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A Nonconvex and Nonsmooth Model for Deblurring Images under Cauchy Noise

A Nonconvex and Nonsmooth Model for Deblurring Images under Cauchy Noise

Year:    2025

Author:    Hongtao Chen, Weina Wang

Advances in Applied Mathematics and Mechanics, Vol. 17 (2025), Iss. 1 : pp. 148–174

Abstract

In this paper, we propose a nonconvex and nonsmooth model for image restoration with Cauchy noise removal. The regularization term is composed of a nonconvex Lipschitz potential function with first-order derivatives of an image, while the data fidelity term is introduced based on the maximum a posteriori estimator to Cauchy distribution. To handle the nonconvexity of regularizers, we adopt the proximal linearization technique to convert the original nonconvex model to a series of convex models, which can be easily implemented by alternating direction method with multipliers. Based on the Kurdyka-Łojasiewicz property, we can verify the global convergence of the proposed algorithm by using an abstract convergence framework. Numerical experiments and comparisons indicate that our method obtains good restorations and is effective for better preserving edges.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.OA-2022-0243

Advances in Applied Mathematics and Mechanics, Vol. 17 (2025), Iss. 1 : pp. 148–174

Published online:    2025-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    27

Keywords:    Nonconvex and nonsmooth Kurdyka-Łojasiewicz property Cauchy noise image restoration.

Author Details

Hongtao Chen

Weina Wang