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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Published in:Fixed point theory and algorithms for sciences and engineering Vol. 2016; no. 1; pp. 1 - 18
Main Authors: Chen, Peijun, Huang, Jianguo, Zhang, Xiaoqun
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 26.04.2016
Springer Nature B.V
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:1687-1812
1687-1812
2730-5422
DOI:10.1186/s13663-016-0543-2