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Abstract and Applied Analysis
Volume 2014, Article ID 765782, 8 pages
Research Article

Linear Total Variation Approximate Regularized Nuclear Norm Optimization for Matrix Completion

Xu Han,1,2 Jiasong Wu,1,2,3,4 Lu Wang,2,3,4 Yang Chen,1,2,3 Lotfi Senhadji,2,3,4 and Huazhong Shu1,2

1Laboratory of Image Science and Technology, Southeast University, Nanjing 210096, China
2Centre de Recherche en Information Médicale Sino-français (CRIBs), France
3INSERM, U1099, Rennes 35000, France
4Université de Rennes 1, LTSI, Rennes 35042, France

Received 15 February 2014; Accepted 7 May 2014; Published 28 May 2014

Academic Editor: Zhiwu Liao

Copyright © 2014 Xu Han et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Matrix completion that estimates missing values in visual data is an important topic in computer vision. Most of the recent studies focused on the low rank matrix approximation via the nuclear norm. However, the visual data, such as images, is rich in texture which may not be well approximated by low rank constraint. In this paper, we propose a novel matrix completion method, which combines the nuclear norm with the local geometric regularizer to solve the problem of matrix completion for redundant texture images. And in this paper we mainly consider one of the most commonly graph regularized parameters: the total variation norm which is a widely used measure for enforcing intensity continuity and recovering a piecewise smooth image. The experimental results show that the encouraging results can be obtained by the proposed method on real texture images compared to the state-of-the-art methods.