Sparse Optimization with Least-Squares Constraints

van den Berg, Ewout; Friedlander, Michael P.

doi:doi:10.1137/100785028

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SIAM J. on Optimization / Volume 21 / Issue 4

SIAM J. Optim. 21, pp. 1201-1229 (29 pages)

Sparse Optimization with Least-Squares Constraints

Ewout van den Berg and Michael P. Friedlander

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Abstract

References (64)

The use of convex optimization for the recovery of sparse signals from incomplete or compressed data is now common practice. Motivated by the success of basis pursuit in recovering sparse vectors, new formulations have been proposed that take advantage of different types of sparsity. In this paper we propose an efficient algorithm for solving a general class of sparsifying formulations. For several common types of sparsity we provide applications, along with details on how to apply the algorithm, and experimental results.

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KEYWORDS

Keywords

basis pursuit, compressed sensing, convex program, duality, group sparsity, matrix completion, Newton's method, root-finding, sparse solutions

AMS Subject Headings

49M29, 65K05, 90C25, 90C06

PUBLICATION DATA

ISSN

1052-6234 (print)

1095-7189 (online)

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$abstract.society.value is a Member of CrossRef

Society for Industrial and Applied Mathematics

ARTICLE DATA

History

Received February 03, 2010
Accepted February 07, 2011
Published online October 04, 2011

Digital Object Identifier

http://dx.doi.org/10.1137/100785028

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Sparse Optimization with Least-Squares Constraints

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