Block-Sparse Signal Recovery Based on Adaptive Matching Pursuit via Spike and Slab Prior

Spike and Slab prior is a well-suited sparsity promoting prior, which is widely used to recover sampled signal in Bayesian inference. However, some sparse signal further involve more prior information-block sparsity structure which the standard Spike and Slab prior cannot cover. Alternatively, the original optimization problem is a hard non-convex problem, which is usually solved through simplifying the assumptions, relaxations or even relying on strong data computing capability. Therefore, a novel block adaptive matching pursuit (BAMP) method based on a hierarchical Bayesian model is proposed, which both use block spike and slab prior to recover sampled signal with exploiting underlying block sparsity structure and settle the non-convex problem more efficiently. In addition, the intermediate steps of the method are calculated by alternating direction method of multipliers (ADMM) algorithm which makes the method much faster. Experimental results on both synthetic data and real dataset demonstrate the proposed BAMP algorithm perform better superior compared with other novel algorithms released in recent years.