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A nonlocal low rank model for poisson noise removal

Mingchao Zhao, ,Key Laboratory of Computing and Stochastic Mathematics (LCSM), (Ministry of Education of China), School of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan 410081, China, You-Wei Wen, Michael Ng, Hongwei Li, ,The Department of Mathematics, The University of Hong Kong, Hong Kong, China, ,Beijing Advanced Innovation Center for Imaging Theory and Technology, Capital Normal University, Beijing, China
2020 Inverse Problems and Imaging  

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Patch-based methods, which take the advantage of the redundancy and similarity among image patches, have attracted much attention in recent years. However, these methods are mainly limited to Gaussian noise removal. In this paper, the Poisson noise removal problem is considered. Unlike Gaussian noise which has an identical and independent distribution, Poisson noise is signal dependent, which makes the problem more challenging. By incorporating the prior that a group of similar patches should
more » ... ar patches should possess a low-rank structure, and applying the maximum a posterior (MAP) estimation, the Poisson noise removal problem is formulated as an optimization one. Then, an alternating minimization algorithm is developed to find the minimizer of the objective function efficiently. Convergence of the minimizing sequence will be established, and the efficiency and effectiveness of the proposed algorithm will be demonstrated by numerical experiments. 2020 Mathematics Subject Classification. 94A08, 68U10, 65K10.
doi:10.3934/ipi.2021003 fatcat:vleeiqedcrarxbw5hyhmg3vi2q
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Mingchao Zhao, ,Key Laboratory of Computing and Stochastic Mathematics (LCSM), (Ministry of Education of China), School of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan 410081, China, You-Wei Wen, Michael Ng, Hongwei Li, ,The Department of Mathematics, The University of Hong Kong, Hong Kong, China, ,Beijing Advanced Innovation Center for Imaging Theory and Technology, Capital Normal University, Beijing, China. "A nonlocal low rank model for poisson noise removal." Inverse Problems and Imaging (2020) 1-19