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Discrete Dynamics in Nature and Society
Volume 2014 (2014), Article ID 914963, 9 pages
Research Article

Mixture Augmented Lagrange Multiplier Method for Tensor Recovery and Its Applications

1Department of Transportation Engineering, Beijing Institute of Technology, Beijing 100081, China
2Integrated Information System Research Center, Institute of Automation, Chinese Academy of Sciences, Beijing 100190, China
3Marvell Semiconductor Inc., 5488 Marvell LN, Santa Clara, CA 95054, USA

Received 30 November 2013; Accepted 30 January 2014; Published 17 March 2014

Academic Editor: Huimin Niu

Copyright © 2014 Huachun Tan 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.


The problem of data recovery in multiway arrays (i.e., tensors) arises in many fields such as computer vision, image processing, and traffic data analysis. In this paper, we propose a scalable and fast algorithm for recovering a low--rank tensor with an unknown fraction of its entries being arbitrarily corrupted. In the new algorithm, the tensor recovery problem is formulated as a mixture convex multilinear Robust Principal Component Analysis (RPCA) optimization problem by minimizing a sum of the nuclear norm and the -norm. The problem is well structured in both the objective function and constraints. We apply augmented Lagrange multiplier method which can make use of the good structure for efficiently solving this problem. In the experiments, the algorithm is compared with the state-of-art algorithm both on synthetic data and real data including traffic data, image data, and video data.