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.

中文翻译：

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用于泊松噪声去除的非局部低秩模型

近年来，利用图像补丁之间的冗余和相似性的基于补丁的方法引起了人们的广泛关注。但是，这些方法主要限于高斯噪声去除。本文考虑了泊松噪声去除问题。与具有相同且独立分布的高斯噪声不同，泊松噪声取决于信号，这使问题更具挑战性。通过合并一组相似补丁应具有低秩结构的先验条件，并应用最大的后验（MAP）估计，泊松噪声去除问题被表述为优化问题。然后，开发了一种交替最小化算法，以有效地找到目标函数的最小化器。最小化序列的收敛将被建立，