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 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 functi...

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Bibliographic Details
Published in:arXiv.org 2015-12
Main Authors: Chen, Peijun, Huang, Jianguo, Zhang, Xiaoqun
Format: Article
Language:English
Subjects:
Algorithms
Continuity (mathematics)
Fixed points (mathematics)
Image processing
Image restoration
Linear operators
Operators (mathematics)
Optimization
Regularization
Signal processing
Signal reconstruction
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Summary:Many problems arising in image processing and signal recovery with multi-regularization 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 fully splitting symmetric scheme, only involving explicit gradient and linear operators without inner iteration, when the nonsmooth functions can be easily solved via their proximity operators, such as \(\ell_1\) type regularization. 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.
ISSN:2331-8422