Exploiting wavelet-domain intra-scale and inter-scale dependencies in Bayesian compressive sensing with context modeling

We propose a novel Bayesian compressive sensing reconstruction algorithm based on the context modeling of intra-scale wavelet coefficients, which utilizes the statistical dependencies in different directions. We assume that the wavelet coefficients obey a spike-and-slab probability model, whose parameters can be estimated according to a novel context-based model. In the context-based model, 3×3, 5×5 and 7×7 neighboring blocks are classified into 3 classes, 4 classes and 4 classes respectively. By determining the significance state of each class and parent coefficient, we estimate the significance probability of the current coefficient. Based on the above new wavelet coefficients' prior probability model, we propose the corresponding Bayesian compressive sensing reconstruction algorithm by using Markov Chain Monte Carlo (MCMC) method. Experimental results show that compared with the tree-structured wavelet compressive sensing (TSW-CS) which only uses the interscale dependencies, the proposed algorithm improves the peak-signal-to-noise-ratio (PSNR) up to nearly 2dB at the sampling rate of 0.9.