Structure based Bayesian sparse reconstruction using non-Gaussian prior

In this paper, we present a fast Bayesian method for sparse signal recovery that makes a collective use of the sparsity information, a priori statistical properties, and the structure involved in the problem to obtain near optimal estimates at very low complexity. Specifically, we utilize the rich structure present in the sensing matrix encountered in many signal processing applications to develop a fast reconstruction algorithm when the statistics of the sparse signal are non-Gaussian or unknown. The proposed method outperforms the widely used convex relaxation approaches as well as greedy matching pursuit techniques all while operating at a much lower complexity.