A Douglas-Rachford Splitting Approach to Nonsmooth Convex Variational Signal Recovery

被引：330

作者：

Combettes, Patrick L. ^{[1
]}

Pesquet, Jean-Christophe ^{[2
,3
]}

机构：

[1] Univ Paris 06, Fac Math, CNRS, Lab Jacques Louis Lions,UMR 7598, F-75005 Paris, France

[2] Univ Paris Est Marne la Vallee, Inst Gaspard Monge, F-77454 Marne La Vallee 2, France

[3] Univ Paris Est Marne la Vallee, CNRS, UMR 8049, F-77454 Marne La Vallee 2, France

来源：

IEEE JOURNAL OF SELECTED TOPICS IN SIGNAL PROCESSING | 2007年 / 1卷 / 04期

关键词：

Convex optimization; denoising; Douglas-Rachford; frame; nondifferentiable optimization; Poisson noise; proximal algorithm; wavelets; IMAGE-RESTORATION; FEASIBILITY PROBLEMS; INVERSE PROBLEMS; THRESHOLDING ALGORITHM; PROJECTIONS; OPERATORS; REPRESENTATIONS; RECONSTRUCTION; CONSTRAINT; TRANSFORM;

D O I：

10.1109/JSTSP.2007.910264

中图分类号：

TM [电工技术]; TN [电子技术、通信技术];

学科分类号：

0808 ; 0809 ;

摘要：

Under consideration is the large body of signal recovery problems that can be formulated as the problem of minimizing the sum of two (not necessarily smooth) lower semicontinuous convex functions in a real Hilbert space. This generic problem is analyzed and a decomposition method is proposed to solve it. The convergence of the method, which is based on the Douglas-Rachford algorithm for monotone operator-splitting, is obtained under general conditions. Applications to non-Gaussian image denoising in a tight frame are also demonstrated.

引用

页码：564 / 574

页数：11

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