is the number of decomposition levels of analyzedimage signal which depends on the application Here it isenough to consider the number of decomposition levels asfour levels where an energy criterion can help to removethe noise The reason behind selecting the median absolutedeviation of detail coefficients as noise estimator because ofit is a robust noise estimator and much less sensitive thanthe usual standard deviation and mean to extreme values[25] The denoised image (output image) can be obtainedby performing the inverse of 2D DT-CWT after modifyingthe wavelet coefficients according to some thresholds orrules The 2D DT-CWT gives the 2D images a four-timeredundancy (expensive) and this redundancy allows bothshift invariance and good directional sensitivity

4 Experiment

This section shows the results of applying our image denois-ing based on 2D DT-CWT to a set of natural indoor-outdoorscene images Moreover we make a comparison between theresults of proposed method with the results of applying 2DDWT and 2D SWT for the same set of images The proposedmethod is developed with MATLAB R2012a programmingenvironment Coefficients in the wavelet domain have beenmodified by hard threshold function before image recon-struction The hardware configuration is composed of IntelCore 2 Duo T6500 210GHz processor with 2GB of RAMand 320GB Hard Disk The operating system is MicrosoftWindows 7 Professional Under these configurations thetest samples the performance metrics and the experimentalresults will be given in the following subsections


Figure 3 Test samples of indoor-outdoor scene images numbered from left to right row by row from 1 to 6

41 Test Samples of Indoor-Outdoor Scene Images In ourexperiment six scene images as shown in Figure 3 of dimen-sions 640 times 480 pixels are used as test samples Four of which(Image 1 to Image 4) are selected from KAIST scene imagesdatabase English subset taken by Sony Cyber-Shot DSC-T70camera [46]They are captured in both outdoors and indoorsenvironments under different lighting conditions The tworemaining images (Image 5 and Image 6) are outdoor imagestaken by Kodak EasyShare C613 ZOOM camera from twoplaces (preparatory year and SAMBA bank) at King SaudUniversity

42 Performance Metrics Performance of the proposedimage denoising approach is quantitatively evaluated by usingthree image quality metrics Normalized Absolute Error(NAE) Peak Signal to Noise Ratio (PSNR) andMean SquareError (MSE) as well as the processing time of the proposedmethod The image quality metrics are computed based onthe original and the denoised scene images NAE is a criterionto evaluate the ability of preserving the information of theoriginal image where the large value of NAE means thatdenoised image is poor quality [47] It is defined as follows

NAE =sum119872

119898=1sum119873

119899=1|119874 (119898 119899) minus 119863 (119898 119899)|

sum119872

119898=1sum119873

119899=1|119874 (119898 119899)|

(11)

where 119874 is the original image and 119863 is the denoised imageand also119898 and 119899 are the number of pixels in row and columndirections respectively On the other hand the PSNR is atypical metric used to measure the ability of noise reduction

performance where the small value of PSNR means thatdenoised image is of poor quality [47] PSNR is defined asfollows

PSNR = 10 log10

(Max2

MSE) (12)

where Max is the maximum gray scale of pixels for example255 for 8 bits and MSE is the mean square error between theoriginal image (119874) and denoised image (119863) which is definedas [47]

MSE =1

119872119873 sum119872

119898=1sum119873

119899=1(119874 (119898 119899) minus 119863 (119898 119899))

2 (13)

where 119898 and 119899 represent the number of pixels in row andcolumndirections respectivelyThe last performancemetricsis the processing time of method which can be calculated byrunning the codes of method in MATLAB R2012a on thesame hardware configuration mentioned above Processingtime is an important measure for image denoising methodsin real-time image processing applications Here it can becalculated by running the codes of different image denoisingmethods in MATLAB R2012a on the same hardware config-uration mentioned above

43 Results and Discussion In order to verify the reliabilityof our proposed approach all test samples were degradedartificially with Gaussian white noise of different levels 1020 30 and 40 respectively The experimental resultsof different denoising methods are assessed and computed


Table 1 NAE results of de-nosing methods at different noise levelsand four-levels of decomposition

Image with NoiseLevel

Image De-noising Methods

2D DWT-basedMethod

2D SWT-basedMethod

Proposed 2DDT-CWT-based

MethodImage 1

120590 = 10 00329 00284 00236120590 = 20 00409 00353 00313120590 = 30 00464 00410 00364120590 = 40 00516 00473 00423

Image 2120590 = 10 00247 00220 00175120590 = 20 00329 00290 00256120590 = 30 00408 00363 00334120590 = 40 00479 00434 00405

Image 3120590 = 10 00236 00212 00152120590 = 20 00317 00307 00238120590 = 30 00376 00369 00313120590 = 40 00427 00423 00369

Image 4120590 = 10 00326 00274 00205120590 = 20 00471 00416 00339120590 = 30 00590 00516 00448120590 = 40 00701 00616 00573

Image 5120590 = 10 00308 00193 00190120590 = 20 00459 00365 00348120590 = 30 00588 00495 00480120590 = 40 00705 00605 00606

Image 6120590 = 10 00229 00181 00158120590 = 20 00336 00296 00254120590 = 30 00418 00378 00345120590 = 40 00496 00450 00437

using NAE as well as processing time Table 1 exhibits theexperiment results of NAE at different noise levels for thedenoised images of three methods Graphical representationof NAE results versus noise standard deviation (120590) for Image1 and Image 6 can be seen clearly in Figure 4 It proves thatthe proposed method results in less NAE compared with theother methods for all tested images

In addition the value of NAE is decreased with lownoise conditions and is increased with high noise conditionsHowever the proposed 2DDT-CWT-basedmethod of imagedenoising gives better quantitative results than 2D DWTand 2D SWT-based methods of image denoising for allcomparison parameters

Table 2 shows the results of MSE and PSNR at differentnoise levels for the denoised images of three methods where

Table 2 MSE and PSNR (dB) results of De-nosing methods atdifferent noise levels and four-levels of decomposition



2D DWT-basedMethod

2D SWT-basedMethod


MethodImage 1

120590 = 10 5553 (3069) 3664 (3249) 2392 (3434)120590 = 20 9406 (2840) 8002 (2910) 4642 (3146)120590 = 30 12702 (2709) 11061 (2770) 6409 (3006)120590 = 40 15600 (2620) 14688 (2646) 8557 (2881)

Image 2120590 = 10 2310 (3450) 1785 (3562) 1014 (3807)120590 = 20 4671 (3144) 3930 (3219) 2487 (3418)120590 = 30 7241 (2953) 5983 (3036) 4383 (3171)120590 = 40 9744 (2824) 8085 (2905) 6156 (3024)

Image 3120590 = 10 2866 (3356) 8939 (2861) 1025 (3805)120590 = 20 5339 (3086) 5085 (3107) 2632 (3393)120590 = 30 7459 (2940) 7031 (2966) 4401 (3170)120590 = 40 9482 (2836) 9025 (2858) 5874 (3044)

Image 4120590 = 10 3602 (3257) 2290 (3453) 1217 (3728)120590 = 20 7588 (2933) 6098 (3028) 3677 (3248)120590 = 30 11077 (2769) 8636 (2877) 5969 (3037)120590 = 40 14619 (2648) 11394 (2756) 9002 (2859)

