Wyner-Ziv Image Coding from Random Projections
In this paper, we present a Wyner-Ziv coding based on random projections for image compression with side information at the decoder. The proposed coder consists of random projections (RPs), nested scalar quantization (NSQ), and Slepian-Wolf coding (SWC). Most of natural images are compressible or sparse in the sense that they are well-approximated by a linear combination of a few coefficients taken from a known basis, e.g., FFT or Wavelet basis. Recent results show that it is surprisingly possible to reconstruct compressible signal to within very high accuracy from limited random projections by solving a simple convex optimization program. Nested quantization provides a practical scheme for lossy source coding with side information at the decoder to achieve further compression. SWC is lossless source coding with side information at the decoder. In this paper, ideal SWC is assumed, thus rates are conditional entropies of NSQ quantization indices. Recently theoretical analysis shows that for the quadratic Gaussian case and at high rate, NSQ with ideal SWC performs the same as conventional entropy-coded quantization with side information available at both the encoder and decoder. We note that the measurements of random projects for a natural large-size image can behave like Gaussian random variables because most of random measurement matrices behave like Gaussian ones if their sizes are large. Hence, by combining random projections with NSQ and SWC, the tradeoff between compression rate and distortion will be improved. Simulation results support the proposed joint codec design and demonstrate considerable performance of the proposed compression systems.