Joint Recovery of Sparse Signal Ensemble using Rank-Sparsity Decomposition

Abstract

Distributed Compressive Sensing (DCS) is an extension of compressive sensing from single measurement vector to multiple signal vectors. The theory rests on the concept of joint sparsity of a signal ensemble which enables new algorithms that exploit both intra and inter-signal correlation. We consider DCS in the context of joint sparse model 1 (JSM-1). JSM-1 consists of an ensemble of correlated signals that can be decomposed into a sparse common component and a sparse innovation component. This paper proposes a new DCS recovery method for JSM-1. We recast JSM-1 as a sum of a sparse and low rank matrix and develop an algorithm to recover the signal from the compressed measurements using a rank-sparsity decomposition. The proposed method requires less number of measurements and provides better recovery accuracy compared to the existing algorithms.