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Tensor Factorization with Total Variation and Tikhonov Regularization for Low-Rank Tensor Completion in Imaging Data

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Abstract

The main aim of this paper is to study tensor factorization for low-rank tensor completion in imaging data. Due to the underlying redundancy of real-world imaging data, the low-tubal-rank tensor factorization (the tensor–tensor product of two factor tensors) can be used to approximate such tensor very well. Motivated by the spatial/temporal smoothness of factor tensors in real-world imaging data, we propose to incorporate a hybrid regularization combining total variation and Tikhonov regularization into low-tubal-rank tensor factorization model for low-rank tensor completion problem. We also develop an efficient proximal alternating minimization (PAM) algorithm to tackle the corresponding minimization problem and establish a global convergence of the PAM algorithm. Numerical results on color images, color videos, and multispectral images are reported to illustrate the superiority of the proposed method over competing methods.

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Notes

  1. http://trace.eas.asu.edu/yuv/.

  2. http://www.cs.columbia.edu/CAVE/databases/multispectral/.

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Authors and Affiliations

  1. Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong

    Xue-Lei Lin

  2. Department of Mathematics, The University of Hong Kong, Pokfulam, Hong Kong

    Michael K. Ng

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

    Xi-Le Zhao

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  1. Xue-Lei Lin
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Correspondence to Xi-Le Zhao.

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The research is supported by research grants HKRGC GRF (12306616, 12200317, 12300519, 12300218), HKU Grant (104005583), and NSFC (61876203, 61772003, 11801479)

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Lin, XL., Ng, M.K. & Zhao, XL. Tensor Factorization with Total Variation and Tikhonov Regularization for Low-Rank Tensor Completion in Imaging Data. J Math Imaging Vis 62, 900–918 (2020). https://doi.org/10.1007/s10851-019-00933-9

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