Greedy-like algorithms for the cosparse analysis model

R. Giryes, S. Nam, M. Elad, R. Gribonval, M. E. Davies

Research output: Contribution to journalArticlepeer-review

Abstract

The cosparse analysis model has been introduced recently as an interesting alternative to the standard sparse synthesis approach. A prominent question brought up by this new construction is the analysis pursuit problem - the need to find a signal belonging to this model, given a set of corrupted measurements of it. Several pursuit methods have already been proposed based on ℓ1 relaxation and a greedy approach. In this work we pursue this question further, and propose a new family of pursuit algorithms for the cosparse analysis model, mimicking the greedy-like methods - compressive sampling matching pursuit (CoSaMP), subspace pursuit (SP), iterative hard thresholding (IHT) and hard thresholding pursuit (HTP). Assuming the availability of a near optimal projection scheme that finds the nearest cosparse subspace to any vector, we provide performance guarantees for these algorithms. Our theoretical study relies on a restricted isometry property adapted to the context of the cosparse analysis model. We explore empirically the performance of these algorithms by adopting a plain thresholding projection, demonstrating their good performance.

Original languageEnglish
Pages (from-to)22-60
Number of pages39
JournalLinear Algebra and Its Applications
Volume441
DOIs
StatePublished - 15 Jan 2014
Externally publishedYes

Keywords

  • Analysis
  • CoSaMP
  • Compressed sensing
  • Hard thresholding pursuit
  • Iterative hard thresholding
  • Sparse representations
  • Subspace-pursuit
  • Synthesis

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