Image 5120590 = 10 5383 (3082) 1718 (3578) 1517 (3632)120590 = 20 10310 (2800) 6506 (3000) 4606 (3150)120590 = 30 15326 (2628) 11774 (2742) 8870 (2865)120590 = 40 20763 (2496) 16610 (2593) 14297 (2658)

Image 6120590 = 10 2623 (3394) 1102 (3771) 870 (3874)120590 = 20 6321 (3012) 4653 (3145) 2629 (3393)120590 = 30 9501 (2835) 8054 (2907) 5010 (3113)120590 = 40 12497 (2716) 11068 (2769) 7084 (2963)

The value in the parenthesis is the PSNR measure

the values in the parenthesis are the PSNR measure Largevalues of MSE mean that images are of poor quality andthe large values of PSNR mean that images are of highquality Here we can see that the results of 2D SWT-basedmethod are better than 2D DWT-based method in terms ofMSE and PSNR but the results of proposed 2D DT-CWT-based method are the best for all comparisons It is worthmentioning that whenever the value of noise level increasesthe value of MSE also increases and the value of PSNRdecreases in all of the three methods

For visual evaluation Figures 5 6 7 8 9 and 10 show theresult of three denoising methods on all images in the testsample They contain the noisy image with noise level (120590 =40) and the denoised image of the proposed method and theother two methods


Image denoising using 2D DWTImage denoising using 2D SWTProposed image denoising using 2D DT-CWT

120590 = 10 120590 = 20 120590 = 30 120590 = 40

0001002003004005006007008

(a)


120590 = 10 120590 = 20 120590 = 30 120590 = 40

0001002003004005006007008

(b)

Figure 4 NAE versus noise standard deviation 120590 at four levels of decomposition by different denoising methods for (a) Image 1 and (b)Image 6

(a) (b)

(c) (d)

Figure 5 The denoising results of Image 1 from test sample at four levels of decomposition by different methods (a) Noisy image with 120590

= 40 (b) denoised scene image using 2D DWT (c) denoised scene image using 2D SWT (d) denoised scene image using the proposed 2DDT-CWT

The visual evaluation emphasizes that the proposed 2DDT-CWT-based method gives best results of patterns andedges on denoised images with no degradation or artifactsbecause it deals with the edges on the images in six directionsAlso we can see that the DWT-based method does notachieve good results of patterns on denoised images in allcases because of its lack of directionality and shift invariant

Results of NAE and visual evaluation show that thedenoised images by 2D SWT-based method are better than2D DWT-based method because it is shift invariant but theyare not better than the denoised images of the proposed 2DDT-CWT-based method since it does not consider the sixdirections of edges information of decomposed images

Although the results of all used images in our experimentshow that the decomposition process until four levels is prac-tically good to remove Gaussian noise from images acquiredbyWMSNs devices however more real demonstrations with

deeper analysis are investigated to show how the accuracy ofthe proposed method can be affected by varying the numberof decomposition levels Accordingly we tested our proposedmethod by applying several values of decomposition level (1ndash5) on all the test images at noise level 120590 = 40 as shown inTable 3

Through Table 3 we note that most restored images havehigh PSNR and low MSE values (bold black values) at fourlevels of decomposition except two cases (Image 4 and Image5)These two cases have high PSNRand lowMSE values (boldblack values) at three levels of decomposition Thereforethe limitation of the proposed method is how to determinethe optimum value of decomposition level However theobtained results of the proposed method compared to othermethods confirm that the four levels of decomposition aregood enough to remove Gaussian noise from images ofWMSNs applications Figures 11 and 12 show the denoised


(a)

(b)

(c)

(d)

Figure 6 The denoising results of Image 2 from test sample at fourlevels of decomposition by different methods (a) Noisy image with120590 = 40 (b) denoised scene image using 2DDWT (c) denoised sceneimage using 2D SWT (d) denoised scene image using the proposed2D DT-CWT

images obtained by the proposed method at four and threelevels of decomposition respectively at noise level 120590 = 40FromFigures 11 and 12 we can see that the denoised images inthree levels of decomposition have a better quality than thosedenoised images in four levels of decomposition

Sensitivity analysis for different threshold values versusPSNR metric is employed here to validate the ideal valueof MAD threshold We applied different threshold valuesranked from 0 to 100 incremented by 5 on all tested imagesat noise levels 120590 = 20 and 120590 = 40 Then for each thresholdvalue used to denoise the noisy image the PSNR metric iscomputed as shown in Figures 13ndash18 This step is employed

Table 3 MSE and PSNR (dB) results of proposed method at five-levels of decomposition and noise level 120590 =40

Image level ofnoise

Number ofdecomposition level MSE PSNR

Image 1120590 = 40

1 308089 232442 1151715 2751743 859083 2879054 855702 2880765 855702 288076

Image 2120590 = 40

1 2988552 2337622 99408 2815663 638291 3008064 615572 302385 66874 298782

Image 3120590 = 40

1 3036185 2330752 97354 2824733 60672 3030094 587403 3044145 638291 300806

Image 4120590 = 40

1 2999368 2336052 1134212 2758393 844663 288644 900184 2858755 965508 282832

Image 5120590 = 40

1 2412989 2430532 1605966 2607343 1406729 2664874 1429727 2657835 1478107 264337

Image 6120590 = 40

1 2083282 2494332 1066155 2785263 752598 2936524 708417 2962795 720599 295539

technically to search for the optimal threshold point whichyields the maximum PSNR value Eventually we comparedthe obtained maximum PSNR values with the PSNR valuesproduced by the MAD technique as illustrated in Table 2

From Figures 13ndash18 and Table 2 we can notice thatthe maximum PSNR values obtained by applying differentthresholds are approximately the same as the PSNR valuescalculated by MAD-based threshold For example Figure 13for denoised image (Image 1) showed that the maximumPSNR values are 3146 and 2881 with noise variances 120590 =20 and 120590 = 40 respectively These values are roughly equalto the PSNR values calculated by MAD-based threshold inTable 2 Added to that Figures 13ndash18 illustrated the effects ofthe threshold parameter for determining the amount of usefulsignals and smoothness Thus the selected threshold valuesbased on the MAD are almost optimal which consequentlyshowed the effectiveness of using MAD strategy in theproposed method


(a)

(b)

(c)

(d)


Table 4 Average processing time in seconds of three de-noisingmethods on our test samples

De-noisingMethod

2DDWT-basedMethod

2D SWT-basedMethod


MethodAvgProcessingTime (s)

04837 13354 08138

Finally a comparison of the average processing time ofthe 2DDWT- and 2D SWT-basedmethods and the proposedmethod for our test samples is presented in Table 4

(a)

(b)

(c)

(d)


From Table 4 it is clear to show that the averageprocessing time of 2D SWT-based method is higher thanthat of the proposed 2D DT-CWT- and 2D DWT-basedmethods Even though the proposedmethod consumesmoreprocessing time than the 2D DWT-based method the abovequalitative and quantitative results of image quality metricssupport the efficiency of the proposed 2D DT-CWT-basedmethod for image denoising Experimental results provethat the proposed method is efficient and appropriate forimage denoising Thus this method can be embedded aspreprocessing stage to improve the efficiency of currentWMSNs applications


(a) (b)

(c) (d)



(a) (b)

(c) (d)



