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.