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Distributed compressed sensing (2005)

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by Dror Baron , Michael B. Wakin , Marco F. Duarte , Shriram Sarvotham , Richard G. Baraniuk
Citations:136 - 26 self
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@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   

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