Convex feasibility modeling and projection methods for sparse signal recovery

Avishy Carmi, Yair Censor, Pini Gurfil

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

A computationally-efficient method for recovering sparse signals from a series of noisy observations, known as the problem of compressed sensing (CS), is presented. The theory of CS usually leads to a constrained convex minimization problem. In this work, an alternative outlook is proposed. Instead of solving the CS problem as an optimization problem, it is suggested to transform the optimization problem into a convex feasibility problem (CFP), and solve it using feasibility-seeking sequential and simultaneous subgradient projection methods, which are iterative, fast, robust and convergent schemes for solving CFPs. As opposed to some of the commonly-used CS algorithms, such as Bayesian CS and Gradient Projections for sparse reconstruction, which become inefficient as the problem dimension and sparseness degree increase, the proposed methods exhibit robustness with respect to these parameters. Moreover, it is shown that the CFP-based projection methods are superior to some of the state-of-the-art methods in recovering the signal's support. Numerical experiments show that the CFP-based projection methods are viable for solving large-scale CS problems with compressible signals.

Original languageEnglish
Pages (from-to)4318-4335
Number of pages18
JournalJournal of Computational and Applied Mathematics
Volume236
Issue number17
DOIs
StatePublished - 1 Nov 2012
Externally publishedYes

Keywords

  • Compressed sensing
  • Convex feasibility problems
  • Signal processing
  • Subgradient projection methods

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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