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    Detection and estimation with compressive measurements

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    Author
    Baraniuk, Richard G.; Davenport, Mark A.; Wakin, Michael B.
    Date
    2006-11-01
    Abstract
    The recently introduced theory of compressed sensing enables the reconstruction of sparse or compressible signals from a small set of nonadaptive, linear measurements. If properly chosen, the number of measurements can be much smaller than the number of Nyquist rate samples. Interestingly, it has been shown that random projections are a satisfactory measurement scheme. This has inspired the design of physical systems that directly implement similar measurement schemes. However, despite the intense focus on the reconstruction of signals, many (if not most) signal processing problems do not require a full reconstruction of the signal { we are often interested only in solving some sort of detection problem or in the estimation of some function of the data. In this report, we show that the compressed sensing framework is useful for a wide range of statistical inference tasks. In particular, we demonstrate how to solve a variety of signal detection and estimation problems given the measurements without ever reconstructing the signals themselves. We provide theoretical bounds along with experimental results.
    Citation
    R. G. Baraniuk, M. A. Davenport and M. B. Wakin, "Detection and estimation with compressive measurements," 2006.
    Keyword
    compressive sensing; detection; estimation
    Type
    Report
    Related Work(s)
    Rice University ECE Technical Report;TREE 0610
    Citable link to this page
    https://hdl.handle.net/1911/21677
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    Managed by the Digital Scholarship Services at Fondren Library, Rice University
    Physical Address: 6100 Main Street, Houston, Texas 77005
    Mailing Address: MS-44, P.O.BOX 1892, Houston, Texas 77251-1892
    Site Map