5 Conclusions and Future Work

In this work we have studied the mathematical model ofDT-CWT for multilevel reconstruction of signals Based onthe properties of DC-CWT for signal image decompositionan efficient 2D DT-CWT-based image denoising method isproposed for real-time applications ofWMSNsThe excellentfeatures of the DT-CWT such as multidirectionality andshift-invariance make it more suitable for image denoising

of real-time applications The proposed 2D DT-CWT-basedmethod reduced the noise of images by applying an optimalthreshold value of hard threshold function using MAD strat-egy This threshold not only forms the near-optimal waveletcoefficients but also makes it a more stable magnitude forpatterns on the images It was developed in the MATLABR2012a and tested over test samples of indoor-outdoor sceneimages taken by Sony Cyber-Shot andKodak EasyShare cam-eras The taken images were captured in real environments


(a) (b)

(c)

Figure 11 The denoising results of Image 4 from test sample (a) Noisy image with 120590 = 40 (b) denoised scene image using the proposed 2DDT-CWT at four levels of decomposition (c) denoised scene image using the proposed 2D DT-CWT at three levels of decomposition whichis better quality than denoised image in (b)

(a) (b)

(c)


which are similar to images captured by wireless sensordevices Processing time and image quality metrics have beencalculated and compared for estimating the efficiency of the2D DT-CWT filtering method The results obtained fromthis study prove the performance and efficiency of the 2DDT-CWT filtering method at four levels of decomposition Ithas achieved excellent denoising characteristics in preservingthe edges of texture patterns compared to the 2D DWT and

2D SWT with limited redundancy and moderate process-ing time for image processing-based WMSNs applicationsResults showed that applying the 2D DT-CWT method toenhance WMSNs images improved its efficiency in reducingthe noise of images acquired by WMSNs devices Thus itcan be embedded as preprocessing stage to improve theefficiency of current WMSNs applications Even though theproposed method was conducted on real sensing images in


0 10 20 30 40 50 60 70 80 90 100Threshold values

02468

10121416182022242628303234

PSN

R va

lues

When noise variance 120590 = 20


Figure 13 PSNR values versus threshold values with noise variances120590 = 20 and 120590 = 40 for Image 1


02468

10121416182022242628303234

PSN

R va

lues





02468

10121416182022242628303234

PSN

R va

lues





02468

10121416182022242628303234

PSN

R va

lues





02468

10121416182022242628303234

PSN

R va

lues





02468

10121416182022242628303234

PSN

R va

lues





the future works we will test our method on images takenby camera sensors connected to wireless multimedia sensornetworks

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This project was funded by the National Plan for ScienceTechnology and Innovation (MAARIFAH) King AbdulazizCity for Science and Technology Kingdom of Saudi ArabiaAward no INF2696-02-12

References

[1] I F Akyildiz T Melodia and K R Chowdhury ldquoWirelessmultimedia sensor networks applications and testbedsrdquo Pro-ceedings of the IEEE vol 96 no 10 pp 1588ndash1605 2008

[2] I Ha M Djuraev and B Ahn ldquoAn energy-efficient datacollection method for wireless multimedia sensor networksrdquoInternational Journal of Distributed Sensor Networks vol 2014Article ID 698452 8 pages 2014

[3] M S Alhilal A Soudani and A Al-Dhelaan ldquoImage-basedobject identification for efficient event-driven sensing in wire-less multimedia sensor networksrdquo International Journal ofDistributed Sensor Networks vol 2015 Article ID 850869 11pages 2015

[4] R Sammouda N Adgaba A Touir and A Al-Ghamdi ldquoAgri-culture satellite image segmentation using a modified artificialHopfield neural networkrdquo Computers in Human Behavior vol30 pp 436ndash441 2014

[5] A Gumaei A El-Zaart M Hussien and M Berbar ldquoBreastsegmentation using k-means algorithm with a mixture ofgamma distributionsrdquo in Proceedings of the Symposium onBroadband Networks and Fast Internet (RELABIRA rsquo12) pp 97ndash102 Baabda Lebanon May 2012

[6] A AlSalman A El-Zaart S Al-Salman and A Gumaei ldquoAnovel approach for Braille images segmentationrdquo in Proceedingsof the International Conference on Multimedia Computing andSystems (ICMCS rsquo12) pp 190ndash195 IEEE Tangier Morocco May2012

[7] A Gumaei A El-Zaart and H Mathkour ldquoAn efficient irissegmentation approachrdquo in International Conference onGraphicand Image Processing (ICGIP rsquo11) vol 8285 of Proceedings ofSPIE Cairo Egypt September 2011

[8] A C Bovik Handbook of Image and Video Processing ElsevierAcademic Press San Diego Calif USA 2nd edition 2005

[9] B Jahne Practical Handbook on Image Processing for ScientificApplications CRC Press Boca Raton Fla USA 1997

[10] T-C Lin ldquoA new adaptive center weighted median filter forsuppressing impulsive noise in imagesrdquo Information Sciencesvol 177 no 4 pp 1073ndash1087 2007

[11] T Chen and H R Wu ldquoAdaptive impulse detection usingcenter-weighted median filtersrdquo IEEE Signal Processing Lettersvol 8 no 1 pp 1ndash3 2001

[12] T Chen and H R Wu ldquoSpace variant median filters for therestoration of impulse noise corrupted imagesrdquo IEEE Trans-actions on Circuits and Systems II Analog and Digital SignalProcessing vol 48 no 8 pp 784ndash789 2001

[13] I Aizenberg C Butakoff and D Paliy ldquoImpulsive noiseremoval using threshold Boolean filtering based on the impulsedetecting functionsrdquo IEEE Signal Processing Letters vol 12 no1 pp 63ndash66 2005

[14] R Garnett T Huegerich C Chui andWHe ldquoA universal noiseremoval algorithmwith an impulse detectorrdquo IEEETransactionson Image Processing vol 14 no 11 pp 1747ndash1754 2005

[15] S-Q Yuan and Y-H Tan ldquoImpulse noise removal by a global-local noise detector and adaptive median filterrdquo Signal Process-ing vol 86 no 8 pp 2123ndash2128 2006

[16] M E Yuksel and E Besdok ldquoA simple neuro-fuzzy impulsedetector for efficient blur reduction of impulse noise removaloperators for digital imagesrdquo IEEE Transactions on FuzzySystems vol 12 no 6 pp 854ndash865 2004

[17] S Schulte M Nachtegael V DeWitte D van der Weken andE E Kerre ldquoA fuzzy impulse noise detection and reductionmethodrdquo IEEE Transactions on Image Processing vol 15 no 5pp 1153ndash1162 2006

[18] EMAbreu ldquoSignal-dependent rank-orderedmean (SD-ROM)filterrdquo in Nonlinear Image Processing (Communications Net-working and Multimedia) S K Mitra G L Sicuranza and J DGibson Eds pp 111ndash133 Academic Press Orlando Fla USA2001

[19] D S Zhang and D J Kouri ldquoVarying weight trimmed meanfilter for the restoration of impulse noise corrupted imagesrdquo inProceedings of the IEEE International Conference on AcousticsSpeech and Signal Processing (ICASSP rsquo05) vol 4 pp IV137ndashIV140 Philadelphia Pa USA March 2005

[20] W Luo ldquoAn efficient detail-preserving approach for removingimpulse noise in imagesrdquo IEEE Signal Processing Letters vol 13no 7 pp 413ndash416 2006

