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Mathematical Problems in Engineering
Volume 2014, Article ID 656074, 8 pages
Research Article

A Generalized Robust Minimization Framework for Low-Rank Matrix Recovery

1College of Telecommunications and Information Engineering, Nanjing University of Posts and Telecommunications, Nanjing 210003, China
2School of Mathematics and Statistics, Nanjing Audit University, Nanjing 211815, China
3School of Computer Science and Communication, KTH Royal Institute of Technology, Stockholm 10044, Sweden

Received 18 January 2014; Accepted 23 April 2014; Published 6 May 2014

Academic Editor: Carlo Cattani

Copyright © 2014 Wen-Ze Shao 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.


This paper considers the problem of recovering low-rank matrices which are heavily corrupted by outliers or large errors. To improve the robustness of existing recovery methods, the problem is solved by formulating it as a generalized nonsmooth nonconvex minimization functional via exploiting the Schatten -norm and seminorm. Two numerical algorithms are provided based on the augmented Lagrange multiplier (ALM) and accelerated proximal gradient (APG) methods as well as efficient root-finder strategies. Experimental results demonstrate that the proposed generalized approach is more inclusive and effective compared with state-of-the-art methods, either convex or nonconvex.