Finding needles in noisy haystacks

R.M. Castro, J. Haupt, R. Nowak, G.M. Raz

    Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

    40 Citations (Scopus)
    193 Downloads (Pure)


    The theory of compressed sensing shows that samples in the form of random projections are optimal for recovering sparse signals in high-dimensional spaces (i.e., finding needles in haystacks), provided the measurements are noiseless. However, noise is almost always present in applications, and compressed sensing suffers from it. The signal to noise ratio per dimension using random projections is very poor, since sensing energy is equally distributed over all dimensions. Consequently, the ability of compressed sensing to locate sparse components degrades significantly as noise increases. It is possible, in principle, to improve performance by "shaping" the projections to focus sensing energy in proper dimensions. The main question addressed here is, can projections be adaptively shaped to achieve this focusing effect? The answer is yes, and we demonstrate a simple, computationally efficient procedure that does so.
    Original languageEnglish
    Title of host publicationProceedings IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP'08, Las Vegas NV, USA, March 31-April 3, 2008)
    PublisherInstitute of Electrical and Electronics Engineers
    ISBN (Print)978-1-4244-1483-3
    Publication statusPublished - 2008


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