NESTA: A Fast and Accurate First-Order Method for Sparse Recovery

• Published in: SIAM journal on imaging sciences Vol. 4; no. 1; pp. 1 - 39
• Main Authors: Becker, Stephen, Bobin, Jérôme, Candès, Emmanuel J.
• Format: Journal Article
• Language: English
• Published: Philadelphia Society for Industrial and Applied Mathematics 01.01.2011
• Subjects: Algorithms; Convex analysis; Sparsity; Studies
• ISSN: 1936-4954; 1936-4954
• DOI: 10.1137/090756855

Accurate signal recovery or image reconstruction from indirect and possibly undersampled data is a topic of considerable interest; for example, the literature in the recent field of compressed sensing is already quite immense. This paper applies a smoothing technique and an accelerated first-order algorithm, both from Nesterov, and demonstrates that this approach is ideally suited for solving large-scale compressed sensing reconstruction problems as (1) it is computationally efficient, (2) it is accurate and returns solutions with several correct digits, (3) it is flexible and amenable to many kinds of reconstruction problems, and (4) it is robust in the sense that its excellent performance across a wide range of problems does not depend on the fine tuning of several parameters. The authors also apply the algorithm to solve other problems for which there are fewer alternatives, such as total-variation minimization and convex programs seeking to minimize the ... norm of Wx under constraints, in which W is not diagonal.(ProQuest: ... denotes formulae/symbols omitted.)