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Mathematical Problems in Engineering
Volume 2014, Article ID 937560, 17 pages
http://dx.doi.org/10.1155/2014/937560
Research Article

Truncated Nuclear Norm Minimization for Image Restoration Based on Iterative Support Detection

School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China

Received 20 June 2014; Accepted 21 August 2014; Published 17 November 2014

Academic Editor: Chien-Yu Lu

Copyright © 2014 Yilun Wang and Xinhua Su. 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.

Abstract

Recovering a large matrix from limited measurements is a challenging task arising in many real applications, such as image inpainting, compressive sensing, and medical imaging, and these kinds of problems are mostly formulated as low-rank matrix approximation problems. Due to the rank operator being nonconvex and discontinuous, most of the recent theoretical studies use the nuclear norm as a convex relaxation and the low-rank matrix recovery problem is solved through minimization of the nuclear norm regularized problem. However, a major limitation of nuclear norm minimization is that all the singular values are simultaneously minimized and the rank may not be well approximated (Hu et al., 2013). Correspondingly, in this paper, we propose a new multistage algorithm, which makes use of the concept of Truncated Nuclear Norm Regularization (TNNR) proposed by Hu et al., 2013, and iterative support detection (ISD) proposed by Wang and Yin, 2010, to overcome the above limitation. Besides matrix completion problems considered by Hu et al., 2013, the proposed method can be also extended to the general low-rank matrix recovery problems. Extensive experiments well validate the superiority of our new algorithms over other state-of-the-art methods.