[21] S Schulte V De Witte and E E Kerre ldquoA fuzzy noisereduction method for color imagesrdquo IEEE Transactions onImage Processing vol 16 no 5 pp 1425ndash1436 2007

[22] A Toprak and I Guler ldquoImpulse noise reduction in medicalimages with the use of switch mode fuzzy adaptive medianfilterrdquo Digital Signal Processing vol 17 no 4 pp 711ndash723 2007

[23] S Morillas V Gregori G Peris-Fajarnes and A Sapena ldquoLocalself-adaptive fuzzy filter for impulsive noise removal in colorimagesrdquo Signal Processing vol 88 no 2 pp 390ndash398 2008

[24] M T Yildirim A Basturk and M E Yuksel ldquoImpulse noiseremoval from digital images by a detail-preserving filter basedon type-2 fuzzy logicrdquo IEEE Transactions on Fuzzy Systems vol16 no 4 pp 920ndash928 2008

[25] D L Donoho and J M Johnstone ldquoIdeal spatial adaptation bywavelet shrinkagerdquo Biometrika vol 81 no 3 pp 425ndash455 1994

[26] G Aglika K Rika and K F ImolaUndecimatedWavelet Trans-forms for Image De-Noising Aglika Gyaourova Department2002

[27] E O Brigham The Fast Fourier Transform Prentice Hall NewYork NY USA 2002

[28] G Yu and G Sapiro ldquoDCT image denoising a simple andeffective image denoising algorithmrdquo Image Processing on Linevol 1 2011

[29] S G Chang and M Vetterli ldquoSpatial adaptive wavelet thresh-olding for image denoisingrdquo in Proceedings of the IEEE Inter-national Conference on Image Processing pp 374ndash377 SantaBarbara Calif USA October 1997


[30] A Chambolle R A DeVore N-Y Lee and B J LucierldquoNonlinear wavelet image processing variational problemscompression and noise removal through wavelet shrinkagerdquoIEEE Transactions on Image Processing vol 7 no 3 pp 319ndash3351998

[31] D L Donoho ldquoWavelet thresholding and WVD a 10-minutetourrdquo in Proceedings of the International Conference onWaveletsand Applications Toulouse France June 1992

[32] D L Donoho ldquoDe-noising by soft thresholdingrdquo IEEE Transac-tions on Information Theory vol 41 no 3 pp 613ndash627 1995

[33] L Sendur and I W Selesnick ldquoBivariate shrinkage with localvariance estimationrdquo IEEE Signal Processing Letters vol 9 no12 pp 438ndash441 2002

[34] S G Chang B Yu andMVetterli ldquoAdaptivewavelet threshold-ing for image denoising and compressionrdquo IEEETransactions onImage Processing vol 9 no 9 pp 1532ndash1546 2000

[35] X Wang X Ou B-W Chen and M Kim ldquoImage denoisingbased on improved wavelet threshold function for wirelesscamera networks and transmissionsrdquo International Journal ofDistributed Sensor Networks vol 2015 Article ID 670216 8pages 2015

[36] J-C Pesquet H Krim and H Carfantan ldquoTime-invariantorthonormal wavelet representationsrdquo IEEE Transactions onSignal Processing vol 44 no 8 pp 1964ndash1970 1996

[37] V Sekar and D Nedumaran ldquoDe-noising of fingerprint imagesusing discrete stationary wavelet transformrdquo in Proceedings ofthe National Symposium on Instrumentation (NSI-32 rsquo07) pp55ndash57 Erode India November 2007

[38] I W Selesnick ldquoHilbert transform pairs of wavelet basesrdquo IEEESignal Processing Letters vol 8 no 6 pp 170ndash173 2001

[39] R van Spaendonck T Blu R Baraniuk and M VetterlildquoOrthogonal Hilbert transform filter banks and waveletsrdquo inProceedings of the IEEE International Conference on AccousticsSpeech and Signal Processing (ICASSP rsquo03) pp 505ndash508 April2003

[40] N Kingsbury and J Magarey ldquoMotion estimation using com-plex waveletsrdquo Tech Rep Engineering Department Cam-bridge University Cambridge UK 1995

[41] N Kingsbury ldquoImage processing with complex waveletsrdquo Philo-sophical Transactions of the Royal Society A MathematicalPhysical and Engineering Sciences vol 357 no 1760 pp 2543ndash2560 1999

[42] N G Kingsbury ldquoComplex wavelets for shift invariant analysisand filtering of signalsrdquo Applied and Computational HarmonicAnalysis vol 10 no 3 pp 234ndash253 2001

[43] F Fernandes R van Spaendonck M J Coates and C SBurrus ldquoDirectional complex-wavelet processingrdquo in WaveletApplications in Signal and Image Processing VIII vol 4119 ofProceedings of SPIE San Diego Calif USA December 2000

[44] N G Kingsbury ldquoThe dual-tree complex wavelet transform anew technique for shift invariance and directional filtersrdquo inProceedings of the IEEE Digital Signal Processing Workshop pp319ndash322 1998

[45] I W Selesnick R G Baraniuk and N G Kingsbury ldquoThedual-tree complex wavelet transformrdquo IEEE Signal ProcessingMagazine vol 22 no 6 pp 123ndash151 2005

[46] H K Jin and L Seonghun ldquoKAIST scene text databaserdquo 2011httpwwwiapr-tc11orgmediawikiindexphpKAIST SceneText Database

[47] A M Eskicioglu and P S Fisher ldquoImage quality measures andtheir performancerdquo IEEE Transactions on Communications vol43 no 12 pp 2959ndash2965 1995

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Active and Passive Electronic Components

Control Scienceand Engineering

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Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



images are transformed into another domain to performsome operations on image coefficients [25 26] Then theinverse of the transformation is calculated and returned backinto image domain Discrete Fourier Transform (DFT) is themost popular transformation that is widely used for signaland image processing applications with satisfactory accuracy[27 28] However DFT filter method loses the correct local-ization in both time and frequency domains Thus it is notsuitable to be used for nonstationary signals like images Theother common transformation method is Discrete CosineTransform (DCT) DCT is a simple and effective tool fordenoising [28] Nevertheless some drawbacks of DCT suchas high loss of information and low resolution make itunsuitable for real-time processing of critical applicationsOver the past decade Discrete Wavelet Transform (DWT)was widely used as a more accurate tool than DFT andDCT because of its excellent localization property DWTwas considered an essential signal and image processing toolfor many applications such as compression and denoising[26 29ndash33] It provides applications with a suitable basis forseparating the noise signal from the image signal by usingthe appropriate threshold valuewithout affecting informationof the original image Several researches were conductedto find the appropriate selection for the wavelet thresholdthat can be used for signal and image denoising [29 32ndash35] In most of them DWT was commonly used but ithas three major problems These problems are lack of shiftinvariant poor directionality and lack of phase informationThe problem of shift-variant can be reduced by applyingthe Stationary Wavelet Transform (SWT) as introduced in1996 as an improvement of standard DWT [36] AlthoughSWT improves the power of wavelet in image denoisingconsiderably it suffers from the cost of very high redundancywhich makes it computationally expensive [37] Recentlymany mathematical algorithms have been proposed to solvethe DWT problems by using different forms of ComplexWavelet Transforms (CWT) [38ndash43] Dual-Tree ComplexWavelet Transform (DT-CWT) is considered as one of themost efficient forms of CWT as reported in [44 45] It givestexture information oriented in six different directions withlimited redundancy Consequently in this study we proposedan efficient image denoising method by using the DT-CWTfor real-time image processing of WMSNs applications

