A primal-dual fixed point algorithm for minimization of the sum of three convex separable functions

Many problems arising in image processing and signal recovery with multi-regularization and constraints can be formulated as minimization of a sum of three convex separable functions. Typically, the objective function involves a smooth function with Lipschitz continuous gradient, a linear composite...

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Vydáno v:	Fixed point theory and algorithms for sciences and engineering Ročník 2016; číslo 1; s. 1 - 18
Hlavní autoři:	Chen, Peijun, Huang, Jianguo, Zhang, Xiaoqun
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Cham Springer International Publishing 26.04.2016 Springer Nature B.V
Témata:	Algorithms Analysis Applications of Mathematics Convergence Differential Geometry Exact solutions Fixed points (mathematics) Mathematical analysis Mathematical and Computational Biology Mathematics Mathematics and Statistics Minimization Optimization Regularization Splitting Topology convex separable minimization sparsity regularization proximity operator primal-dual fixed point algorithm
ISSN:	1687-1812, 1687-1812, 2730-5422
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Abstract	Many problems arising in image processing and signal recovery with multi-regularization and constraints can be formulated as minimization of a sum of three convex separable functions. Typically, the objective function involves a smooth function with Lipschitz continuous gradient, a linear composite nonsmooth function, and a nonsmooth function. In this paper, we propose a primal-dual fixed point (PDFP) scheme to solve the above class of problems. The proposed algorithm for three-block problems is a symmetric and fully splitting scheme, only involving an explicit gradient, a linear transform, and the proximity operators which may have a closed-form solution. We study the convergence of the proposed algorithm and illustrate its efficiency through examples on fused LASSO and image restoration with non-negative constraint and sparse regularization.
AbstractList	Many problems arising in image processing and signal recovery with multi-regularization and constraints can be formulated as minimization of a sum of three convex separable functions. Typically, the objective function involves a smooth function with Lipschitz continuous gradient, a linear composite nonsmooth function, and a nonsmooth function. In this paper, we propose a primal-dual fixed point (PDFP) scheme to solve the above class of problems. The proposed algorithm for three-block problems is a symmetric and fully splitting scheme, only involving an explicit gradient, a linear transform, and the proximity operators which may have a closed-form solution. We study the convergence of the proposed algorithm and illustrate its efficiency through examples on fused LASSO and image restoration with non-negative constraint and sparse regularization.
ArticleNumber	54
Author	Huang, Jianguo Zhang, Xiaoqun Chen, Peijun
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Cites_doi	10.1561/2200000016 10.1145/1835804.1835847 10.1109/ICCV.2011.6126441 10.1007/s10957-012-0245-9 10.1137/080725891 10.1007/s10444-014-9363-2 10.1088/0266-5611/27/12/125007 10.1088/0266-5611/29/2/025011 10.1111/j.1467-9868.2005.00532.x 10.1137/050626090 10.1002/cmr.b.20081 10.1137/10081602X 10.1088/0266-5611/28/11/115005 10.1109/ICIP.2014.7025841 10.1007/s11228-011-0191-y 10.1137/090746379 10.1111/j.1467-9868.2005.00490.x 10.1137/09076934X 10.1007/s10851-010-0251-1 10.1109/MSP.2014.2377273 10.1007/s10114-016-5625-x
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Snippet	Many problems arising in image processing and signal recovery with multi-regularization and constraints can be formulated as minimization of a sum of three...
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SubjectTerms	Algorithms Analysis Applications of Mathematics Convergence Differential Geometry Exact solutions Fixed points (mathematics) Mathematical analysis Mathematical and Computational Biology Mathematics Mathematics and Statistics Minimization Optimization Regularization Splitting Topology
Title	A primal-dual fixed point algorithm for minimization of the sum of three convex separable functions
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