[ieee 2013 8th international symposium on image and signal processing and analysis (ispa) - trieste,...

Image Deblocking by Transcoding DCT Blocks toWavelet Subbands

Viswanath KapinaiahDept. of Telecommunication Engg.

SIT-Tumkur, INDIAEmail: [email protected]

Jayanta MukhopadhyayDept. of CS&E

IIT-Kharagpur, INDIAEmail: [email protected]

Prabir Kumar BiswasDept. of E&ECE

IIT-Kharagpur, INDIAEmail: [email protected]

Abstract—In this paper, we show how the DCT blocks canbe transcoded to wavelet subbands for image deblocking inthe wavelet domain. The approach is based on the transcod-ing of DCT blocks to wavelet coefficient subbands directly inthe transform domain. The transcoding uses filtering (waveletanalysis) along with re-sampling (down) operation in the blockDCT space. To perform transcoding, linear filtering is used inthe block DCT domain. In this technique, filtering is performedon the three adjacent blocks. The complexity is reduced byperforming sampling rate change and filtering operations ina single combined step. The proposed approach achieves thequality as same as the spatial domain technique at a reducedcomputational cost.

Index Terms—Transform Domain Processing, Deblocking,Transcoding, Block DCT, DWT, Post-processing.

I. INTRODUCTION

Enormous amount of information has to be stored, processedand transmitted everyday. Compressing the data prior to stor-age and/or transmission is of significant practical and commer-cial interest. Compression addresses the problem of reducingthe amount of data required to represent the digital images.This is achieved by alternate coefficient representation ofimages in a different domain. The Discrete Cosine Transform(DCT) [1] and the Discrete Wavelet Transform (DWT) [2]are the two important transforms used in image and videoprocessing applications. The DWT has been adopted by theimage compression standard JPEG2000 [3]. It is observed [4]that the wavelet based image encoding outperforms other typeof coders in terms of reconstruction quality as well as codingefficiency. On the other hand, the DCT is used in the JPEG [5],MPEG-2 and H.263 standards because of its de-correlationand energy compaction properties [6]. The DCT based codersare still widely used and are shared by a wide range ofreceivers accommodating heterogeneous services together. Thepopularity of DCT is also due to the implementation of theDCT hardware (or software) is less expensive than that of theDWT [4]. Also, efficient algorithms in the DCT domain makedata processing advantageous for several imaging applications.

However, the block based coding schemes produce discon-tinuities across block boundaries. These discontinuities arereferred to as blocking artifacts, which seriously deteriorateimage quality at lower bit rates. This degradation is highlyobjectionable and affect the judgement of final observers. Themost popular strategy for alleviating blocking artifacts is to use

post-processing techniques at the decoder end. This strategy isof practical interest since it only requires the decoded image,and hence it is fully compatible with the imaging standards.

An ideal deblocking technique should remove visible block-ing artifacts while maintaining original image content as muchas possible. Recently, wavelet based deblocking algorithms [7],[8], [9], [10] have gained more attention. This is due tothe ability of wavelet based algorithms to suppress blockingartifacts while preserving true edges and textural information.

Elimination of blocking artifacts (deblocking) in the waveletdomain requires decoded image in the spatial domain. Also,to achieve efficient bandwidth as well as buffer utilization bywavelet coding and adding flexibility to the DCT based ser-vices, there is a requirement of intermediate transcoder [11],[12]. Transcoding directly in the transform domain savescomputation by avoiding inverse/re-transform operations. Thebasic principle of transform domain processing is to con-vert the spatial domain operations to their equivalent in thetransform domain. Transcoding of DCT to wavelet subbandsand vice versa, find various applications in handling imagesand videos [13], [14], [15], [16]. Interestingly, transcodingof DCT blocks into wavelet coefficients subbands (and alsoreverse operation) provides a framework for developing post-processing algorithms in the wavelet domain, which eliminatethe blocking artifacts in the decoded images. In this paper,reduction of blocking artifacts in the DCT encoded imagesis described using the transcoding DCT blocks to waveletcoefficients [16]. Here equivalent computation of waveletanalysis is performed in the block DCT space.

