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An Iterative Support Shrinking Algorithm for non-Lipschitz optimization in Image Restoration

JOURNAL OF MATHEMATICAL IMAGING AND VISION 2019年第1期61卷 122-139页

作者： Zeng, Chao Jia, Rui Wu, Chunlin Nankai Univ Sch Math Sci Tianjin Peoples R China

We consider a class of non-Lipschitz regularization problems that include the TVp model as a special case. A lower bound theory of the non-Lipschitz regularization is obtained, which inspires us to propose an algorithm guaranteeing the non-expansiveness of the images gradient support set. After being proximally linearized, this algorithm can be easily implemented. Some standard techniques in image processing, like the fast Fourier transform, could be utilized. The global convergence is also established. Moreover, we prove that the restorations by the algorithm have edge preservation property. Numerical examples are given to show good performance of the algorithm and the rationality of the theories.

关键词： non-convex non-smooth optimization non-Lipschitz optimization Lower bound theory Kurdyka-ojasiewicz property Total variation regularization Image restoration

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Whiteness Constraints in a Unified Variational Framework for Image Restoration

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JOURNAL OF MATHEMATICAL IMAGING AND VISION 2018年第9期60卷 1503-1526页

作者： Lanza, Alessandro Morigi, Serena Sciacchitano, Federica Sgallari, Fiorella Univ Bologna Dept Math Bologna Italy Univ Genoa Dept Math Genoa Italy

We propose a robust variational model for the restoration of images corrupted by blur and the general class of additive white noises. The key idea behind our proposal relies on a novel hard constraint imposed on the residual of the restoration, namely we characterize a residual whiteness set to which the restored image must belong. As the feasible set is unbounded, solution existence results for the proposed variational model are given. Moreover, based on theoretical derivations as well as on Monte Carlo simulations, we provide well-founded guidelines for setting the whiteness constraint limits. The solution of the non-trivial optimization problem, due to the non-smooth non-convex proposed model, is efficiently obtained by an alternating directions method of multipliers, which in particular reduces the solution to a sequence of convex optimization subproblems. Numerical results show the potentiality of the proposed model for restoring blurred images corrupted by several kinds of additive white noises.

关键词： Variational image restoration Additive white noise Total variation non-convex non-smooth optimization ADMM

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A Unified Framework for the Restoration of Images Corrupted by Additive White Noise 6th

A Unified Framework for the Restoration of Images Corrupted ...

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6th International Conference on Scale Space and Variational Methods in Computer Vision (SSVM)

作者： Lanza, Alessandro Sciacchitano, Federica Morigi, Serena Sgallari, Fiorella Univ Bologna Dept Math Bologna Italy Univ Genoa Dept Math Genoa Italy

ISBN: (纸本)9783319587714;9783319587707

We propose a robust variational model for the restoration of images corrupted by blur and the general class of additive white noises. The solution of the non-trivial optimization problem, due to the non-smooth non-convex proposed model, is efficiently obtained by an Alternating Directions Method of Multipliers (ADMM), which in particular reduces the solution to a sequence of convex optimization sub-problems. Numerical results show the potentiality of the proposed model for restoring blurred images corrupted by several kinds of additive white noises.

关键词： Variational image restoration Additive white noise Total Variation non-convex non-smooth optimization ADMM

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