Image Denoising via Nonlocal Low Rank Approximation With Local Structure Preserving

Abstract

The nuclear norm minimization method emerged from a patch-based low-rank model leads to an excellent image denoising performance, where the non-local self-similarity over image patches is exploited. However, natural images are normally with complex and irregular image patches, which cannot be well represented using only a low-rank model, and thus most of them suffer from the over-penalty problem especially for images with lots of local irregular structures (e.g., fine details or sharp edges), and then results in over-smoothing problem after denoising. On the other hand, in order to represent the irregular components, edges defined over pixel level are often exploited. While the total variation (TV) is a well-known prior to remove noises and preserve edges, it might yield undesired staircase artifacts. The total generalized variation (TGV), a generalization of TV, can largely alleviate such staircase artifacts. Consequently, in order to deal with the over-smoothing problem aroused by a low-rank model, we propose a re-weighted TGV regularized nuclear norm minimization model for local structure preserving image denoising. Thanks to the split Bregman method, our proposed model can be effectively solved. A re-weighted strategy is developed to adaptively update the weight parameters of TGV regularization. The encouraging experimental results on noisy images demonstrate the effectiveness of our proposed method.