II. WAVELET TRANSFORMS WITH FILTER BANKS

In this section, we introduce the DWT and their imple-mentations using filter banks. Wavelet transforms are com-puted using two-channel analysis and synthesis filter banks. Asimple one-stage implementation of the DWT is illustrated inFigure 1(a). A one-stage wavelet transform uses two analysisfilters, h(n) and g(n) followed by subsampling. Here, adiscrete signal x0(n) is passed through lowpass and highpassfilters (Decomposition/Analysis filters) with impulse responsesh(n) and g(n) respectively. The filtered signals are downsam-pled by a factor of 2, to provide approximation and detailcoefficients respectively. The approximation coefficients aregiven by a1(n) = [x0(n) ∗ h(n)] ↓ 2. The detail coefficients

8th International Symposium on Image and Signal Processing and Analysis (ISPA 2013) September 4-6, 2013, Trieste, Italy

Image ProcessingImage and Video Coding Techniques 251

are given by d1(n) = [x0(n) ∗ g(n)] ↓ 2, where, the operator‘*’ denotes convolution. In this work, convolution is performeddirectly in the block DCT domain.

On the other hand, the inverse transform first performs anupsampling step and then uses two synthesis filters h′(n) andg′(n). Here, each pair of filters correspond to a lowpass and ahighpass filters respectively. If the combination of these fourfilters satisfies certain properties, the original signal can bereconstructed without any loss of information. For detaileddiscussion on the properties of such filters and implemen-tation of the DWT and inverse DWT (IDWT) with perfectreconstruction, one may refer to [17].

A 1-D DWT can be easily extended to a 2-D DWT usingtwo 1-D wavelet filters, by their successive application toall rows of the image and then to the resulting columns (orvice versa). When a single level 2-D DWT is applied to animage, as depicted in Figure 1(b), it results in four sets ofwavelet transform coefficients. The four sets are referred toas approximation (LL), horizontal (HL), vertical (LH) anddiagonal (HH) coefficient subbands. Here the first letter L or Hcorresponds to the application of a lowpass (L) or highpass (H)filter to the rows, and the second letter refers to as the sameapplication to the columns. After the filtering, half the samplesare eliminated (downsampled by a factor of 2), simply bydiscarding every other sample. This constitutes one level ofdecomposition. A single filter bank can be iterated (by iteratingthe LL subband as the input for the next stage) to produce amultilevel DWT of the image. In this work, wavelet coefficientsubbands are computed directly from the DCT blocks in theblock space.

A. Deblocking in the Wavelet Domain

Blocking artifacts are clearly visible in the high frequencysubbands (LH, HL, HH) and these artifacts can be easilysuppressed in the wavelet domain. In such a scenario, thetranscoding technique as developed in the work [16] com-putes the wavelet subbands directly from the DCT blocks fordeblocking. We compute four wavelet subbands using thistranscoder, then used wavelet domain deblocking algorithmproposed by Min Shi [8] to demonstrate the results.

B. Suppressing Blocking artifacts in the wavelet domain

A brief overview of the technique as proposed by MinShi [8] for suppressing the blocking artifacts in the waveletdomain is presented in this section. After wavelet decomposi-tion, the blocking artifacts appear as the discontinuity at blockboundaries. The wavelet transformed image concentrates theenergy on the boundaries. In the first level subbands (LL, LH,HL and HH), the 8 × 8 blocking artifacts are visible as 4 × 4ones. The blocking artifacts appear as horizontal line-shapeeffect on the block boundary at the ith row such that mod(i,4) = 0, in HL subband. Similarly, the blocking artifactsappear as vertical line-shape effect on the block boundary onthe jth column such that mod (j,4) = 0, in LH subband.Also, the blocking artifacts appears as 4 grid-shape effectin HH subband. The same principle applies to higher level

decompositions with the reduction of block sizes. But as theblock sizes reduces, these artifacts have little effect on thevisual quality and can be ignored. In this work, the blockingartifacts in HL2, LH2 and HH2 and higher level subbandsare neglected.

Based on the feature analysis, Min Shi [8] algorithmwherein the deblocking operators for each subband are de-fined separately. These operators are used for modifying thesubband coefficients which intern reduce blocking artifacts.For deblocking HL subband, the measures cHL, cHL and thethreshold θHL are obtained as follows:

cHL =1

NHL

∑

i

∑

j

|cHL(i, j)| (1)

cHL =1

NHL

∑

mod(i,4)=0

∑

j

|cHL(i, j)| (2)

θHL =cHL

cHL(3)

where NHL is the number of transform coefficients and NHL

is the number of coefficients with mod (i,4) = 0 in the HLsubband. To suppress the horizontal line-shaped effects in theHL subband, the following operation is used:

cHL(i, j) =

{cHL(i, j) if mod(i, 4) = 0cHL(i,j)

θHLif mod(i, 4) = 0.

