Recovery of compressible signals in unions of subspaces

Marco F. Duarte, Chinmay Hegde, Volkan Cevher, Richard G. Baraniuk

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Abstract

    Compressive sensing (CS) is an alternative to Shannon/Nyquist sampling for acquisition of sparse or compressible signals; instead of taking periodic samples, we measure inner products with M < N random vectors and then recover the signal via a sparsity-seeking optimization or greedy algorithm. Initial research has shown that by leveraging stronger signal models than standard sparsity, the number of measurements required for recovery of an structured sparse signal can be much lower than that of standard recovery. In this paper, we introduce a new framework for structured compressible signals based on the unions of subspaces signal model, along with a new sufficient condition for their recovery that we dub the restricted amplification property (RAmP). The RAmP is the natural counterpart to the restricted isometry property (RIP) of conventional CS. Numerical simulations demonstrate the validity and applicability of our new framework using wavelet-tree compressible signals as an example.

    Original languageEnglish (US)
    Title of host publicationProceedings - 43rd Annual Conference on Information Sciences and Systems, CISS 2009
    Pages175-180
    Number of pages6
    DOIs
    StatePublished - 2009
    Event43rd Annual Conference on Information Sciences and Systems, CISS 2009 - Baltimore, MD, United States
    Duration: Mar 18 2009Mar 20 2009

    Publication series

    NameProceedings - 43rd Annual Conference on Information Sciences and Systems, CISS 2009

    Other

    Other43rd Annual Conference on Information Sciences and Systems, CISS 2009
    CountryUnited States
    CityBaltimore, MD
    Period3/18/093/20/09

    Keywords

    • Compressible signals
    • Compressive sensing
    • Unions of subspaces

    ASJC Scopus subject areas

    • Computer Science Applications
    • Information Systems

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