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Low-Rank Tensor Completion Using Matrix Factorization Based on Tensor Train Rank and Total Variation

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Abstract

Recently, the method called tensor completion by parallel matrix factorization via tensor train (TMac-TT) has achieved promising performance on estimating the missing information. TMac-TT, which borrows \(ket \ augmentation\) to transform a lower-order tensor into a higher-order tensor, suffers from serious block-artifacts. To tackle this issue, we build an optimization model combining low-rank matrix factorization based on tensor train (TT) rank and the total variation to retain the strength of TT rank and alleviate block-artifacts. We develop a block successive upper-bound minimization algorithm to solve the proposed model. Under some mild conditions, we theoretically prove that the proposed algorithm converges to the coordinatewise minimizers. Extensive numerical experiments illustrate the superiority of the proposed method over several existing state-of-the-art methods qualitatively and quantitatively.

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Acknowledgements

The authors would like to thank the anonymous referees and editor for their valuable remarks, questions, and comments that enabled the authors to improve this paper. This research is supported by the National Science Foundation of China (61772003, 61876203), the Fundamental Research Funds for the Central Universities (ZYGX2016J132, 31020180QD126), and Science Strength Promotion Programme of UESTC.

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, 611731, Sichuan, People’s Republic of China

    Meng Ding, Ting-Zhu Huang, Xi-Le Zhao & Jing-Hua Yang

  2. Department of Applied Mathematics, School of Science, Northwestern Polytechnical University, Xi’an, 710072, Shaanxi, People’s Republic of China

    Teng-Yu Ji

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  1. Meng Ding
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  2. Ting-Zhu Huang
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  4. Xi-Le Zhao
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Correspondence to Ting-Zhu Huang or Xi-Le Zhao.

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Ding, M., Huang, TZ., Ji, TY. et al. Low-Rank Tensor Completion Using Matrix Factorization Based on Tensor Train Rank and Total Variation. J Sci Comput 81, 941–964 (2019). https://doi.org/10.1007/s10915-019-01044-8

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