Weighted nuclear norm minimization with application to image denoising

Shuhang Gu, Lei Zhang, Wangmeng Zuo, Xiangchu Feng

Research output: Chapter in book / Conference proceedingConference article published in proceeding or bookAcademic researchpeer-review

918 Citations (Scopus)

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 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.

Original languageEnglish
Title of host publicationProceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
PublisherIEEE Computer Society
Pages2862-2869
Number of pages8
ISBN (Electronic)9781479951178, 9781479951178
DOIs
Publication statusPublished - 24 Sep 2014
Event27th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2014 - Columbus, United States
Duration: 23 Jun 201428 Jun 2014

Publication series

NameProceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
ISSN (Print)1063-6919

Conference

Conference27th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2014
Country/TerritoryUnited States
CityColumbus
Period23/06/1428/06/14

ASJC Scopus subject areas

  • Software
  • Computer Vision and Pattern Recognition

Cite this