(4)

The energy of horizontal line is suppressed and the effect isweakened by using Eq. (4).

For deblocking LH subband, the measures cLH , cLH andthe threshold θLH are obtained as follows:

cLH =1

NLH

∑

i

∑

j

|cLH(i, j)| (5)

cLH =1

NLH

∑

mod(i,4)=0

∑

j

|cLH(i, j)| (6)

θLH =cLH

cLH(7)

where NLH is the number of transform coefficients and NLH

is the number of coefficients with mod (j,4) = 0 in the LHsubband. To suppress the vertical line-shaped effects in the LHsubband, the following operation is used:

cLH(i, j) =

{cLH(i, j) if mod(j, 4) = 0cLH(i,j)

θLHif mod(j, 4) = 0.

(8)

The energy of vertical line is suppressed and the effect isweakened by using Eq. (8).

Similarly for deblocking HH subband, the threshold θHH

is computed by θHH = (θHL+θLH)2 and the cHH , cHH are

obtained as:

cHH(i, j) =

{cHH(i, j) if mod(i, 4) = 0 and mod(j, 4) = 0cLH(i,j)

θHHif mod(i, 4) = 0 or mod(j, 4) = 0.

(9)The energy of grid shape is suppressed and the effect is



2

2

2

2

) ( 0 n x ) ( ~ 0 n x

) ( 1 n d

) ( 1 n a ) ( ' n h

) ( ' n g ) ( n g

) ( n h

(a) 1-D DWT

(b) 2-D DWT on Image

Fig. 1. Forward and Inverse DWT

weakened by using Eq. (9).From the above description, the wavelet domain algorithm

for removing blocking artifacts adopted in this work is sum-marized as follows:

1) Compute single level of wavelet transform using the 5/3bi-orthogonal filter for an image with blocking artifacts,and obtain the LL, HL, LH, and HH subbands.

2) Use the deblocking Eqs. (4-9) to remove the effect ofparallel or grid lines for above subbands except LL.

3) Apply the corresponding reversible wavelet transformfor the processed subbands, and obtain the reconstructedimage with reduced blocking artifacts.

III. FILTERING IN THE BLOCK DCT DOMAIN

In [18], author showed how Linear Separable Filtering canbe performed efficiently with symmetric filters in the blockDCT domain. Following the same notations, the 2-D linearfiltering is expressed in the block DCT domain as:

Yij =1∑

m=−1

1∑

n=−1

VmXi+m,j+nHtn. (10)

where Yij are the filtered DCT blocks for the input DCT blocksXi+m,j+n. The matrices, Vm’s and Hn’s are the vertical andhorizontal filtering matrices in the DCT domain. Note that thefiltering matrices, Vm’s and Hn’s can be pre-computed for agiven filter vertical and horizontal components v(k) and h(l).The 2-D linear filtering in the DCT domain (Eq. 10) can beperformed separately in the vertical and horizontal directionsas follows:

Zij = V−1Xi−1,j + V0Xi,j + V1Xi+1,j (11)

Yij = Zi−1,jHt−1 + Zi,jH

t0 + Zi+1,jH

t1 (12)

where Zij represents the 1-D linear filtered output matrix forthe DCT input matrix Xi,j in the vertical direction.

A. Downsampling in the DCT Domain

The downsampled signal x(m), m = 0, 1, . . . , N/2 − 1,as obtained through even indexed samples ofx(n), n = 0, 1, 2, . . . , N − 1 using IDCT ofX(N)(k), k = 0, 1, 2, . . . , N − 1 is given by:

x(m) =

√2

Nα(k)

N−1∑

k=0

X(N)(k) cos

((m + 1

4 )πk

N/2

),

0 ≤ m ≤ N/2 − 1 (13)

where α(k) in Eq.(13), is√

12 for k = 0, otherwise its value

is 1. For the proof of Eq.(13), one may refer to the work [16].In this work, we use a composite operation of filtering

and down sampling operations (Eqs. (10-13)). This reducesthe computational requirement of transcoding in the transformdomain.

