Multi‐scale patches based image denoising using weighted nuclear norm minimisation

As a prior knowledge, non-local self-similarity (NSS) has been widely utilised in ill-posed problems. Actually, similar textures appear not only in a single scale, but also in different scales. Unlike most existing patch-based methods that only explore NSS in the same scale, a multi-scale patches based image denoising algorithm is proposed in this study. The authors have designed a multi-scale strategy to expand the search space of block-matching, which will increase the probability of finding more similar patches. After that, the weighted nuclear norm minimisation (WNNM) algorithm is employed to reveal latent clean patches. With the join of the multi-scale framework, the performance of WNNM can be improved. The proposed algorithm can be used to solve NSS-based image restoration tasks. In this study, mainly image denoising is studied, and its effectiveness is derived through experiments on widely used test images.