| Proximal Linearized Minimization Algorithm for Nonsmooth Nonconvex Minimization Problems in Image Deblurring with Impulse Noise |
| Received:January 19, 2023 Revised:July 07, 2023 |
| Key Words:
nonconvex data fidelity term impulse noise total variation proximal linearized minimization
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| Fund Project:Supported by the National Natural Science Foundations of China (Grant No.12061045,12031003), the Guangzhou Education Scientific Research Project 2024 (Grant No.202315829) and the Natural Science Foundation of Jiangxi Province (Grant No.20224ACB211004). |
| Author Name | Affiliation | | Shirong DENG | School of Mathematics and Information Science, Guangzhou University, Guangdong 510006, P. R. China
Department of Mathematics, Nanchang University, Jiangxi 330031, P. R. China | | Yuchao TANG | School of Mathematics and Information Science, Guangzhou University, Guangdong 510006, P. R. China
Department of Mathematics, Nanchang University, Jiangxi 330031, P. R. China |
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| Abstract: |
| Impulse noise removal is an important task in image restoration. In this paper, we introduce a general nonsmooth nonconvex model for recovering images degraded by blur and impulsive noise, which can easily include some prior information, such as box constraint or low rank, etc. To deal with the nonconvex problem, we employ the proximal linearized minimization algorithm. For the subproblem, we use the alternating direction method of multipliers to solve it. Furthermore, based on the assumption that the objective function satisfies the Kurdyka-Lojasiewicz property, we prove the global convergence of the proposed algorithm. Numerical experiments demonstrate that our method outperforms both the $\ell_{1}$TV and Nonconvex TV models in terms of subjective and objective quality measurements. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2024.01.010 |
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