B. Transcoding by Filtering and Downsampling

This section, we explain how to use the block based DCTdomain filtering (Eq. 10) for transcoding the DCT blocks towavelet coefficients. Here the transcoding matrices are com-puted by the composite operations of filtering (Eqs. (11-12))and downsampling (Eq. 13). The filtering matrices H

(N,N)n s

and V (N, N)ns are computed using analysis filters h(n) andg(n) respectively. With the input DCT blocks X

(N)i s and the

DCT matrices of analysis lowpass filter H(N,N)m s, the Eq. (11)

for approximation subband transcoding is expressed as:

a(N/2)i =

1∑

m=−1

B(N/2,N)d H(N,N)

m X(N)i+m (14)



where X(N)i+ms are the input DCT blocks and a

(N/2)i s are

the transcoded ’L’ subband blocks. Note here that the ap-proximation subband is in the (N/2) block space, which isthe requirement for deblocking in the wavelet domain. Bydenotin the combined product matrices B

(N/2,N)d H

(N,N)m as

transcoding matrices Pm, the Eq. (14) can be re-written as:

a(N/2)i =

1∑

m=−1

P (N/2,N)m X

(N)i+m. (15)

Typical matrix P(4,8)−1 computed with N=8 (for JPEG based

encoding) using a 5-tap analysis lowpass filter h(n) is asfollows:

P(4,8)t

−1 =

0.0090 0 0 0−0.0144 0 0 0

0.0187 0 0 0−0.0237 0 0 0

0.0271 0 0 0−0.0267 0 0 0

0.0216 0 0 0−0.0121 0 0 0

(16)

Note here that the matrices P(4,8)m are of size 4×8 and require

less number of computations for multiplication with the inputDCT blocks of size 8 × 8. The complexity further reduces inthe case of sparse DCT blocks. Other matrices are not shownhere due to the constraint of space.

Similarly, for the matrices of analysis highpass filter, Qnsand the input DCT blocks, the transcoded detail coefficientsubband blocks, d

(N/2)i s can be computed using Eq. (14) as

follows:

d(N/2)i =

1∑

n=−1

Q(N/2,N)n X

(N)i+m (17)

Note that the matrices P(N/2,N)m s and Q

(N/2,N)n as in the

Eqs. (15 and (17) are computed with 5/3 analysis lowpassand Highpass filters. Similar concepts can be extended to 2-Dby simply applying 1-D transcoding to columns of the inputblocks and then to rows of the resulting blocks.

C. Transcoding for Wavelet Domain Deblocking (TWD)

For deblocking through transcoding, the wavelet subbandsare computed by the block DCT to wavelet transcodingtechnique. The wavelet coefficient subbands are computed bythe proposed transcoder using the quantized DCT blocks byextending the Eqs. (15 and (17). For approximation coeffi-cients, P

(N/2,N)m s are considered for both directions to ob-

tain transcoded subband (LL). Similarly other subbands (HL,LH, and HH) are obtained with the corresponding matrices,P

(N/2,N)m s and Q

(N/2,N)n computed using analysis lowpass and

highpass filters. Here the matrices the matrices Pm and Qn

are computed using 5/3 filters (same filters are used by theauthor [8]). Figure 2 illustrates the deblocking process withtranscoding. Note that the transcoding technique operates onthe DCT blocks and computes the downsampled coefficientsin the spatial domain (wavelet subbands). This is an essentialrequirement of the DCT to wavelet heterogenous transcoding.The coefficients are already available in the wavelet domainfor further processing.

IV. COMPUTATIONAL COMPLEXITY

In this section, we discuss the computation costs associatedwith the spatial domain and transform domain approaches.Let the cost of a single multiplication and a single additionbe denoted as M and A respectively. The total cost for anoperation requiring a number of multiplications and b numberof additions is denoted as aM + bA. Combined cost (CC)measure is obtained by considering the cost of a multiplicationoperation three times of the cost of addition [19]. Since thetranscoding matrices are pre-computed, their cost is excludedfrom the complexity.

A. Spatial Domain Transcoding (SWD)

Here, transcoding is performed using wavelet transformsafter obtaining the image in spatial domain by performing theIDCT on each block. The cost associated with the transcodingis due to the computations: (i) IDCT and (ii) Wavelet subbandcomputation. (iii) Block DCT on the post processed image. Inthis work, cost of an 8 × 8 block DCT/IDCT computation isbased on the results reported by Wu and Man in [20].

