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Tensor robust principal component analysis with total generalized variation for high-dimensional data recovery

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Listed:
  • Xu, Zhi
  • Yang, Jing-Hua
  • Wang, Chuan-long
  • Wang, Fusheng
  • Yan, Xi-hong

Abstract

In the past few years, tensor robust principal component analysis (TRPCA) which is based on tensor singular value decomposition (t-SVD) has got a lot of attention in recovering low-rank tensor corrupted by sparse noise. However, most TRPCA methods only consider the global structure of the image, ignoring the local details and sharp edge information of the image, resulting in the unsatisfactory restoration results. In this paper, to fully preserve the local details and edge information of the image, we propose a new TRPCA method by introducing a total generalized variation (TGV) regularization. The proposed method can simultaneously explore the global and local prior information of high-dimensional data. Specifically, the tensor nuclear norm (TNN) is employed to develop the global structure feature. Moreover, we introduce the TGV, a higher-order generalization of total variation (TV), to preserve the local details and edges of the underlying image. Subsequently, the alternating direction method of multiplier (ADMM) algorithm is introduced to solve the proposed model. Sufficient experiments on color images and videos have demonstrated that our method is superior to other comparison methods.

Suggested Citation

  • Xu, Zhi & Yang, Jing-Hua & Wang, Chuan-long & Wang, Fusheng & Yan, Xi-hong, 2024. "Tensor robust principal component analysis with total generalized variation for high-dimensional data recovery," Applied Mathematics and Computation, Elsevier, vol. 483(C).
    • Handle: RePEc:eee:apmaco:v:483:y:2024:i:c:s0096300324004417
    DOI: 10.1016/j.amc.2024.128980
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    References listed on IDEAS

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    1. 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).
    2. Jushan Bai & Junlong Feng, 2019. "Robust Principal Component Analysis with Non-Sparse Errors," Papers 1902.08735, arXiv.org, revised Nov 2019.
    3. Zhang, Shuang & Han, Le, 2023. "Robust tensor recovery with nonconvex and nonsmooth regularization," Applied Mathematics and Computation, Elsevier, vol. 438(C).
    4. Liao, Shenghai & Fu, Shujun & Li, Yuliang & Han, Hongbin, 2023. "Image inpainting using non-convex low rank decomposition and multidirectional search," Applied Mathematics and Computation, Elsevier, vol. 452(C).
    5. Shama, Mu-Ga & Huang, Ting-Zhu & Liu, Jun & Wang, Si, 2016. "A convex total generalized variation regularized model for multiplicative noise and blur removal," Applied Mathematics and Computation, Elsevier, vol. 276(C), pages 109-121.
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