An information-theoretic approach to distributed compressed sensing

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 concept that we term the joint sparsity of a signal ensemble. We study a model for jointly sparse signals, propose algorithms for joint recovery of multi-ple signals from incoherent projections, and characterize the number of measure-ments per sensor required for accurate reconstruction. We establish a parallel with the Slepian-Wolf theorem from information theory and establish upper and lower bounds on the measurement rates required for encoding jointly sparse signals. In some sense DCS is a framework for distributed compression of sources with mem-ory, which has remained a challenging problem for some time. DCS is immediately applicable to a range of problems in sensor networks and arrays.