TY - GEN
T1 - Weighted nuclear norm minimization with application to image denoising
AU - Gu, Shuhang
AU - Zhang, Lei
AU - Zuo, Wangmeng
AU - Feng, Xiangchu
PY - 2014/9/24
Y1 - 2014/9/24
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84911360659&partnerID=8YFLogxK
U2 - 10.1109/CVPR.2014.366
DO - 10.1109/CVPR.2014.366
M3 - Conference article published in proceeding or book
AN - SCOPUS:84911360659
T3 - Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
SP - 2862
EP - 2869
BT - Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
PB - IEEE Computer Society
T2 - 27th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2014
Y2 - 23 June 2014 through 28 June 2014
ER -