In computing DWT, the lengths of analysis lowpass andhighpass filters (h and g) are considered for computing cost.For simplicity in computational analysis, the spatial domain(i.e. IDCT-DWT approach) is referred to as spatial domainwavelet deblocking (SWD). Also, for filter bank and liftingscheme implementation are referred to as SWD-FB and SWD-LS respectively while computing the wavelet transform in theproposed technique. Here we present the costs with highestlength of the filter, that is for 5/3 filters, length is equal to 5.For computational costs for transcoding with different lengthsof filter, one can refer [16].

B. Proposed TWD

Cost associated with the TWD is due to computationsinvolved in: multiplication of the downsampling matrices(refer Eq. (15)), to obtain the transcoding subbands. We followsimilar approach as discussed in [21] for obtaining the costof matrix multiplication. In computing the cost, we haveconsidered that an element x in the matrix is a zero elementif |x| < Threshold and two elements x and y become non-distinct if ||x| − |y|| < Threshold. For computing the costwith the proposed technique, a Threshold value of 10−4 isused.

Table I shows the per pixel cost comparison of the spatialdomain transcoding technique (i.e. SWD-FB and SWD-LS).From Table I, it is evident that the proposed transform domainapproach is computationally efficient than spatial domainapproach using the 5/3 wavelet (analysis) filters. In case ofnon-sparse input data, 24.09% and 21.74% computation savingis achieved compared to the spatial domain SWD-FB andSWD-LS techniques. Similarly for sparse input, 62.04% and60.87% computation saving is achieved compared to the SWD-FB and SWD-LS techniques. It may be noted that the proposedtechnique achieves the same quality of reconstruction as thatof spatial domain approach. Also, the spatial domain techniquedoes not benefit from the sparseness of the DCT blocks.



LL HL

LH HH

DCT Blocks

Wavelet Subbands

Transcoding

LL HL

LH HH

Processed Image

Processed Subbands

IDWT Deblocking

Fig. 2. Wavelet domain deblocking with transcoding.

TABLE ICOMPARISON OF COMPUTATIONAL COSTS (PER PIXEL) FOR THE SPATIAL/TRANSFORM DOMAIN APPROACHES.

Deblocking Sparse DCT Blocks Non-sparse DCT BlocksApproach M A CC M A CC

TWD 6.0 5 23 3 2.5 11.5SWD-FB 6.37 11.28 30.30 6.37 11.28 30.30SWD-LS 4.87 10.78 29.39 4.87 10.78 29.39

Whereas the proposed approach can exploit the sparseness ofinput DCT blocks.

V. RESULTS

The symmetric ‘5/3’ wavelet filters (same filters are used byMin Shi [8]) are considered for evaluating the performance ofthe technique. Gray scale images such as ‘Lena,’ ‘Baboon,’‘Peppers’ and ‘Girl’ are used for demonstrating the results.The spatial domain images are obtained by performing theIDCT on the DCT blocks. The images with blocking artifacts(with different bit rates of JPEG) are obtained using twoquantization tables Q1 and Q2. For spatial domain deblocking,SWD these images are first decomposed by the wavelettransform by using analysis filters. The first level LH, HL, andHH subbands are considered for wavelet domain deblocking.For deblocking with transcoding, the subbands with first leveldecomposition computed through the proposed technique areused by the algorithm [8]. After deblocking in the waveletdomain (refer Eqs. (4-9), the IDWT of the processed sub-bands produces the deblocked image. The PSNR values arecomputed using this blocking artifact reduced images andoriginal image as reference. The PSNR performances for threequantization tables used in the JPEG compression standardare provided in Table II. One such quantization table (Q1) isprovided in the Eq. (18) from the reference [9].

Q1 =

50 60 70 70 90 120 255 25560 60 70 96 130 255 255 25570 70 80 120 200 255 255 25570 96 120 145 255 255 255 25590 130 200 255 255 255 255 255

120 255 255 255 255 255 255 255255 255 255 255 255 255 255 255255 255 255 255 255 255 255 255

(18)

In this work, quality of an image (decoded) in termsof the visibility of blocking artifacts is expressed by ametric proposed in [22]. This measure is relevant for im-ages decoded from block DCT representations and is ano-reference measure referred to as JPEG Quality-Metric

(JPQM) in this work. The computation of this metric isdescribed in [22] and the MATLAB code is obtained from theweb-site http://anchovy.ece.utexas.edu/ z˜wang/ research/ nrjpeg quality/ ndex.html. For an image of good visual quality,the JPQM value should be close to 10 or above. With JPQMmeasure, one may judge the quality of image reconstructedfrom the block DCT space to take into account of visibleblocking and blurring artifacts. For measuring the similaritybetween two images (TWD-SWD), the Structural SIMilarity(SSIM) index [23] been provided in the table II. Here SSIMvalues are computed with images obtained using the transformdomain and spatial domain. One can observe that the imagesobtained both the techniques are almost same(close to 1).

