Multiple Description Coding for quincunx images. Application to satellite transmission. Manuela Pereira, Annabelle Gouze, Marc Antonini and Michel Barlaud { pereira, gouze, am, barlaud }@i3s.unice.fr I3S Laboratory of CNRS University of Nice Sophia Antipolis France HSNMC 2003 p.1
Outline Problem Statement Our Contributions Results Conclusion HSNMC 2003 p.2
Outline Problem Statement Coding of quincunx images Satellite transmission Our Contributions Results Conclusion HSNMC 2003 p.2
Coding of quincunx images CCD 1 CCD 2 Quincunx image HSNMC 2003 p.3
Application to satellite transmission Increase demand of satellite images Continuous effort in order to improve image quality Traditional schemes use FEC for each image independently HSNMC 2003 p.4
Outline Problem Statement Our contributions General MDC Proposed MDC for quincunx images Central distortion modeling Redundancy Parameter (r N ) Solution of the problem Two channel solution Results Conclusion HSNMC 2003 p.5
General MDC Take into account the dependencies between the pixels of the two CCD arrays HSNMC 2003 p.6
General MDC Take into account the dependencies between the pixels of the two CCD arrays Uses the noise characteristics to be adapted to satellite channel model HSNMC 2003 p.6
General MDC Take into account the dependencies between the pixels of the two CCD arrays Uses the noise characteristics to be adapted to satellite channel model Perform source-channel coding using Multiple Description Coding HSNMC 2003 p.6
General MDC: scheme ( R l, D l ) Side Decoder ( R 1, D 1 ) Wavelet coefficients MDC ( R 1, D 1 ) ( R 2, D 2 ) Quality Control or Rate Control bitstream bitstream channel noisy Central Decoder ( R 0, D 0 ) BER Side Decoder ( R 2, D 2 ) HSNMC 2003 p.7
General MDC: formulation For a given channel model and state Compute the combination of scalar quantizers across the various wavelet coefficients subbands To minimize the total central distortion While satisfying the side bit rates and/or the side distortion constraints HSNMC 2003 p.8
Proposed MDC for quincunx images MD Bit Allocation + 3 3 P1 ɛ P2 Coder Channel 1 Coder Residual Coder Channel 2 Multiplexing Multiplexing CHANNEL De multiplexing ˆ P 1 ˆ ɛ1 De multiplexing ˆ P 2 ˆɛ1 Decoder Description 1 Central description Description 2 (R 1, D 1 ) (R 0, D 0 ) (R 2, D 2 ) HSNMC 2003 p.9
Proposed MDC for quincunx images (P ) minimize the central distortiond 0 subject to constraints R 1 = R 2 = R l Introduction of Lagrangian operators J ({q i,1, q i,2, q i,ɛ }) = D 0 + 2 j=1 λ j (R j R l ) HSNMC 2003 p.10
Central distortion modeling Central distortion for Generalized Gaussian distributions D 0 = #SB i=1 ( i σi,0d 2 qi,1 i,0, q i,2, q ) i,ɛ σ i,1 σ i,2 σ i,ɛ HSNMC 2003 p.11
Central distortion modeling Central distortion for Generalized Gaussian distributions D 0 = #SB i=1 ( i σi,0d 2 qi,1 i,0, q i,2, q ) i,ɛ σ i,1 σ i,2 σ i,ɛ HSNMC 2003 p.11
Central distortion modeling Central distortion for Generalized Gaussian distributions D 0 = #SB i=1 ( i σi,0d 2 qi,1 i,0, q i,2, q ) i,ɛ σ i,1 σ i,2 σ i,ɛ Central distortion for subband i [ 1 (σ ) 2 i,1d i,1 + σi,2d 2 i,2 + σ 2 i,0 ] 2r N (1 + r N ) σ2 i,ɛd i,ɛ HSNMC 2003 p.11
Redundancy Parameter (r N ) We propose r N = max p(x) (H(X)) C max p(x) (H(x)) where H(x) is the entropy of the input and C is the channel capacity (see [1]). [1] M. Pereira, M. Antonini and M. Barlaud, Multiple description image and video coding for wireless channels, EURASIP Signal Processing: Image Communication, Special issue on Recent Advances in Wireless Video 2003 HSNMC 2003 p.12
Redundancy Parameter Binary Symmetric Channel r N = plog 2 p + (1 p)log 2 (1 p) Where (1 p) is the probability for a symbol of being changed. Additive White Gaussian Noise channel (for a QPSK) r N = 2 log 2(1+ S N ) = 1 log 2(1+ S N ) 2 2 Where, S is the received signal power and N is the AWGN power within the channel bandwidth. Rayleigh channel (for a QPSK) r N = 1 log 2e.e N S ( e+ln S N + N S ) 2 HSNMC 2003 p.13
Solution of the problem Lagrangian functional J ({q i,1, q i,2, q i,ɛ }) = #SB X i=1 i σ 2 i,0 D i,0 qi,1, q i,2, q «i,ɛ + σ i,1 σ i,2 σ i,ɛ 2X λ j Q j j=1 Constraints: R 1 = R 2 = R l Q j = 0 @ #SB X i=1 «««qi,j qi,ɛ a i R i,j + R i,ɛ σ i,j σ i,ɛ 1 R l A HSNMC 2003 p.14
Two channel solution D i,k R i,k ( qi,k σ i,k ) = A ka i i σ 2 i,k C k #SB i=1 a i ( ( ) qi,j R i,j σ i,j ( )) qi,ɛ + R i,ɛ σ i,ɛ R l = 0 A k=1,2 = λ k ; A k=ɛ = λ 1 + λ 2 C k=1,2 = 1; C k=ɛ = 2r N 1+r N HSNMC 2003 p.15
Plan Problem Statement Proposed MD Bit Allocation Results Classical MDC for quincunx images Satellite channel simulator PSNR s results Visual results Conclusion and Perspectives HSNMC 2003 p.16
Classical MDC for quincunx images MD Bit Allocation Merge 2 Coder Channel 1 Coder Channel 2 CHANNEL Decoder Description 1 Central description Description 2 (R 1, D 1 ) (R 0, D 0 ) (R 2, D 2 ) HSNMC 2003 p.17
Satellite channel simulator 0.0005 0.00005 0.995 0.9995 0.9329 0.0677 0.0305 1 2 3 4 0.2499 0.2999 0.4196 Three-good state, single error state Fritchman model for 40 pass. HSNMC 2003 p.18
PSNR s results : Nimes image r N = 0.01 Side Central r N = 0.5 Side Central PSNR PSNR PSNR PSNR 2 bpp Method I 32.71 40.26 Method II 31.29 38.74 3 bpp Method I 33.04 42.27 Method II 31.62 37.82 2 bpp Method I 33.92 37.76 Method II 31.88 39.48 3 bpp Method I 32.77 39.60 Method II 31.84 40.12 HSNMC 2003 p.19
Visual results : classical MDC Channel 1 Channel 2 HSNMC 2003 p.20
Visual results : proposed MDC Channel 1 Channel 2 HSNMC 2003 p.21
Visual results : Central Nimes images Classical MDC Proposed MDC HSNMC 2003 p.22
Plan Problem Statement Proposed MD Bit Allocation Results Conclusion HSNMC 2003 p.23
Conclusion We propose an MDC for quincunx images that perform joint source-channel coding uses satellite model characteristics to find a good trade off quality-robustness HSNMC 2003 p.24