Weighted Nuclear Norm Minimization with Application to Image Denoising

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 singular value equally to pursue the convexity of the objective function. Howe...

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Bibliographic Details
Published in:2014 IEEE Conference on Computer Vision and Pattern Recognition pp. 2862 - 2869
Main Authors: Gu, Shuhang, Zhang, Lei, Zuo, Wangmeng, Feng, Xiangchu
Format: Conference Proceeding Journal Article
Language:English
Published: IEEE 01.06.2014
Subjects:
Algorithms
Approximation algorithms
Approximation methods
Computer vision
Image denoising
Mathematical models
Minimization
Noise reduction
Norms
Optimization
Pattern recognition
Vectors
ISSN:1063-6919, 1063-6919
Online Access:Get full text
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Summary: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 singular 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.
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ISSN:1063-6919
1063-6919
DOI:10.1109/CVPR.2014.366