期刊
JOURNAL OF SCIENTIFIC COMPUTING
卷 74, 期 2, 页码 767-785出版社
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10915-017-0463-2
关键词
Compressive sensing; Proximal operator; Forward-backward splitting; Alternating direction method of multipliers; Difference-of-convex
资金
- NSF [DMS-1522786, DMS-1621798]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1621798] Funding Source: National Science Foundation
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1522786] Funding Source: National Science Foundation
This paper aims to develop new and fast algorithms for recovering a sparse vector from a small number of measurements, which is a fundamental problem in the field of compressive sensing (CS). Currently, CS favors incoherent systems, in which any two measurements are as little correlated as possible. In reality, however, many problems are coherent, and conventional methods such as minimization do not work well. Recently, the difference of the and norms, denoted as -, is shown to have superior performance over the classic method, but it is computationally expensive. We derive an analytical solution for the proximal operator of the - metric, and it makes some fast solvers such as forward-backward splitting (FBS) and alternating direction method of multipliers (ADMM) applicable for -. We describe in details how to incorporate the proximal operator into FBS and ADMM and show that the resulting algorithms are convergent under mild conditions. Both algorithms are shown to be much more efficient than the original implementation of - based on a difference-of-convex approach in the numerical experiments.
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