A nonlocal low rank model for poisson noise removal

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.