Bayesian multiple measurement vector problem with spatial structured sparsity patterns

Abstract

A promising research that has drawn considerable attentions is exploiting the inherent structures in the sparse signal. In this work, we apply the property to the multiple measurement vector (MMV) problem, in which a group of collected sparse signals that share an identical sparsity support are recovered from undersampled measurements. The main objective of this paper is to introduce a Bayesian model with taking both spatial and temporal dependencies into account and show how this model can be used for MMV with spatial structured sparsity patterns. Due to the property of the beta process that the sparse representation can be decomposed to values and sparsity indicators, the proposed algorithm ingeniously captures the temporal correlation structure by the learning of amplitudes and the spatial correlation structure by the estimation of clustered sparsity patterns. Detailed numerical experiments including synthetic and real data demonstrate the effectiveness of the proposed algorithm.