TWO-STAGE MULTIPLE DESCRIPTION IMAGE ...

September 23, 2009 16:51 WSPC/181-IJWMIP

00318

International Journal of Wavelets, Multiresolution and Information Processing Vol. 7, No. 5 (2009) 665–673 c World Scientific Publishing Company


TWO-STAGE MULTIPLE DESCRIPTION IMAGE CODING USING TCQ

CHUNYU LIN∗ and YAO ZHAO† Institute of Information Science, Beijing Jiaotong University Beijing, 100044, P. R. China ∗[email protected] †[email protected] CE ZHU School of Electrical and Electronic Engineering Nanyang Technological University, 639798, Singapore [email protected] Received 13 August 2008 Revised 10 February 2009 In this paper, we incorporate Trellis Coded Quantization (TCQ) into a two-stage multiple description coding structure to obtain granular gain over two-stage multiple description Scalar Quantizer (SQ). Analysis and experiment on Gaussian signal show that the performance of the proposed scheme can achieve larger gain than that of the two-stage SQ scheme because of better performance of TCQ. The proposed scheme for image coding is shown to be more effective than other relevant multiple description image coding schemes in terms of central-side-distortion rate performance. Keywords: Image compression; multiple description coding; trellis coded quantization. AMS Subject Classification: 68U10, 68P30, 94A08

1. Introduction Multiple Description Coding (MDC) is an effective method to protect multimedia information transmitted over non-prioritized networks. It can effectively combat packet loss without any retransmission thus satisfying the demand of real time services and relieving the network congestion. In this work, we will only consider the two-channel balanced multiple description coding. In the MDC approach, two coded streams (descriptions) are generated individually and sent through separate channels. If only one channel works, the source can be reconstructed by side decoder with an acceptable quality. If both of the two channels work, the source can be reconstructed by central decoder with a better quality. For the two-channel MDC scheme, let R1 and R2 be the rates, D1 and D2 denote the side distortions of 665

September 23, 2009 16:51 WSPC/181-IJWMIP

666

00318

C. Lin, Y. Zhao & C. Zhu

two-side descriptions, respectively, and D0 represents the central distortion. With the mean squared error as the error measure, the achievable rate-distortion region for {R1 , R2 , D1 , D2 , D0 } on Gaussian source has been characterized in Ref. 1. In the balanced case, that is, R1 = R2 and D1 = D2 , D0 and D1 cannot both be the lowest, and achieving different tradeoffs between them is the main task of any MDC schemes. Some approaches have been proposed to realize MDC scheme. One of them is the Multiple Description Scalar Quantizer (MDSQ), which was first proposed as a practical solution to the MD problem.2 Servetto et al. applied MDSQ to the wavelet transformed image and achieved good performance in Ref. 3. Multiple description based on Lattice Vector Quantization (LVQ) can be seen as the generalization of MDSQ. With the better performance of LVQ, certain gain can be achieved over the MDSQ. The analysis on MDLVQ can be found in Ref. 4 and it has been applied to image coding based on A2 lattice in Ref. 5. Multiple description based on Trellis Coded Quantization (TCQ) is first considered in Ref. 6, where asymptotic analysis was used. However, achieving different tradeoff points is not easy in practical application for the above schemes. For example, the redundancy of MDSQ is controlled by the diagonals of a matrix. Therefore, the tradeoff points are fixed by the number of diagonals in a matrix. In addition, there is little gain by using more than two diagonals in practice, which limits its tuning of tradeoff points on central and side performance. In fact, the quality of the side performance has to be reduced by 7–8 dB in order to gain less than 1 dB gain in Peak Signal to Noise Ratio (PSNR) on the central performance.3 The MDLVQ scheme has the similar terrible performance at this situation. The two-stage structure provides a flexible redundancy tuning scheme, which can achieve any tradeoff points. In Ref. 7, a two-stage multiple description scheme is analyzed, which can be seen as a two-stage SQ scheme. In this paper, a two-stage structure with TCQ is adopted. Because of the two-stage structure and the better performance of TCQ, a larger gain can be achieved by using TCQ instead of SQ. In the remaining of the paper, Sec. 2 introduces the proposed two-stage MDC scheme based on TCQ with analysis, followed by the effective quadtree classification and trellis coded quantization (QTCQ) based multiple description image coding scheme. Experimental results are shown in Sec. 3 and the work is concluded in the last section.

2. Two-Stage MDC Scheme with TCQ 2.1. Proposed scheme TCQ adopts a structured codebook with an expanded set of quantization levels. To transmit r bits per sample, 2r+1 codevectors (doubled codebook size) are used. Based on Ungerboeck’s notion of set partitioning, the trellis structure then prunes the expanded number of quantization levels down to the desired encoding rate.