The rest of the paper is organized as follows Section 2introduces the mathematical basics of DT-CWT Section 3presents the proposed 2D DT-CWT-based method for imagedenoising Section 4 explains the research experiment thatused to verify the reliability of the proposed method Finallya brief conclusion about this work is drawn in Section 5

2 Dual Tree-Complex WaveletTransform (DT-CWT)

Dual Tree-Complex Wavelet Transform (DT-CWT) is anenhancement extension of DWT with important propertiesof wavelet It uses analytic filter to perform the waveletanalysis instead of real-valued filter coefficients therefore itsolves problems of DWT at the cost of limited redundancy

Analysis Synthesis

Real tree

Tree a (hxhy)

Tree b (gxgy)

Tree c (hxgy)

Tree d (gxhy)

Imaginary tree

f(t)simf(t)

Tree sima (simhxsimhy)

Tree simb (simgxsimgy)

Tree simc (simhxsimhy)

Tree simd (simgxsimgy)

Figure 1 Filter bank structure for 2D DT-CWT

Kingsbury proposed the DT-CWT technique to achieve anaccurate reconstructionwhile providing the other advantagesof complex wavelets [44] It is closely shift invariant anddirectionally selective in two and higher dimensions Thiscan be achieved with redundancy factor of only 2

119889 for d-dimensional signals which is significantly lower than theStationary Wavelet Transform (SWT) [45] In fact DT-CWTgives more information about the detail of an image byproducing six directional subbands per level for each pixeloriented at angles plusmn15∘ plusmn45∘ and plusmn75∘ with 4 1 redundancy[38] While DWT produces three directional subbands perlevel for each pixel conveying image features oriented atangles 90∘ plusmn45∘ and 0∘ it decomposes a signal into real(119903) and imaginary (119894) parts in terms of mother wavelet120595(119909) and scaling function 120593(119909) The coefficients of real andimaginary parts can be used to compute amplitude and phaseinformation The real (119903) and imaginary (119894) parts of thewavelet 120595(119909) and scaling 120593(119909) functions for one-dimensionalcase can be defined as

120595119903 (119905) = radic2

119899

sum

119894=0

119867119886 (119899) 120593119903 (2119905 minus 119899) (1)

120595119894 (119905) = radic2

119899

sum

119894=0

119867119887 (119899) 120593119894 (2119905 minus 119899) (2)

120593119903 (119905) = radic2

119899

sum

119894=0

119871119886 (119899) 120595119903 (2119905 minus 119899) (3)

120593119894 (119905) = radic2

119899

sum

119894=0

119871119887 (119899) 120595119894 (2119905 minus 119899) (4)

120595119888 (119905) = 120595119903 (119905) + 119895120595119894 (119905) (5)

where 120595119903 and 120595119894 represent the wavelet functions 119871 representsthe low-pass filters and 119867 represents the high-pass filtersThe wavelet functions 120595119903 and 120595119894 yield the complex waveletfunction 120595119888 which is given by (5)

To compute DT-CWT of an image it can be extendedto two-dimensional case by applying its filter bank in alldimensions separately 2D structure of DT-CWT needs fourtrees (eg trees a b c and d) for analysis and also forsynthesis (see Figure 1)



Camera sensor

Capturing image


Input image Y



Output image Z



(ℎ119909 + 119895119892119909) (ℎ119910 + 119895119892119910)

= (ℎ119909ℎ119910 + 119892119909119892119910) + 119895 (ℎ119909119892119910 + 119892119909ℎ119910)

(6)

3 Proposed Method


119884 = 119883 + 120590119873 (7)




Hard threshold

120596119894119895119885 =

120596119894119895119884 if 10038161003816100381610038161003816120596119894119895119884

10038161003816100381610038161003816gt 119879

0 if 10038161003816100381610038161003816120596119894119895119884

10038161003816100381610038161003816le 119879

(8)




MAD119895 =

median (10038161003816100381610038161003816120596119871minus1119895

10038161003816100381610038161003816)

06745 119895 = 0 1 2



4 Experiment






NAE =sum119872

119898=1sum119873

119899=1|119874 (119898 119899) minus 119863 (119898 119899)|

sum119872

119898=1sum119873

119899=1|119874 (119898 119899)|

(11)



PSNR = 10 log10

(Max2

MSE) (12)


MSE =1

119872119873 sum119872

119898=1sum119873

119899=1(119874 (119898 119899) minus 119863 (119898 119899))

2 (13)







2D DWT-basedMethod

2D SWT-basedMethod


MethodImage 1

120590 = 10 00329 00284 00236120590 = 20 00409 00353 00313120590 = 30 00464 00410 00364120590 = 40 00516 00473 00423

Image 2120590 = 10 00247 00220 00175120590 = 20 00329 00290 00256120590 = 30 00408 00363 00334120590 = 40 00479 00434 00405

Image 3120590 = 10 00236 00212 00152120590 = 20 00317 00307 00238120590 = 30 00376 00369 00313120590 = 40 00427 00423 00369

Image 4120590 = 10 00326 00274 00205120590 = 20 00471 00416 00339120590 = 30 00590 00516 00448120590 = 40 00701 00616 00573

Image 5120590 = 10 00308 00193 00190120590 = 20 00459 00365 00348120590 = 30 00588 00495 00480120590 = 40 00705 00605 00606

Image 6120590 = 10 00229 00181 00158120590 = 20 00336 00296 00254120590 = 30 00418 00378 00345120590 = 40 00496 00450 00437







2D DWT-basedMethod

2D SWT-basedMethod


MethodImage 1

120590 = 10 5553 (3069) 3664 (3249) 2392 (3434)120590 = 20 9406 (2840) 8002 (2910) 4642 (3146)120590 = 30 12702 (2709) 11061 (2770) 6409 (3006)120590 = 40 15600 (2620) 14688 (2646) 8557 (2881)

Image 2120590 = 10 2310 (3450) 1785 (3562) 1014 (3807)120590 = 20 4671 (3144) 3930 (3219) 2487 (3418)120590 = 30 7241 (2953) 5983 (3036) 4383 (3171)120590 = 40 9744 (2824) 8085 (2905) 6156 (3024)

Image 3120590 = 10 2866 (3356) 8939 (2861) 1025 (3805)120590 = 20 5339 (3086) 5085 (3107) 2632 (3393)120590 = 30 7459 (2940) 7031 (2966) 4401 (3170)120590 = 40 9482 (2836) 9025 (2858) 5874 (3044)

Image 4120590 = 10 3602 (3257) 2290 (3453) 1217 (3728)120590 = 20 7588 (2933) 6098 (3028) 3677 (3248)120590 = 30 11077 (2769) 8636 (2877) 5969 (3037)120590 = 40 14619 (2648) 11394 (2756) 9002 (2859)

Image 5120590 = 10 5383 (3082) 1718 (3578) 1517 (3632)120590 = 20 10310 (2800) 6506 (3000) 4606 (3150)120590 = 30 15326 (2628) 11774 (2742) 8870 (2865)120590 = 40 20763 (2496) 16610 (2593) 14297 (2658)

