Augmented Lagrangian Alternating Direction Method for Tensor RPCA
Received:February 03, 2017  Revised:March 24, 2017
Key Word: tensor RPCA   alternating direction method   augmented Lagrangian function   high-order SVD  
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant Nos.61572099; 61320106008; 91230103) and National Science and Technology Major Project (Grant Nos.2013ZX04005021; 2014ZX04001011).
Author NameAffiliation
Ruru HAO School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China 
Zhixun SU School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China 
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Abstract:
      Tensor robust principal component analysis (TRPCA) problem aims to separate a low-rank tensor and a sparse tensor from their sum. This problem has recently attracted considerable research attention due to its wide range of potential applications in computer vision and pattern recognition. In this paper, we propose a new model to deal with the TRPCA problem by an alternation minimization algorithm along with two adaptive rank-adjusting strategies. For the underlying low-rank tensor, we simultaneously perform low-rank matrix factorizations to its all-mode matricizations; while for the underlying sparse tensor, a soft-threshold shrinkage scheme is applied. Our method can be used to deal with the separation between either an exact or an approximate low-rank tensor and a sparse one. We established the subsequence convergence of our algorithm in the sense that any limit point of the iterates satisfies the KKT conditions. When the iteration stops, the output will be modified by applying a high-order SVD approach to achieve an exactly low-rank final result as the accurate rank has been calculated. The numerical experiments demonstrate that our method could achieve better results than the compared methods.
Citation:
DOI:10.3770/j.issn:2095-2651.2017.03.014
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