A New Bayesian Method for Jointly Sparse Signal Recovery

In this paper, we address the recovery of a set of jointly sparse vectors from incomplete measurements. We provide a Bayesian inference scheme for the multiple measurement vector model and develop a novel method to carry out maximum a posteriori estimation for the Bayesian inference based on the prior information on the sparsity structure. Instead of implementing Bayesian variables estimation, we establish the corresponding minimization algorithms for all of the sparse vectors by applying block coordinate descent techniques, and then solve them iteratively and sequently through a re-weighted method. Numerical experiments demonstrate the enhancement of joint sparsity via the new method and its robust recovery performance in the case of a low sampling ratio.