Linearly Constrained Non-Lipschitz Optimization for Image Restoration
SIAM JOURNAL ON IMAGING SCIENCES(2015)
摘要
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 l(p) norm (0 < p < 1) of the gradient of the underlying image in the l(2)-l(p) problem as a special case. We prove that any cluster point of is an element of scaled first order stationary points satisfies a first order necessary condition for a local minimizer of the optimization problem as is an element of 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 is an element of scaled first order stationary point in at most O(is an element of(-2)) iterations from any starting point. Numerical examples are given to show good performance of the SQR algorithm for image restoration.
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关键词
image restoration,total variation regularization,non-Lipschitz optimization,smoothing quadratic regularization method,worst-case complexity
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