Low-Rank Regularized Collaborative Filtering for Image Denoising

Effective noise removal from image signals strongly relies on good image prior, which that comes from the ill-posed nature of image denoising problem. Nonlocal self-similarity and sparsity are two popular and widely used image priors which have led to several state-of-the-art methods in natural image denoising. In recent years, much progress has been made on low-rank modeling and it has achieved great successes in various image analysis problems. In this paper, we propose a new denoising algorithm based on iterative low-rank regularized collaborative filtering of image patches under a nonlocal framework. This collaborative filtering is formulated as recovery of low rank matrices from noisy data. Based on recent results from random matrix theory, an optimal singular value shrinkage operator is applied to efficiently solve this problem. Our experimental results demonstrate the superior denoising performance of the proposed algorithm as compared with the state-of-the-art methods.