Bernoulli-Gaussian Scale Mixture Model and BP Method for Multi-Snapshot Sparse Signal Recovery

We present a general Bernoulli Gaussian scale mixture based approach for modeling priors that can represent a large class of random signals. For inference, we introduce belief propagation (BP) to multi-snapshot signal recovery based on the minimum mean square error estimation criteria. Our method relies on intra-snapshot messages that update the signal vector for each snapshot and inter-snapshot messages that share probabilistic information related to the common sparsity structure across snapshots. Despite the very general model, our BP method can efficiently compute accurate approximations of marginal posterior PDFs. Preliminary numerical results illustrate the superior convergence rate and improved performance of the proposed method compared to approaches based on sparse Bayesian learning (SBL).