Details on O-SBL(MCMC): A Compressive Sensing Algorithm for Sparse Signal Recovery for the SMV/MMV Problem Using Sparse Bayesian Learning and Markov Chain Monte Carlo Inference

This report provides details on O-SBL(MCMC) algorithm for the recovery of jointly-sparse signals for the multiple measurement vector (MMV) problem. For the MMVs with this structure, the solution matrix, which is a collection of sparse vectors, is expected to exhibit joint sparsity across the columns. The notion of joint sparsity here means that the columns of the solution matrix share common supports. This algorithm employs a sparse Bayesian learning (SBL) model to encourage the joint sparsity structure across the columns of the solution. While the proposed algorithm is constructed for the MMV problems, it can also be applied to the single measurement vector (SMV) problems. Part of this work has been published in [1, 2]. Keywords— Compressive sensing, Sparse Bayesian learning (SBL), single measurement vector (SMV), multiple measurement vectors (MMVs).