Weighted Schatten <i>p</i>-Norm Low Rank Error Constraint for Image Denoising

• Main Authors: Jiucheng Xu, Yihao Cheng, Yuanyuan Ma
• Format: Article
• Language: English
• Published: MDPI AG 2021-01-01
• Series: Entropy
• Subjects: image denoising; low rank representation; weighted schatten p-norm; low rank error constraint
• Online Access: https://www.mdpi.com/1099-4300/23/2/158

Traditional image denoising algorithms obtain prior information from noisy images that are directly based on low rank matrix restoration, which pays little attention to the nonlocal self-similarity errors between clear images and noisy images. This paper proposes a new image denoising algorithm based on low rank matrix restoration in order to solve this problem. The proposed algorithm introduces the non-local self-similarity error between the clear image and noisy image into the weighted Schatten <i>p</i>-norm minimization model using the non-local self-similarity of the image. In addition, the low rank error is constrained by using Schatten <i>p</i>-norm to obtain a better low rank matrix in order to improve the performance of the image denoising algorithm. The results demonstrate that, on the classic data set, when comparing with block matching 3D filtering (BM3D), weighted nuclear norm minimization (WNNM), weighted Schatten <i>p</i>-norm minimization (WSNM), and FFDNet, the proposed algorithm achieves a higher peak signal-to-noise ratio, better denoising effect, and visual effects with improved robustness and generalization.