Image 6120590 = 10 2623 (3394) 1102 (3771) 870 (3874)120590 = 20 6321 (3012) 4653 (3145) 2629 (3393)120590 = 30 9501 (2835) 8054 (2907) 5010 (3113)120590 = 40 12497 (2716) 11068 (2769) 7084 (2963)






120590 = 10 120590 = 20 120590 = 30 120590 = 40

0001002003004005006007008

(a)


120590 = 10 120590 = 20 120590 = 30 120590 = 40

0001002003004005006007008

(b)


(a) (b)

(c) (d)









(a)

(b)

(c)

(d)





Image level ofnoise


Image 1120590 = 40

1 308089 232442 1151715 2751743 859083 2879054 855702 2880765 855702 288076

Image 2120590 = 40

1 2988552 2337622 99408 2815663 638291 3008064 615572 302385 66874 298782

Image 3120590 = 40

1 3036185 2330752 97354 2824733 60672 3030094 587403 3044145 638291 300806

Image 4120590 = 40

1 2999368 2336052 1134212 2758393 844663 288644 900184 2858755 965508 282832

Image 5120590 = 40

1 2412989 2430532 1605966 2607343 1406729 2664874 1429727 2657835 1478107 264337

Image 6120590 = 40

1 2083282 2494332 1066155 2785263 752598 2936524 708417 2962795 720599 295539




(a)

(b)

(c)

(d)



De-noisingMethod

2DDWT-basedMethod

2D SWT-basedMethod



04837 13354 08138


(a)

(b)

(c)

(d)




(a) (b)

(c) (d)



(a) (b)

(c) (d)







(a) (b)

(c)


(a) (b)

(c)






02468

10121416182022242628303234

PSN

R va

lues





02468

10121416182022242628303234

PSN

R va

lues





02468

10121416182022242628303234

PSN

R va

lues





02468

10121416182022242628303234

PSN

R va

lues





02468

10121416182022242628303234

PSN

R va

lues





02468

10121416182022242628303234

PSN

R va

lues








Acknowledgment


References



















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











Camera sensor

Capturing image


Input image Y



Output image Z



(ℎ119909 + 119895119892119909) (ℎ119910 + 119895119892119910)

= (ℎ119909ℎ119910 + 119892119909119892119910) + 119895 (ℎ119909119892119910 + 119892119909ℎ119910)

(6)

3 Proposed Method


119884 = 119883 + 120590119873 (7)




Hard threshold

120596119894119895119885 =

120596119894119895119884 if 10038161003816100381610038161003816120596119894119895119884

10038161003816100381610038161003816gt 119879

0 if 10038161003816100381610038161003816120596119894119895119884

10038161003816100381610038161003816le 119879

(8)




MAD119895 =

median (10038161003816100381610038161003816120596119871minus1119895

10038161003816100381610038161003816)

06745 119895 = 0 1 2



4 Experiment






NAE =sum119872

119898=1sum119873

119899=1|119874 (119898 119899) minus 119863 (119898 119899)|

sum119872

119898=1sum119873

119899=1|119874 (119898 119899)|

(11)



PSNR = 10 log10

(Max2

MSE) (12)


MSE =1

119872119873 sum119872

119898=1sum119873

119899=1(119874 (119898 119899) minus 119863 (119898 119899))

2 (13)







2D DWT-basedMethod

2D SWT-basedMethod


MethodImage 1

120590 = 10 00329 00284 00236120590 = 20 00409 00353 00313120590 = 30 00464 00410 00364120590 = 40 00516 00473 00423

Image 2120590 = 10 00247 00220 00175120590 = 20 00329 00290 00256120590 = 30 00408 00363 00334120590 = 40 00479 00434 00405

Image 3120590 = 10 00236 00212 00152120590 = 20 00317 00307 00238120590 = 30 00376 00369 00313120590 = 40 00427 00423 00369

Image 4120590 = 10 00326 00274 00205120590 = 20 00471 00416 00339120590 = 30 00590 00516 00448120590 = 40 00701 00616 00573

Image 5120590 = 10 00308 00193 00190120590 = 20 00459 00365 00348120590 = 30 00588 00495 00480120590 = 40 00705 00605 00606

Image 6120590 = 10 00229 00181 00158120590 = 20 00336 00296 00254120590 = 30 00418 00378 00345120590 = 40 00496 00450 00437







2D DWT-basedMethod

2D SWT-basedMethod


MethodImage 1

120590 = 10 5553 (3069) 3664 (3249) 2392 (3434)120590 = 20 9406 (2840) 8002 (2910) 4642 (3146)120590 = 30 12702 (2709) 11061 (2770) 6409 (3006)120590 = 40 15600 (2620) 14688 (2646) 8557 (2881)

Image 2120590 = 10 2310 (3450) 1785 (3562) 1014 (3807)120590 = 20 4671 (3144) 3930 (3219) 2487 (3418)120590 = 30 7241 (2953) 5983 (3036) 4383 (3171)120590 = 40 9744 (2824) 8085 (2905) 6156 (3024)

Image 3120590 = 10 2866 (3356) 8939 (2861) 1025 (3805)120590 = 20 5339 (3086) 5085 (3107) 2632 (3393)120590 = 30 7459 (2940) 7031 (2966) 4401 (3170)120590 = 40 9482 (2836) 9025 (2858) 5874 (3044)

Image 4120590 = 10 3602 (3257) 2290 (3453) 1217 (3728)120590 = 20 7588 (2933) 6098 (3028) 3677 (3248)120590 = 30 11077 (2769) 8636 (2877) 5969 (3037)120590 = 40 14619 (2648) 11394 (2756) 9002 (2859)

Image 5120590 = 10 5383 (3082) 1718 (3578) 1517 (3632)120590 = 20 10310 (2800) 6506 (3000) 4606 (3150)120590 = 30 15326 (2628) 11774 (2742) 8870 (2865)120590 = 40 20763 (2496) 16610 (2593) 14297 (2658)

Image 6120590 = 10 2623 (3394) 1102 (3771) 870 (3874)120590 = 20 6321 (3012) 4653 (3145) 2629 (3393)120590 = 30 9501 (2835) 8054 (2907) 5010 (3113)120590 = 40 12497 (2716) 11068 (2769) 7084 (2963)






120590 = 10 120590 = 20 120590 = 30 120590 = 40

0001002003004005006007008

(a)


120590 = 10 120590 = 20 120590 = 30 120590 = 40

0001002003004005006007008

(b)


(a) (b)

(c) (d)









(a)

(b)

(c)

(d)





Image level ofnoise


Image 1120590 = 40

1 308089 232442 1151715 2751743 859083 2879054 855702 2880765 855702 288076

Image 2120590 = 40

1 2988552 2337622 99408 2815663 638291 3008064 615572 302385 66874 298782

Image 3120590 = 40

1 3036185 2330752 97354 2824733 60672 3030094 587403 3044145 638291 300806

Image 4120590 = 40

1 2999368 2336052 1134212 2758393 844663 288644 900184 2858755 965508 282832

Image 5120590 = 40

1 2412989 2430532 1605966 2607343 1406729 2664874 1429727 2657835 1478107 264337

Image 6120590 = 40

1 2083282 2494332 1066155 2785263 752598 2936524 708417 2962795 720599 295539




(a)

