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Adaptive total variation and second-order total variation-based model for low-rank tensor completion

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Abstract

Recently, low-rank regularization has achieved great success in tensor completion. However, only considering the global low-rankness is not sufficient, especially for a low sampling rate (SR). Total variation (TV) is introduced into low-rank tensor completion (LRTC) problem to promote the local smoothness by incorporating the first-order derivatives information. However, TV usually leads to undesirable staircase effects. To alleviate these staircase effects, we suggest a first- and second-order TV-based parallel matrix factorization model for LRTC problem, which integrates the local smoothness and global low-rankness by simultaneously exploiting the first- and second-order derivatives information. To solve the proposed model, an efficient proximal alternating optimization (PAO)-based algorithm is developed with theoretical guarantee. Moreover, we suggest a regularization parameter selection strategy to automatically update two regularization parameters, which is able to take advantage of the best properties of each of the two regularization terms. Extensive experiments on different tensor data show the superiority of the proposed method over other methods, particularly for extremely low SRs.

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Funding

This work is financially supported by the National Natural Science Foundation of China (61772003, 61876203) and the Fundamental Research Funds for the Central Universities (31020180QD126).

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Authors and Affiliations

  1. School of Mathematical Sciences/Research Center for Image and Vision Computing, University of Electronic Science and Technology of China, Chengdu, 611731, Sichuan, People’s Republic of China

    Xin Li, Ting-Zhu Huang, Xi-Le Zhao, Yu-Bang Zheng & Liang-Jian Deng

  2. School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an, 710072, Shaanxi, People’s Republic of China

    Teng-Yu Ji

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  1. Xin Li
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  2. Ting-Zhu Huang
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Correspondence to Ting-Zhu Huang or Xi-Le Zhao.

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Li, X., Huang, TZ., Zhao, XL. et al. Adaptive total variation and second-order total variation-based model for low-rank tensor completion. Numer Algor 86, 1–24 (2021). https://doi.org/10.1007/s11075-020-00876-y

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