Signal recovery on incoherent manifolds

Chinmay Hegde, Richard G. Baraniuk

Research output: Contribution to journalArticle

21 Scopus citations

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 - Nov 27 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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