Recovery of Jointly Sparse Signals from Few Random Projections

Abstract

Compressed sensing is an emerging field based on the revelation that a small group of linear projections of a sparse signal contains enough information for reconstruc- tion. In this paper we introduce a new theory for distributed compressed sensing (DCS) that enables new distributed coding algorithms for multi-signal ensembles that exploit both intra- and inter-signal correlation structures. The DCS theory rests on a new concept that we term the joint sparsity of a signal ensemble. We study three simple models for jointly sparse signals, propose algorithms for joint recov- ery of multiple signals from incoherent projections, and characterize theoretically and empirically the number of measurements per sensor required for accurate re- construction. In some sense DCS is a framework for distributed compression of sources with memory, which has remained a challenging problem in information theory for some time. DCS is immediately applicable to a range of problems in sensor networks and arrays.