A nonlocal low rank model for poisson noise removal

IF 1.2 4区数学 Q2 MATHEMATICS, APPLIED

Inverse Problems and Imaging Pub Date : 2021-01-01 DOI:10.3934/ipi.2021003

Mingchao Zhao, Y. Wen, Michael K. Ng, Hongwei Li

引用次数: 7

Abstract

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 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.

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泊松噪声去除的非局部低秩模型

基于patch的方法利用图像patch之间的冗余性和相似性，近年来备受关注。然而，这些方法主要局限于高斯噪声的去除。本文研究了泊松噪声的去除问题。与高斯噪声具有相同且独立的分布不同，泊松噪声与信号相关，这使得问题更具挑战性。通过结合一组相似斑块应具有低秩结构的先验性，并应用最大后验(MAP)估计，将泊松噪声去除问题制定为优化问题。在此基础上，提出了一种交替最小化算法，以有效地找到目标函数的最小化点。建立了最小序列的收敛性，并通过数值实验验证了该算法的有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Inverse Problems and Imaging 数学-物理：数学物理

CiteScore

2.50

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Inverse Problems and Imaging publishes research articles of the highest quality that employ innovative mathematical and modeling techniques to study inverse and imaging problems arising in engineering and other sciences. Every published paper has a strong mathematical orientation employing methods from such areas as control theory, discrete mathematics, differential geometry, harmonic analysis, functional analysis, integral geometry, mathematical physics, numerical analysis, optimization, partial differential equations, and stochastic and statistical methods. The field of applications includes medical and other imaging, nondestructive testing, geophysical prospection and remote sensing as well as image analysis and image processing. This journal is committed to recording important new results in its field and will maintain the highest standards of innovation and quality. To be published in this journal, a paper must be correct, novel, nontrivial and of interest to a substantial number of researchers and readers.