(b)

(c)

(d)



De-noisingMethod

2DDWT-basedMethod

2D SWT-basedMethod



04837 13354 08138


(a)

(b)

(c)

(d)




(a) (b)

(c) (d)



(a) (b)

(c) (d)







(a) (b)

(c)


(a) (b)

(c)






02468

10121416182022242628303234

PSN

R va

lues





02468

10121416182022242628303234

PSN

R va

lues





02468

10121416182022242628303234

PSN

R va

lues





02468

10121416182022242628303234

PSN

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10121416182022242628303234

PSN

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02468

10121416182022242628303234

PSN

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Acknowledgment


References



















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













NAE =sum119872

119898=1sum119873

119899=1|119874 (119898 119899) minus 119863 (119898 119899)|

sum119872

119898=1sum119873

119899=1|119874 (119898 119899)|

(11)



PSNR = 10 log10

(Max2

MSE) (12)


MSE =1

119872119873 sum119872

119898=1sum119873

119899=1(119874 (119898 119899) minus 119863 (119898 119899))

2 (13)







2D DWT-basedMethod

2D SWT-basedMethod


MethodImage 1

120590 = 10 00329 00284 00236120590 = 20 00409 00353 00313120590 = 30 00464 00410 00364120590 = 40 00516 00473 00423

Image 2120590 = 10 00247 00220 00175120590 = 20 00329 00290 00256120590 = 30 00408 00363 00334120590 = 40 00479 00434 00405

Image 3120590 = 10 00236 00212 00152120590 = 20 00317 00307 00238120590 = 30 00376 00369 00313120590 = 40 00427 00423 00369

Image 4120590 = 10 00326 00274 00205120590 = 20 00471 00416 00339120590 = 30 00590 00516 00448120590 = 40 00701 00616 00573

Image 5120590 = 10 00308 00193 00190120590 = 20 00459 00365 00348120590 = 30 00588 00495 00480120590 = 40 00705 00605 00606

Image 6120590 = 10 00229 00181 00158120590 = 20 00336 00296 00254120590 = 30 00418 00378 00345120590 = 40 00496 00450 00437







2D DWT-basedMethod

2D SWT-basedMethod


MethodImage 1

120590 = 10 5553 (3069) 3664 (3249) 2392 (3434)120590 = 20 9406 (2840) 8002 (2910) 4642 (3146)120590 = 30 12702 (2709) 11061 (2770) 6409 (3006)120590 = 40 15600 (2620) 14688 (2646) 8557 (2881)

Image 2120590 = 10 2310 (3450) 1785 (3562) 1014 (3807)120590 = 20 4671 (3144) 3930 (3219) 2487 (3418)120590 = 30 7241 (2953) 5983 (3036) 4383 (3171)120590 = 40 9744 (2824) 8085 (2905) 6156 (3024)

Image 3120590 = 10 2866 (3356) 8939 (2861) 1025 (3805)120590 = 20 5339 (3086) 5085 (3107) 2632 (3393)120590 = 30 7459 (2940) 7031 (2966) 4401 (3170)120590 = 40 9482 (2836) 9025 (2858) 5874 (3044)

Image 4120590 = 10 3602 (3257) 2290 (3453) 1217 (3728)120590 = 20 7588 (2933) 6098 (3028) 3677 (3248)120590 = 30 11077 (2769) 8636 (2877) 5969 (3037)120590 = 40 14619 (2648) 11394 (2756) 9002 (2859)

Image 5120590 = 10 5383 (3082) 1718 (3578) 1517 (3632)120590 = 20 10310 (2800) 6506 (3000) 4606 (3150)120590 = 30 15326 (2628) 11774 (2742) 8870 (2865)120590 = 40 20763 (2496) 16610 (2593) 14297 (2658)

Image 6120590 = 10 2623 (3394) 1102 (3771) 870 (3874)120590 = 20 6321 (3012) 4653 (3145) 2629 (3393)120590 = 30 9501 (2835) 8054 (2907) 5010 (3113)120590 = 40 12497 (2716) 11068 (2769) 7084 (2963)






120590 = 10 120590 = 20 120590 = 30 120590 = 40

0001002003004005006007008

(a)


120590 = 10 120590 = 20 120590 = 30 120590 = 40

0001002003004005006007008

(b)


(a) (b)

(c) (d)









(a)

(b)

(c)

(d)





Image level ofnoise


Image 1120590 = 40

1 308089 232442 1151715 2751743 859083 2879054 855702 2880765 855702 288076

Image 2120590 = 40

1 2988552 2337622 99408 2815663 638291 3008064 615572 302385 66874 298782

Image 3120590 = 40

1 3036185 2330752 97354 2824733 60672 3030094 587403 3044145 638291 300806

Image 4120590 = 40

1 2999368 2336052 1134212 2758393 844663 288644 900184 2858755 965508 282832

Image 5120590 = 40

1 2412989 2430532 1605966 2607343 1406729 2664874 1429727 2657835 1478107 264337

Image 6120590 = 40

1 2083282 2494332 1066155 2785263 752598 2936524 708417 2962795 720599 295539




(a)

(b)

(c)

(d)



De-noisingMethod

2DDWT-basedMethod

2D SWT-basedMethod



04837 13354 08138


(a)

(b)

(c)

(d)




(a) (b)

(c) (d)



(a) (b)

(c) (d)







(a) (b)

(c)


(a) (b)

(c)






02468

10121416182022242628303234

PSN

R va

lues





02468

10121416182022242628303234

PSN

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lues





02468

10121416182022242628303234

PSN

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lues





02468

10121416182022242628303234

PSN

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lues





02468

10121416182022242628303234

PSN

R va

lues





02468

10121416182022242628303234

PSN

R va

lues








Acknowledgment


References



















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













2D DWT-basedMethod

2D SWT-basedMethod


MethodImage 1

120590 = 10 00329 00284 00236120590 = 20 00409 00353 00313120590 = 30 00464 00410 00364120590 = 40 00516 00473 00423

Image 2120590 = 10 00247 00220 00175120590 = 20 00329 00290 00256120590 = 30 00408 00363 00334120590 = 40 00479 00434 00405

Image 3120590 = 10 00236 00212 00152120590 = 20 00317 00307 00238120590 = 30 00376 00369 00313120590 = 40 00427 00423 00369

Image 4120590 = 10 00326 00274 00205120590 = 20 00471 00416 00339120590 = 30 00590 00516 00448120590 = 40 00701 00616 00573

Image 5120590 = 10 00308 00193 00190120590 = 20 00459 00365 00348120590 = 30 00588 00495 00480120590 = 40 00705 00605 00606

Image 6120590 = 10 00229 00181 00158120590 = 20 00336 00296 00254120590 = 30 00418 00378 00345120590 = 40 00496 00450 00437







2D DWT-basedMethod

2D SWT-basedMethod


MethodImage 1

120590 = 10 5553 (3069) 3664 (3249) 2392 (3434)120590 = 20 9406 (2840) 8002 (2910) 4642 (3146)120590 = 30 12702 (2709) 11061 (2770) 6409 (3006)120590 = 40 15600 (2620) 14688 (2646) 8557 (2881)