The deblocking results obtained for Lena image are shownin Figure 3 for the quantization table Q1. Table II alsoprovides the JPQM values for reconstructed images fromtheir compressed counterparts using two quantization tables.From the results it is evident that deblocking significantlyimproves the quality of the processed images. Interestingly,the JPQM values obtained by the transcoding technique atvarious compression level are quite close to those obtainedfrom the spatial domain technique (IDCT-DWT-Deblocking).As the proposed technique operates in the block DCT space,presence of blocking artifacts are natural in these images.The deblocking algorithm using the transcoder is capable ofreducing this gap to a great extent.

VI. CONCLUSION

In this work, the post-processing of DCT coded images hasbeen demonstrated with transcoding. We have shown how touse the transcoding in the block DCT space to obtain thewavelet subbands for deblocking. The transcoding approachis based on sub-sampling and filtering operations in the DCTdomain. The proposed technique is in the block DCT spaceso that the JPEG based tools can operate directly in the com-pressed domain. The simulation results show that the proposedmethod achieves same PSNR compared to the spatial domain



TABLE IIIMAGE DEBLOCKING: PERFORMANCE COMPARISON FOR THE SPATIAL/TRANSFORM DOMAIN APPROACHES.

Test image values Proposed TWD SWD SSIM [23]Test Image (JPQM) Quantization (bpp) PSNR(dB) JPQM PSNR(dB) JPQM PSNR(dB) JPQM TWD-SWD

Q1 (0.24bpp) 30.70 3.01 31.210 7.16 31.206 8.19 0.9932Lena (10.88) Q2 (0.15bpp) 27.38 -1.12 27.940 5.35 27.936 6.80 0.9928

Q1 (0.24bpp) 23.39 4.50 23.602 6.87 23.602 6.82 0.9952Baboon (9.06) Q2 (0.15bpp) 21.17 0.79 21.416 5.32 21.415 5.76 0.9950

Q1 (0.24bpp) 30.42 3.37 30.812 7.36 30.811 8.21 0.9966Peppers (11.35) Q2 (0.15bpp) 27.22 -0.39 27.726 5.65 27.724 6.99 0.9961

Q1 (0.24bpp) 30.43 2.94 30.837 6.84 30.832 7.74 0.9934Girl (10.83) Q2 (0.15bpp) 27.29 -1.66 27.761 5.80 27.752 6.33 0.9933

(a)

(b) (c)

Fig. 3. Reduction of blocking artifacts with Q1 (0.24 bpp): (a) Test imagePSNR= 30.70dB, JPQM= 3.01 (b) Processed image in the spatial domain(using [8]) PSNR=31.206dB , JPQM=8.19 (c) Processed image in throughtranscoding (proposed) PSNR= 31.21dB, JPQM= 7.16.

approach with reduced complexity. Considering the sparsenessof the DCT blocks, the proposed technique further reduces costof transcoding. The JPQM values for the processed images inthe transform domain technique are quite close to the spatialdomain technique.

REFERENCES

[1] N. Ahmed, N. Natarajan, and K. R. Rao, “Discrete Cosine Transform,”IEEE Transactions on Computers, pp. 90–92, January 1974.

[2] S. Mallat, “A theory for Multiresultion signal decomposition: the waveletrepresentation,” IEEE Trans on Pattern Analysis and Machine Intelli-gence, vol. 11, no. 7, pp. 674–693, 1989.

[3] M. Rabbani and R. Joshi, “An overview of the JPEG 2000 still im-age compression standard,” Signal Processing: Image Communication,vol. 17, pp. 3–48, January 2002.

[4] Z. Xiong, K. Ramchandran, M. T. Orchard, and Y.-Q. Zhang, “AComparative Study of DCT and Wavelet based Image coding,” IEEETransactions on Circuits and Systems for Video Technology, vol. 9,pp. 692–695, August 1999.