September 23, 2009 16:51 WSPC/181-IJWMIP

00318

Two-Stage Multiple Description Image Coding Using TCQ

667

The first stage Signal

+

TCQ(coarse)

Description 1

TCQ−1 (coarse)

-

Subsmapling

TCQ

Subsmapling

TCQ

Description 2

The second stage Fig. 1.

The proposed two-stage TCQ-based MDC scheme.

By using expanded codebooks and the Viterbi algorithm, TCQ is comparable and often superior in mean squared error performance to Scalar Quantizer (SQ).8 Figure 1 is the proposed MDC coding scheme, which includes two stages of processing. In the first stage, the signal is quantized by TCQ with a larger quantization step-size. In the second stage, the residual signal is subsampled and quantized by a finer TCQ. Thus, each description consists of the coarse signal approximation and half of the finer-quantized residual signal coefficients. It can be seen that the redundancy is explicitly introduced in the first stage, which can be tuned easily by changing the quantization step-size. 2.2. Performance analysis and experiment on Gaussian signal In Ref. 7, a two-stage multiple description coder based on SQ is analyzed. The two-stage with SQ structure is simple and flexible, but both of the two stages suffer a loss compared with the optimum. It has been shown that TCQ can achieve much better performance than SQ. For the memoryless uniform source using a simple 4-state trellis, the performance of TCQ is better than any vector quantizer of dimension less than 15.8 For the 256-state trellis, the sample average distortion is within 0.21 dB of the distortion-rate function. For other sources like memoryless Gaussian and Laplacian sources, it has been studied that substantial performance increase is possible with TCQ over the Lloyd–Max quantizer.8 Therefore, it will be expected of better performance by using TCQ in the two-stage MDC scheme. For simplicity, we will consider the level-constrained quantizer on memoryless Gaussian signal with zero mean and unit-variance. Consider an n-point signal, nr1 and nr2 denote bit budget in the first and second stages, respectively, where r1 and r2 are bit rates per sample. The bit cost for one side description is nr1 + 12 nr2 = 1 1 2 nr1 + 2 n(r1 + r2 ), which can be interpreted as half of the samples are quantized at rate r1 and the other half are quantized at rate r1 + r2 . With a total bit rate of 2nr 1 +nr 2 , it can be seen that the redundancy rate is nr1 . When the channel failure probability is high, select r1
r2 , the side distortion D1 will be very close to the

September 23, 2009 16:51 WSPC/181-IJWMIP

668

00318

C. Lin, Y. Zhao & C. Zhu

central distortion D0 . If the channel failure probability is low, the redundancy rate should be r1  r2 , where each description only carries slightly more than half of the total information. In between of the two extreme cases, we can tune the tradeoff of the side distortion and central distortion by changing the rate r1 and rate r2 . In Fig. 2, the curve of the central distortion versus side distortion is plotted. In the two-stage SQ scheme, the Lloyd–Max quantizer is used. Similarly, in the twostage TCQ scheme, we choose the Lloyd–Max quantizer output points at rate r1 + 1 as the initial output alphabet for TCQ at rate r1 . The eight-state TCQ scheme is selected for its simplicity and better performance. When the number of states is larger, the two-stage TCQ scheme tends to produce much better performance with more complexity. The rate of the first stage is selected as r1 = 1 bit per description. By adjusting the rate r2 , different tradeoffs of side and central distortions can be obtained. In our case, five tradeoff points (r1 , r2 ) = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5)} are shown. For simplicity, we assume the residual error between the reconstruction values of the first stage and the original value as Gaussian signal, which may get some loss. However, both of the two schemes adopt the same assumption. It has been known that the performance of TCQ is higher than that of SQ scheme about 1 dB in single description scheme.8 Therefore, the performance of the two-stage TCQ scheme will gain 2 dB over that of the two-stage SQ. This can be seen in the Fig. 2. In addition, the gap between the performances of the two schemes is larger

10

Central distortion

10

10

10

0

-1

-2

-3

Two-stage scheme with TCQ Two-stage scheme with SQ

10

-4

0.16

Fig. 2.

0.17

0.18

0.19 0.2 0.21 Side distortion

0.22

0.23

0.24

Central-MSE and side-MSE comparison for Gaussian source.

