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Distributed compressed sensing (2005)
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BibTeX
@TECHREPORT{Baron05distributedcompressed,
author = {Dror Baron and Michael B. Wakin and Marco F. Duarte and Shriram Sarvotham and Richard G. Baraniuk},
title = {Distributed compressed sensing},
institution = {},
year = {2005}
}
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Abstract
Compressed sensing is an emerging field based on the revelation that a small collection 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 in detail 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. 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 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.
Keyphrases
sparse signal new theory challenging problem sparse signal contains enough information moderate number sensor network sense dc coding algorithm distributed compression joint sparsity new concept compressed sensing multi-signal ensemble signal ensemble multiple signal simple model inter-signal correlation structure practical algorithm joint recovery dc theory rest incoherent projection measurement rate linear projection accurate reconstruction slepian-wolf theorem small collection information theory
