Signal recovery on incoherent manifolds

Chinmay Hegde, Richard G. Baraniuk

    Research output: Contribution to journalArticle

    Abstract

    Suppose that we observe noisy linear measurements of an unknown signal that can be modeled as the sum of two component signals, each of which arises from a nonlinear submanifold of a high-dimensional ambient space. We introduce successive projections onto incoherent manifolds (SPIN), a first-order projected gradient method to recover the signal components. Despite the nonconvex nature of the recovery problem and the possibility of underdetermined measurements, SPIN provably recovers the signal components, provided that the signal manifolds are incoherent and that the measurement operator satisfies a certain restricted isometry property. SPIN significantly extends the scope of current recovery models and algorithms for low-dimensional linear inverse problems and matches (or exceeds) the current state of the art in terms of performance.

    Original languageEnglish (US)
    Article number6255789
    Pages (from-to)7204-7214
    Number of pages11
    JournalIEEE Transactions on Information Theory
    Volume58
    Issue number12
    DOIs
    StatePublished - 2012

    Keywords

    • Compressed sensing
    • sampling theory
    • signal deconvolution

    ASJC Scopus subject areas

    • Information Systems
    • Computer Science Applications
    • Library and Information Sciences

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