Recovery of jointly sparse signals from few random projections

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 reconstruction. 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 recovery of multiple signals from incoherent projections, and characterize theoretically and empirically the number of measurements per sensor required for accurate reconstruction. 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.