Image 2120590 = 10 2310 (3450) 1785 (3562) 1014 (3807)120590 = 20 4671 (3144) 3930 (3219) 2487 (3418)120590 = 30 7241 (2953) 5983 (3036) 4383 (3171)120590 = 40 9744 (2824) 8085 (2905) 6156 (3024)

Image 3120590 = 10 2866 (3356) 8939 (2861) 1025 (3805)120590 = 20 5339 (3086) 5085 (3107) 2632 (3393)120590 = 30 7459 (2940) 7031 (2966) 4401 (3170)120590 = 40 9482 (2836) 9025 (2858) 5874 (3044)

Image 4120590 = 10 3602 (3257) 2290 (3453) 1217 (3728)120590 = 20 7588 (2933) 6098 (3028) 3677 (3248)120590 = 30 11077 (2769) 8636 (2877) 5969 (3037)120590 = 40 14619 (2648) 11394 (2756) 9002 (2859)

Image 5120590 = 10 5383 (3082) 1718 (3578) 1517 (3632)120590 = 20 10310 (2800) 6506 (3000) 4606 (3150)120590 = 30 15326 (2628) 11774 (2742) 8870 (2865)120590 = 40 20763 (2496) 16610 (2593) 14297 (2658)

Image 6120590 = 10 2623 (3394) 1102 (3771) 870 (3874)120590 = 20 6321 (3012) 4653 (3145) 2629 (3393)120590 = 30 9501 (2835) 8054 (2907) 5010 (3113)120590 = 40 12497 (2716) 11068 (2769) 7084 (2963)






120590 = 10 120590 = 20 120590 = 30 120590 = 40

0001002003004005006007008

(a)


120590 = 10 120590 = 20 120590 = 30 120590 = 40

0001002003004005006007008

(b)


(a) (b)

(c) (d)









(a)

(b)

(c)

(d)





Image level ofnoise


Image 1120590 = 40

1 308089 232442 1151715 2751743 859083 2879054 855702 2880765 855702 288076

Image 2120590 = 40

1 2988552 2337622 99408 2815663 638291 3008064 615572 302385 66874 298782

Image 3120590 = 40

1 3036185 2330752 97354 2824733 60672 3030094 587403 3044145 638291 300806

Image 4120590 = 40

1 2999368 2336052 1134212 2758393 844663 288644 900184 2858755 965508 282832

Image 5120590 = 40

1 2412989 2430532 1605966 2607343 1406729 2664874 1429727 2657835 1478107 264337

Image 6120590 = 40

1 2083282 2494332 1066155 2785263 752598 2936524 708417 2962795 720599 295539




(a)

(b)

(c)

(d)



De-noisingMethod

2DDWT-basedMethod

2D SWT-basedMethod



04837 13354 08138


(a)

(b)

(c)

(d)




(a) (b)

(c) (d)



(a) (b)

(c) (d)







(a) (b)

(c)


(a) (b)

(c)






02468

10121416182022242628303234

PSN

R va

lues





02468

10121416182022242628303234

PSN

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02468

10121416182022242628303234

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02468

10121416182022242628303234

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02468

10121416182022242628303234

PSN

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02468

10121416182022242628303234

PSN

R va

lues








Acknowledgment


References



















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











120590 = 10 120590 = 20 120590 = 30 120590 = 40

0001002003004005006007008

(a)


120590 = 10 120590 = 20 120590 = 30 120590 = 40

0001002003004005006007008

(b)


(a) (b)

(c) (d)









(a)

(b)

(c)

(d)





Image level ofnoise


Image 1120590 = 40

1 308089 232442 1151715 2751743 859083 2879054 855702 2880765 855702 288076

Image 2120590 = 40

1 2988552 2337622 99408 2815663 638291 3008064 615572 302385 66874 298782

Image 3120590 = 40

1 3036185 2330752 97354 2824733 60672 3030094 587403 3044145 638291 300806

Image 4120590 = 40

1 2999368 2336052 1134212 2758393 844663 288644 900184 2858755 965508 282832

Image 5120590 = 40

1 2412989 2430532 1605966 2607343 1406729 2664874 1429727 2657835 1478107 264337

Image 6120590 = 40

1 2083282 2494332 1066155 2785263 752598 2936524 708417 2962795 720599 295539




(a)

(b)

(c)

(d)



De-noisingMethod

2DDWT-basedMethod

2D SWT-basedMethod



04837 13354 08138


(a)

(b)

(c)

(d)




(a) (b)

(c) (d)



(a) (b)

(c) (d)







(a) (b)

(c)


(a) (b)

(c)






02468

10121416182022242628303234

PSN

R va

lues





02468

10121416182022242628303234

PSN

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lues





02468

10121416182022242628303234

PSN

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02468

10121416182022242628303234

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02468

10121416182022242628303234

PSN

R va

lues





02468

10121416182022242628303234

PSN

R va

lues








Acknowledgment


References



















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(a)

(b)

(c)

(d)





Image level ofnoise


Image 1120590 = 40

1 308089 232442 1151715 2751743 859083 2879054 855702 2880765 855702 288076

Image 2120590 = 40

1 2988552 2337622 99408 2815663 638291 3008064 615572 302385 66874 298782

Image 3120590 = 40

1 3036185 2330752 97354 2824733 60672 3030094 587403 3044145 638291 300806

Image 4120590 = 40

1 2999368 2336052 1134212 2758393 844663 288644 900184 2858755 965508 282832

Image 5120590 = 40

1 2412989 2430532 1605966 2607343 1406729 2664874 1429727 2657835 1478107 264337

Image 6120590 = 40

1 2083282 2494332 1066155 2785263 752598 2936524 708417 2962795 720599 295539




(a)

(b)

(c)

(d)



De-noisingMethod

2DDWT-basedMethod

2D SWT-basedMethod



04837 13354 08138


(a)

(b)

(c)

(d)




(a) (b)

(c) (d)



(a) (b)

(c) (d)







(a) (b)

(c)


(a) (b)

(c)






02468

10121416182022242628303234

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lues





02468

10121416182022242628303234

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02468

10121416182022242628303234

PSN

R va

lues








Acknowledgment


References



















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(a)

(b)

(c)

(d)



De-noisingMethod

2DDWT-basedMethod

2D SWT-basedMethod



04837 13354 08138


(a)

(b)

(c)

(d)




(a) (b)

(c) (d)



(a) (b)

(c) (d)







(a) (b)

(c)


(a) (b)

(c)






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10121416182022242628303234

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02468

10121416182022242628303234

PSN

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02468

10121416182022242628303234

PSN

R va

lues








Acknowledgment


References



















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(a) (b)

(c) (d)



(a) (b)

(c) (d)







(a) (b)

(c)


(a) (b)

(c)






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02468

10121416182022242628303234

PSN

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Acknowledgment


References



















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(a) (b)

(c)


(a) (b)

(c)






02468

10121416182022242628303234

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02468

10121416182022242628303234

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10121416182022242628303234

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02468

10121416182022242628303234

PSN

R va

lues








Acknowledgment


References



















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











02468

10121416182022242628303234

PSN

R va

lues





02468

10121416182022242628303234

PSN

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lues





02468

10121416182022242628303234

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02468

10121416182022242628303234

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02468

10121416182022242628303234

PSN

R va

lues





02468

10121416182022242628303234

PSN

R va

lues








Acknowledgment


References



















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













Acknowledgment


References



















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









research article an efficient image denoising method for...

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