Distributed compressive sensing

We have introduced a new theory for Distributed Compressive 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 have studied in detail three simple models for jointly sparse signals, proposed algorithms for joint recovery of multiple signals from incoherent projections, and characterized theoretically and empirically the number of measurements per sensor required for accurate reconstruction. We have also established a parallel with the Slepian-Wolf theorem from information theory and established upper and lower bounds on the measurement rates required for encoding jointly sparse signals. In two of our three models, the results are asymptotically best-possible, meaning that both the upper and lower bounds match the performance of our practical algorithms. Moreover, simulations indicate that the asymptotics take effect with just a moderate number of signals. In some sense DCS is a framework for distributed compression of sources with memory, which has remained a challenging problem for some time. DCS is immediately applicable to a range of problems in sensor networks and arrays.

Authors: Dror Baron, Marco F. Duarte, Michael B. Wakin, Shriram Sarvotham, Richard G. Baraniuk

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