0.25

September 23, 2009 16:51 WSPC/181-IJWMIP

00318

Two-Stage Multiple Description Image Coding Using TCQ

669

when the rate of the second stage is larger. From the analysis, we can see that the two-stage MDC scheme with TCQ is an effective scheme. 2.3. Two-stage MDC in image coding with QTCQ In this section, the proposed scheme is applied to image coding to verify its effectiveness. Quadtree classification and trellis coded quantization (QTCQ) has shown its superior performance in image coding, which uses quadtree structure to classify the wavelet coefficients and apply TCQ to quantize the classified wavelet coefficients.9 Therefore, we adopt the QTCQ in the two-stage MDC structure for image coding. The coding process is similar to the Fig. 1. However, the image signals must be wavelet transformed firstly. Then both of the two stages are performed in the wavelet domain, which is different from the scheme of Ref. 7. In fact, the wavelet transform can be more effective if we adopt lifting scheme with quincunx lifting in Ref. 10, which is not our focus here. In the first stage, QTCQ with larger quantization step is applied to the coefficients, and the coarse bit stream is generated for both descriptions. In the second stage, the residual coefficients are subsampled based on some kind of wavelet tree structure. In Fig. 3, we take a 3-level wavelet transform as an example to illustrate the subsampling method, which is the same as Ref. 11. The wavelet coefficients in different subbands corresponding to the same spatial location are grouped as a tree block denoted as TB. Then these TBs are subsampled in the odd/even order to form the two descriptions. Because of the correlations in the tree structure, this subsampling method provides a good ratedistortion performance. Then the subsampled wavelet coefficients will take a second QTCQ coding to form the two descriptions, respectively. 3. Experimental Results We test our algorithm on two standard gray-scale images “Lena” and “Barbara” of 512 × 512. Although there are some different image quality assessment method such as Ref. 12., PSNR is selected for its simplicity and generality. For the sake

LL3HL3

LH2

LH1

HL2

TB0 HL1 …

LH3HH3

HH2

HH1

Fig. 3.

Wavelet tree based blocks.

TB1

TB2

…

September 23, 2009 16:51 WSPC/181-IJWMIP

670

00318

C. Lin, Y. Zhao & C. Zhu

of comparison, we also give the performance of MDSQ based on wavelet coder (MDSQ + Wavelet) by Servetto et al.,3 the JPEG2000-based MD approach,13 feature-oriented MDC (FOMDC)14 and the optimized MDLVQ for wavelet image (MDLVQ + Wavelet).5 MDSQ with wavelet coder applies MDSQ to the wavelet transformed image. JPEG2000-based MDC adopts JPEG2000 in its image coding scheme and has been extended to n-description MD scheme in Ref. 15. FOMDC adopts a scheme which is similar to space-frequency quantization (SFQ) in its image coding scheme while the optimized MDLVQ for wavelet image applies a optimized lattice vector quantization to wavelet transformed image. All the five methods including ours make use of wavelet transform in their coding scheme. The test bit rate is 0.5 bits/pixel per description. A six-level wavelet decomposition is used with the Daubechies 9/7 filters and 8-state TCQ was employed in the QTCQ scheme. The central-side PSNR comparisons of image “Lena” and “Barbara” are shown in Figs. 4 and 5, respectively. The results clearly show that the proposed scheme outperforms other related ones, especially when the redundancy is low. For the MDSQ and MDLVQ scheme, it can also be seen that the side performance will get a large distortion with little improvement on the central performance. In Fig. 6, the central and side distortions are shown as functions of changing rates. The results of JPEG2000-based MDC and Ref. 7 are given for reference. To demonstrate better comparison, we make our proposed scheme produce close (yet slightly better) central distortion-rate performance to the JPEG2000based MDC, which allows us to compare the side performance fairly. In Ref. 7, the

40.5 40

Central distortion (dB)

39.5 39 38.5

Proposed scheme MDSQ+Wavelet JPEG2000-based FOMDC MDLVQ+Wavelet

38 37.5 37 36.5 22

Fig. 4.

24

26

28 30 32 Side distortion (dB)

34

36

38

Central and side PSNR comparisons for “Lena” at 0.5 bits/pixel/description.

September 23, 2009 16:51 WSPC/181-IJWMIP

00318

Two-Stage Multiple Description Image Coding Using TCQ

36.5 36

Central distortion (dB)

35.5 35 34.5 34

Proposed scheme MDSQ+Wavelet

33.5

FOMDC MDLVQ+Wavelet

33 32.5 32 31.5

Fig. 5.

18

20

22

24 26 Side distortion (dB)

28

30

32

Central and side PSNR comparison for “Barbara” at 0.5 bits/pixel/description.

