Tensor completion using total variation and low-rank matrix factorization

In this paper, we study the problem of recovering a tensor with missing data. We propose a new model combining the total variation regularization and low-rank matrix factorization. A block coordinate decent (BCD) algorithm is developed to efficiently solve the proposed optimization model. We theoret...

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Bibliographic Details
Published in:Information sciences 2016-01, Vol.326, p.243-257
Main Authors: Ji, Teng-Yu, Huang, Ting-Zhu, Zhao, Xi-Le, Ma, Tian-Hui, Liu, Gang
Format: Article
Language:English
Subjects:
Algorithms
Block coordinate descent
Blocking
Factorization
Low-rank matrix factorization
Mathematical analysis
Mathematical models
Optimization
Regularization
Tensor completion
Tensors
Total variation
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Summary:In this paper, we study the problem of recovering a tensor with missing data. We propose a new model combining the total variation regularization and low-rank matrix factorization. A block coordinate decent (BCD) algorithm is developed to efficiently solve the proposed optimization model. We theoretically show that under some mild conditions, the algorithm converges to the coordinatewise minimizers. Experimental results are reported to demonstrate the effectiveness of the proposed model and the efficiency of the numerical scheme.
ISSN:0020-0255
1872-6291
DOI:10.1016/j.ins.2015.07.049