## 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 language | English |
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Pages (from-to) | 4318-4335 |

Number of pages | 18 |

Journal | Journal of Computational and Applied Mathematics |

Volume | 236 |

Issue number | 17 |

DOIs | |

State | Published - Nov 2012 |

### Bibliographical note

Funding Information:The work of Y. Censor is supported by Grant No. 2009012 from the United States–Israel Binational Science Foundation (BSF) and by US Department of Army award number W81XWH-10-1-0170.

## Keywords

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

## ASJC Scopus subject areas

- Computational Mathematics
- Applied Mathematics