42

40

38

PSNR (dB)

36

34

32

Central descripton of proposed scheme Side descripton of proposed scheme Central description of two-stage SPIHT

30

Side description of two-stage SPIHT Central description based on JPEG2000 Side description based on JPEG2000

28

26 0.2

0.4

Fig. 6.

0.6

0.8 1 bit rate (bpp)

1.2

1.4

Rate-distortion performance comparison for “Lena”.

1.6

671

September 23, 2009 16:51 WSPC/181-IJWMIP

672

00318

C. Lin, Y. Zhao & C. Zhu

experimental results of the two-stage coding based on set partitioning in hierarchical trees (SPIHT) is given, which is denoted as two-stage SPIHT in Fig. 6. It can be seen that the proposed scheme achieves better distortion-rate results than the other referenced schemes over a wide range of total bit rates ranging from 0.2 bpp to 1.6 bpp. 4. Conclusion We have found that the two-stage MDC scheme with TCQ is a more effective scheme compared to the two-stage SQ. In the proposed MDC scheme, we can tune the rates in the two stages for a tradeoff between the side and central distortion, and the results on Gaussian source have shown its better performance over two-stage SQ. Applying the scheme to image coding has exhibited certain gain than other relevant MDC image coders tested. Acknowledgments This work was supported in part by the National Natural Science Foundation of China (No. 60776794, No. 90604032), 973 program (No. 2006CB303104), 863 program (No. 2007AA01Z175), PCSIRT (No. IRT0707) and Specialized Research Foundation of BJTU. References 1. V. A. Vaishampayan and J. C. Batllo, Asymptotic analysis of multiple description quantizers, IEEE Trans. Inform. Theory 44(1) (1998) 278–284. 2. V. A. Vaishampayan, Design of multiple description scalar quantizers, IEEE Trans. Inform. Theory 39(3) (1993) 821–834. 3. S. D. Servetto, K. Ramchandran, V. A. Vaishampayan and K. Nahrstedt, Multiple description wavelet based image coding, IEEE Trans. Image Process. 9(5) (2000) 813–826. 4. V. A. Vaishampayan, N. J. A. Sloane and S. D. Servetto, Multiple-description vector quantization with lattice codebooks: Design and analysis, IEEE Trans. Inform. Theory 47(5) (2001) 1718–1734. 5. H. Bai, C. Zhu and Y. Zhao, Optimized multiple description lattice vector quantization for wavelet image coding, IEEE Trans. Circuits Syst. Vid. Technol. 17(7) (2007) 912–917. 6. V. Vaishampayan, J. C. Batllo and A. R. Calderbank, On reducing granular distortion in multiple description quantization, in Abstracts of Papers, Proc. IEEE Int. Symp. Inform. Theory (IEEE Press, 1998), p. 98. 7. A. Norkin, A. Gotchev, K. Egiazarian and J. Astola, Two-stage multiple description image coders: Analysis and comparative study, Signal Process.: Image Commun. 21(8) (2006) 609–625. 8. M. W. Marcellin and T. R. Fischer, Trellis coded quantization of memoryless and Gauss-Markov sources, IEEE Trans. Commun. 38(1) (1990) 82–93. 9. B. A. Banister and T. R. Fischer, Quadtree classification and TCQ image coding, IEEE Trans. Circuits Syst. Vid. Technol. 11(1) (2001) 3–8.

September 23, 2009 16:51 WSPC/181-IJWMIP

00318

Two-Stage Multiple Description Image Coding Using TCQ

673

10. C.-Y. Wang, Z.-X. Hou and A.-P. Yang, Binary tree image coding algorithm based on non-separable wavelet transform via lifting scheme, Int. J. Wavelets Multiresolut. Inf. Process. 6(5) (2008) 761–775. 11. C. Lin, Y. Zhao and C. Zhu, Two-stage diversity-based multiple description image coding, IEEE Signal Process. Lett. 15 (2008) 837–840. 12. W. Lu, X.-B. Gao, D.-C. Tao and X.-L. Li, A wavelet-based image quality assessment method, Int. J. Wavelets Multiresolut. Inf. Process. 6(4) (2008) 541–551. 13. T. Tillo, M. Grangetto and G. Olmo, Multiple description image coding based on lagrangian rate allocation, IEEE Trans. Image Process. 16(3) (2007) 673–683. 14. Y. Liu and S. Oraintara, Feature-oriented multiple description wavelet-based image coding, IEEE Trans. Image Process. 16(1) (2007) 121–131. 15. E. Baccaglini, T. Tillo and G. Olmo, A flexible R-D-based multiple description scheme for JPEG2000, IEEE Signal Process. Lett. 14(3) (2007) 197–200.