Distributed Compressive Sensing

TL;DR

This paper introduces a new theoretical framework for distributed compressive sensing (DCS) that leverages joint sparsity in multi-signal ensembles, providing performance limits and practical algorithms for signal recovery in sensor networks.

Contribution

It develops a novel DCS theory based on joint sparsity, characterizes fundamental recovery limits, and proposes practical algorithms for multi-signal reconstruction.

Findings

Theoretical bounds match practical algorithm performance in two models.

Asymptotic optimality achieved with moderate number of signals.

Framework applicable to sensor arrays and network signal processing.

Abstract

Compressive sensing is a signal acquisition framework based on the revelation that a small collection of linear projections of a sparse signal contains enough information for stable recovery. In this paper we introduce 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. Our theoretical contribution is to characterize the fundamental performance limits of DCS recovery for jointly sparse signal ensembles in the noiseless measurement setting; our result connects single-signal, joint, and distributed (multi-encoder) compressive sensing. To demonstrate the efficacy of our framework and to show that additional challenges such as computational tractability can be addressed, we study in detail three example models for jointly sparse signals. For these models, we develop practical algorithms for joint recovery of multiple signals from incoherent projections. 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. DCS is immediately applicable to a range of problems in sensor arrays and networks.