[5] G. K. Wallace, “The JPEG still picture compression standard,” Commu-nications of the ACM, vol. 34, no. 4, pp. 30–44, 1991.

[6] K. R. Rao and P. Yip, eds., The Transform and Data CompressionHandbook. Boca Raton, FL, USA: CRC Press, Inc., 2000.

[7] T.-C. Hsung, D. Pak-Kong Lun, and W.-C. Siu, “A deblocking techniquefor block-transform compressed image using wavelet transform modulusmaximal,” IEEE Transactions on Image Processing, vol. 7, pp. 1488–1496, October 1998.

[8] M. Shi, “A new deblocking algorithm based on feature analysis inwavelet domain,” in Proceedings of the Fourth International Conferenceon Machine Learning and Cybernetics, vol. 9, (Guangzhou), pp. 5210–5215, 18-21 August 2005.

[9] S. Wu, H. Yan, and Z. Tan, “An efficient wavelet-based deblockingalgorithm for highly compressed images,” IEEE Transactions on Circuitsand Systems for Video Technology, vol. 11, pp. 1193–1198, November2001.

[10] Z. Xiong, M. Orchard, and Y.-Q. Zhang, “A deblocking algorithm forjpeg compressed image using over complete wavelet representation,”IEEE Transactions on Circuits and Systems for Video Technology, vol. 7,pp. 433–437, April 1997.

[11] P. Hu, M. Kavesh, and Z. Zhang, “A wavelet to DCT progressive imagetranscoder,” in Proceedings of the IEEE International Conference onImage Processing, vol. 1, pp. 968–971, 10–13 September 2000.

[12] A. Navarro and V. Silva, “Fast Conversion between DCT andWavelet Transform Coefficients,” in 3rd International Workshopon Mathematical Techniques and Problems in Telecommunications(http://www.mtpt.it.pt/papers/13.pdf), September 2006.

[13] K. Viswanath, J. Mukherjee, P. K. Biswas, and R. N. Pal, “Wavelet toDCT transcoding in transform domain,” Journal on Signal, Image andVideo Processing (SIVP), vol. 4, no. 2, pp. 129–144, 2010.

[14] K. Viswanath, J. Mukherjee, and P. K. Biswas, “Transcoding in theBlock DCT Space,” in IEEE International Conference on Image Pro-cessing, (Cairo, Egypt), 7-11 November 2009.

[15] K. Viswanath, J. Mukherjee, and P. K. Biswas, “Wavelet transcodingin the block DCT space,” Image Processing, IET, vol. 4, pp. 143–157,June 2010.

[16] K. Viswanath, J. Mukherjee, and P. K. Biswas, “Block DCT to WaveletTranscoding In the Transform Domain,” Signal, Image and VideoProcessing, vol. 6, no. 2, pp. 179–195, 2012.

[17] G. Strang and T. Nguyen, Wavelets and Filter Banks. Wellesly-Cambridge Press, 1996.

[18] C. Yim, “An Efficient Method for DCT-Domain Separable Symmetric2-D Linear Filtering,” IEEE Transactions on Circuits and Systems forVideo Technology, vol. 14, pp. 517–521, April 2004.

[19] J. Mukherjee and S. K. Mitra, “Image Filtering in the CompressedDomain,” in Fifth Indian Conference on Computer Vision, Graphics &Image Processing, (Madurai, India), pp. 194–205, LNCS-4338, 13-16December 2006.

[20] H. R. Wu and Z. Man, “Comments on “fast algorithms and implementa-tion of 2-D discrete cosine transform”,” IEEE Transactions on Circuitsand Systems for Video Technology, vol. 8, pp. 128–129, April 1998.

[21] J. Mukherjee and S. K. Mitra, “Arbitrary resizing of images in DCTspace,” in Proceedings of the IEE Vision, Image and Signal Processing,vol. 152, pp. 155–164, April 2005.

[22] Z. Wang, H. R. Sheikh, and A. C. Bovik, “No-reference perceptualquality assessment of JPEG compressed images,” IEEE ProceedingsInternational Conference on Image Processing, vol. 1, pp. I–477–I–480,September 2002.

[23] Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Imagequality assessment: From error visibility to structural similarity,” IEEETransactions on Image Processing, vol. 13, pp. 600–612, April 2004.



[ieee 2013 8th international symposium on image and signal processing and analysis (ispa) - trieste,...

Documents