Optimization Method of Redundant Coefficients for Multiple Description Image Coding

Transcription

1 1 2 Optimization Method of Redundant Coefficients for Multiple Description Image Coding Takaaki Ishikawa 1 and Hiroshi Watanabe 2 We propose a new optimization method of redundant coefficients for multiple description image coding. Encoder of multiple description coding divide an input signal into various source of information, and then encode the information to multiple bitstreams individually. Through the encoding process, the encoder can multiplex arbitral redundant information in each bitstream. It increases robustness against packet losses during an image transmission. The proposed method interpolates the amplitude component of redundant coefficients, which is represented in complex values, and then it encodes and multiplexes the phase component. Experimental results show that the proposed method can encode the redundant coefficients of multiple description coding more efficiently compared to conventional method. 1 Global Information and Telecommunication Institute of Waseda University 2 Graduate School of Global Information and Telecommunication Studies of Waseda University 1. Forward Error Correction FEC FEC ) El Gamal Cover 2) 3) 4)5) Sadri 1 c 10 Information Processing Society of Japan

2 6) 7) Wang Compressive sensing 8) Goyal 9) X 1 X 2 Central X 2 (R 2 ) Side Side X 1 (ρ 1 ) X 2 (R 2 ) X 2 (ρ 2 ) description 1 description 2 Fig. 1 1 NoiseShaping Multiple Descriptions Encoder with Noise Shaping Li Noise Shaping 10) Noise Shaping 1 1 central side 2 Fig. 2 Subband images of CWT. x k x Thresholding k y A Th 0 Delay Inverse A A y k - n k Weight K 3 Noise Shaping Fig. 3 Iterative thresholding in Noise Shaping. 2 c 10 Information Processing Society of Japan

3 Dual Tree Complex Wavelet Transform Noise Shaping Kingsbury Noise Shaping 11) Noise Shaping 4 JPEG 00 12) Noise Shaping Noise Shaping 3 A A STEP1 y x = Ay x 0 y 0 STEP2 x k T h k 0 x k x k STEP3 x k y k STEP4 y 0 y k n k STEP5 n k K x k1 3 STEP2 STEP2 Wang ) L0 11) 3. 4 description 1 5 T I 4 STEP1 STEP2 6 0,1 STEP31 2 A n B ni n 3 c 10 Information Processing Society of Japan

4 description 1 LATTICE X 1 LATTICE X 2 Fig. 4 Central X 2 (R 2 ) T side T amplitude=0 amplitude=0 side X 1 (ρ 1 ) X 2 (ρ 2 ) 4 Multiple Descriptions Encoder using phase information. I T 1 amplitude T 1 side 5 Fig. 5 Multiple Descriptions Side Decoder with amplitude interpolation. ˆX 1 ˆX 2 X 2 (R 2 ) description 1 description 2 Description 1 Description Fig. 6 Coefficients division by lattice (two division). amplitude n = A 2 n Bn 2 (1) { tan 1 ( An 1 An B phase n = n ), tan B n 0 (2) tan 1 ( A n B n ) 2π, tan 1 A n B n < 0 STEP4 0 1 Noise Shaing Noise Shaing STEP5 0 Noise Shaping ) 4 c 10 Information Processing Society of Japan

5 3 4 A n = amplitude n cos(phase n ) (3) { amplitude n sin(phase n), phase n π B n = (4) amplitude n sin(phase n 2π), phase n > π 4. 7 Fig. 7 (Lena) Coding performance at central decoder (Lena). 8 (Barbara) Fig. 8 Coding performance at central decoder (Barbara) [pel] Lena Barbara Noise Shaping Lena 7 Barbara [bpp] Noise Shaping L0 4.3 Lena 9 11 Barbara c 10 Information Processing Society of Japan

6 9 (X 1 = X 2 = 0.5[bpp], Lena) Fig. 9 Coding performance at a side decoder (X 1 = X 2 = 0.5[bpp], Lena). 11 (X 1 = X 2 = 1.0[bpp], Lena) Fig. 11 Coding performance at a side decoder (X 1 = X 2 = 1.0[bpp], Lena). 10 (X 1 = X 2 = 0.5[bpp], Barbara) Fig. 10 Coding performance at a side decoder (X 1 = X 2 = 0.5[bpp], Barnara). 12 (X 1 = X 2 = 1.0[bpp], Barnara) Fig. 12 Coding performance at a side decoder (X 1 = X 2 = 1.0[bpp], Barbara). 1) Goyal, V.: Multiple Description Coding: Compression meets the network, IEEE Signal Processing Mag., Vol.18, pp (01). 2) Gamal, A.E. and Cover, T.M.: Multiple User Information Theory, Proceedings of the IEEE, Vol.68, No.12, pp (1980). 3) AVM39, pp (02). 4) Matty, K.R. and Kondi, L.P.: Balanced Multiple Description Video Coding Using Optimal Partitioning of the DCT Coefficients, IEEE Trans. on Circuits and Systems for Video Technology, Vol.15, No.7, pp (05). 5) Bajic, I.V. and Woods, J.W.: Domain-Based Multiple Description Coding of Image and Video, IEEE Trans. on Image Processing, Vol.12, No.10, pp (03). 6) Sadri, K. and Shirani, S.: Multiple description coding of images using phase scrambling, Acoustics, Speech, and Signal Processing, 04. Proceedings. (ICASSP 04). IEEE International Conference on, Vol.3, pp.iii 41 4 vol.3 (04). 7) Uto, T. and Ohue, K.: Multiple Description Coding Based on Phase Scrambling with Adjustable Spread Range, EURASIP06 European Signal Processing Conference, Vol.5 (06). 8) Wang, L., Wu, X. and Shi;, G.: A compressive sensing approach of multiple descriptions for network multimedia communication, Multimedia Signal Processing, 08 IEEE 10th Workshop on, pp (08). 9) AVM Vol.09-AVM65, No.16, pp.1 6 (09). 10) Li, L. and Cai;, C.: Multiple description image coding using dual-tree discrete wavelet transform, Intelligent Signal Processing and Communication Systems, 09. ISPACS 09. International Symposium on, pp (09). 11) Reeves, T.H. and Kingsbury, N.G.: Overcomplete Image Coding Using Iterative Projection-Based Noise Shaping, IEEE ICIP, Vol.3, No.3, pp (02). 12) J. Yang, Y. Wang, W. X. and Dai, Q.: Image Coding Using Dual-Tree Discrete Wavelet Transform, IEEE Trans. on Image Proc., Vol. 17, No. 9, pp (08). 13) Reeves, T.H. and Kingsbury, N.G.: R-D quantisation of complex coefficients in zerotree coding, Proceedings 11th IEEE Workshop on Statistical Signal Processing 01 (01). 6 c 10 Information Processing Society of Japan