Weighted Nuclear Norm Minimization with Application to Image Denoising

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Authors Shuhang Gu, Lei Zhang, Wangmeng Zuo, Xiangchu Feng
Journal/Conference Name Conference on Computer Vision and Pattern Recognition 2014
Paper Category
Paper Abstract As a convex relaxation of the low rank matrix factorization problem, the nuclear norm minimization has been attracting significant research interest in recent years. The standard nuclear norm minimization regularizes each sin-gular value equally to pursue the convexity of the objective function. However, this greatly restricts its capability and flexibility in dealing with many practical problems (e.g., denoising), where the singular values have clear physical meanings and should be treated differently. In this paper we study the weighted nuclear norm minimization (WNNM) problem, where the singular values are assigned different weights. The solutions of the WNNM problem are analyzed under different weighting conditions. We then apply the proposed WNNM algorithm to image denoising by exploiting the image nonlocal self-similarity. Experimental results clearly show that the proposed WNNM algorithm outperforms many state-of-the-art denoising algorithms such as BM3D in terms of both quantitative measure and visual perception quality.
Date of publication 2014
Code Programming Language MATLAB

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