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A New Tensor Multi-rank Approximation with Total Variation Regularization for Tensor Completion

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Abstract

In this paper, we present a novel tensor completion model which combines the Laplace function and an anisotropic total variation regularization. The Laplace function is utilized to approximate the tensor multi-rank, and the total variation regularization is added to improve the local piecewise smoothness and preserve the edges of the restored tensor data. An efficient alternating direction method of multipliers is proposed to tackle the tensor completion model, and its convergence theorem is also derived. Extensive experimental results on color images, videos, multispectral images and magnetic resonance imaging data show the efficiency and effectiveness of the proposed method.

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Enquiries about data availability should be directed to the authors.

Notes

  1. Available from: http://sipi.usc.edu/database/database.php.

  2. Available from: http://trace.eas.asu.edu/yuv/.

  3. Available from: https://www.cs.columbia.edu/CAVE/databases/multispectral/.

  4. Available from: https://brainweb.bic.mni.mcgill.ca/brainweb.

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Acknowledgements

The authors thank the editor and the reviewers for the constructive and helpful comments on the revision of this article. The authors would like to thank Prof. Qing-Wen Wang of Department of Mathematics, Shanghai University for helpful discussions on the tensor completion problem, which led to an improvement of the paper.

Funding

The work was supported by the National Natural Science Foundation of China (No. 12201149, 12261026), the Natural Science Foundation of Guangxi Province (No. 2017GXNSFBA198082) and the Innovation Project of GUET Graduate Education (No. 2021YCXS113, 2022YCXS147).

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Authors and Affiliations

  1. College of Mathematics and Computational Science, Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, Guilin University of Electronic Technology, Guilin, 541004, People’s Republic of China

    Shan-Qi Duan & Xue-Feng Duan

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

    Xi-Le Zhao

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  1. Shan-Qi Duan
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Correspondence to Xue-Feng Duan.

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The work was supported by the National Natural Science Foundation of China (No. 12201149, 12261026), the Natural Science Foundation of Guangxi Province (No. 2017GXNSFBA198082) and the Innovation Project of GUET Graduate Education (No. 2021YCXS113, 2022YCXS147).

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Duan, SQ., Duan, XF. & Zhao, XL. A New Tensor Multi-rank Approximation with Total Variation Regularization for Tensor Completion. J Sci Comput 93, 61 (2022). https://doi.org/10.1007/s10915-022-02005-4

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