modelbased-acccc-2009 - Model-Based Compressive Sensing for...

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Unformatted text preview: Model-Based Compressive Sensing for Signal Ensembles Marco F. Duarte Program in Applied and Computational Mathematics Princeton University Princeton, NJ 08544 Email: Volkan Cevher, Richard G. Baraniuk Department of Electrical and Computer Engineering Rice University Houston, TX 77005 Email: { volkan,richb } Abstract —Compressive sensing (CS) is an alternative to Shannon/Nyquist sampling for acquiring sparse or com- pressible signals. Instead of taking N periodic samples, we measure M ≪ N inner products with random vectors and then recover the signal via a sparsity-seeking optimization or greedy algorithm. A new framework for CS based on unions of subspaces can improve signal recovery by including dependencies between values and locations of the signal’s significant coefficients. In this paper, we extend this framework to the acquisition of signal ensembles under a common sparse supports model. The new framework provides recovery algorithms with theoretical performance guarantees. Additionally, the framework scales naturally to large sensor networks: the number of measurements needed for each signal does not increase as the network becomes larger. Furthermore, the complexity of the recov- ery algorithm is only linear in the size of the network. We provide experimental results using synthetic and real-world signals that confirm these benefits. I. INTRODUCTION Compressive sensing (CS) is a new approach to simultaneous sensing and compression that enables a potentially large reduction in the sampling and com- putation costs at a sensor for signals having a sparse representation in some basis. CS builds on the work of Cand`es, Romberg, and Tao [1] and Donoho [2], who showed that a signal having a sparse representation in one basis can be recovered from a small set of projections onto a second measurement basis that is incoherent with the first. 1 Random projections play a central role as a universal measurement basis in the sense that they are incoherent with any fixed basis with high probability. The CS measurement process is nonadaptive, and the recovery process is nonlinear, for which a variety of algorithms have been proposed [1–6]. While CS has relied mostly on a simplistic sparse 1 Roughly speaking, incoherence means that no element of one basis has a sparse representation in terms of the other basis. or compressible signal model, there exists a parallel framework for more general structured sparsity models that favor certain configurations for the magnitudes and indices of the significant coefficients of the signal. It is then possible to design recovery algorithms that exploit the knowledge of this structure [7–11]. By reducing the degrees of freedom of a sparse or compressible signal, structured sparsity models provide two immediate benefits to CS. First, they enable a reduction in the number of measurements M required to stably recover a signal. Second, during signal recovery, they enable us to better differentiate true signal information from recovery...
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This note was uploaded on 05/28/2010 for the course EE EE564 taught by Professor Runyiyu during the Spring '10 term at Eastern Mediterranean University.

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modelbased-acccc-2009 - Model-Based Compressive Sensing for...

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