Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/55491
Title: Linearly constrained non-lipschitz optimization for image restoration
Authors: Bian, W
Chen, X 
Keywords: Image restoration
Non-lipschitz optimization
Smoothing quadratic regularization method
Total variation regularization
Worst-case complexity
Issue Date: 2015
Publisher: Society for Industrial and Applied Mathematics
Source: SIAM journal on imaging sciences, 2015, v. 8, no. 4, p. 2294-2322 How to cite?
Journal: SIAM journal on imaging sciences 
Abstract: Nonsmooth nonconvex optimization models have been widely used in the restoration and reconstruction of real images. In this paper, we consider a linearly constrained optimization problem with a non-Lipschitz regularization term in the objective function which includes the lp norm (0 < p < 1) of the gradient of the underlying image in the l2-lp problem as a special case. We prove that any cluster point of ε scaled first order stationary points satisfies a first order necessary condition for a local minimizer of the optimization problem as ε goes to 0. We propose a smoothing quadratic regularization (SQR) method for solving the problem. At each iteration of the SQR algorithm, a new iterate is generated by solving a strongly convex quadratic problem with linear constraints. Moreover, we show that the SQR algorithm can find an ε scaled first order stationary point in at most O(ε−2) iterations from any starting point. Numerical examples are given to show good performance of the SQR algorithm for image restoration.
URI: http://hdl.handle.net/10397/55491
ISSN: 1936-4954 (online)
DOI: 10.1137/140985639
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