Bit-plane compressive sensing with Bayesian decoding for lossy compression

This paper addresses the problem of reconstructing a compressively sampled sparse signal from its lossy and possibly insufficient measurements. The process involves estimations of sparsity pattern and sparse representation, for which we derived a vector estimator based on the Maximum a Posteriori Probability (MAP) rule. By making full use of signal prior knowledge, our scheme can use a measurement number close to sparsity to achieve perfect reconstruction. It also shows a much lower error probability of sparsity pattern than prior work, given insufficient measurements. To better recover the most significant part of the sparse representation, we further introduce the notion of bit-plane separation. When applied to image compression, the technique in combination with our MAP estimator shows promising results as compared to JPEG: the difference in compression ratio is seen to be within a factor of two, given the same decoded quality.