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Low-rank tensor train for tensor robust principal component analysis

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  • Yang, Jing-Hua
  • Zhao, Xi-Le
  • Ji, Teng-Yu
  • Ma, Tian-Hui
  • Huang, Ting-Zhu

Abstract

Recently, tensor train rank, defined by a well-balanced matricization scheme, has been shown the powerful capacity to capture the hidden correlations among different modes of a tensor, leading to great success in tensor completion problem. Most of the high-dimensional data in the real world are more likely to be grossly corrupted with sparse noise. In this paper, based on tensor train rank, we consider a new model for tensor robust principal component analysis which aims to recover a low-rank tensor corrupted by sparse noise. The alternating direction method of multipliers algorithm is developed to solve the proposed model. A tensor augmentation tool called ket augmentation is used to convert lower-order tensors to higher-order tensors to enhance the performance of our method. Experiments of simulated data show the superiority of the proposed method in terms of PSNR and SSIM values. Moreover, experiments of the real rain streaks removal and the real stripe noise removal also illustrate the effectiveness of the proposed method.

Suggested Citation

  • Yang, Jing-Hua & Zhao, Xi-Le & Ji, Teng-Yu & Ma, Tian-Hui & Huang, Ting-Zhu, 2020. "Low-rank tensor train for tensor robust principal component analysis," Applied Mathematics and Computation, Elsevier, vol. 367(C).
    • Handle: RePEc:eee:apmaco:v:367:y:2020:i:c:s0096300319307751
    DOI: 10.1016/j.amc.2019.124783
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    References listed on IDEAS

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    1. Chen, Dali & Chen, YangQuan & Xue, Dingyu, 2015. "Fractional-order total variation image denoising based on proximity algorithm," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 537-545.
    2. Ding, Meng & Huang, Ting-Zhu & Wang, Si & Mei, Jin-Jin & Zhao, Xi-Le, 2019. "Total variation with overlapping group sparsity for deblurring images under Cauchy noise," Applied Mathematics and Computation, Elsevier, vol. 341(C), pages 128-147.
    3. Carl Eckart & Gale Young, 1936. "The approximation of one matrix by another of lower rank," Psychometrika, Springer;The Psychometric Society, vol. 1(3), pages 211-218, September.
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    Cited by:

    1. Ding, Meng & Huang, Ting-Zhu & Ma, Tian-Hui & Zhao, Xi-Le & Yang, Jing-Hua, 2020. "Cauchy noise removal using group-based low-rank prior," Applied Mathematics and Computation, Elsevier, vol. 372(C).
    2. Wu, Tingting & Ng, Michael K. & Zhao, Xi-Le, 2021. "Sparsity reconstruction using nonconvex TGpV-shearlet regularization and constrained projection," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    3. Fanhua Shang & Yuanyuan Liu & Fanjie Shang & Hongying Liu & Lin Kong & Licheng Jiao, 2020. "A Unified Scalable Equivalent Formulation for Schatten Quasi-Norms," Mathematics, MDPI, vol. 8(8), pages 1-19, August.
    4. Wang, Yugang & Huang, Ting-Zhu & Zhao, Xi-Le & Deng, Liang-Jian & Ji, Teng-Yu, 2020. "A convex single image dehazing model via sparse dark channel prior," Applied Mathematics and Computation, Elsevier, vol. 375(C).
    5. Keren Li & Sergey Utyuzhnikov, 2023. "Tensor Train-Based Higher-Order Dynamic Mode Decomposition for Dynamical Systems," Mathematics, MDPI, vol. 11(8), pages 1-14, April.
    6. Karim Ennouri & Slim Smaoui & Mohamed Ali Triki, 2021. "Detection of Urban and Environmental Changes via Remote Sensing," Circular Economy and Sustainability, Springer, vol. 1(4), pages 1423-1437, December.

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