Tensor Robust Principal Component Analysis via Non-convex Low-Rank Approximation Based on the Laplace Function

doi:10.1007/s42967-024-00381-2

Communications on Applied Mathematics and Computation ›› 2025, Vol. 7 ›› Issue (5): 1684-1703.doi: 10.1007/s42967-024-00381-2

• ORIGINAL PAPERS • 上一篇

Tensor Robust Principal Component Analysis via Non-convex Low-Rank Approximation Based on the Laplace Function

Hai-Fei Zeng, Xiao-Fei Peng, Wen Li

School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, Guangdong, China

收稿日期:2023-11-30 修回日期:2024-02-02 接受日期:2024-02-04 出版日期:2024-07-08 发布日期:2024-07-08
通讯作者: Xiao-Fei Peng,E-mail:pxf6628@m.scnu.edu.cn E-mail:pxf6628@m.scnu.edu.cn

Tensor Robust Principal Component Analysis via Non-convex Low-Rank Approximation Based on the Laplace Function

Hai-Fei Zeng, Xiao-Fei Peng, Wen Li

School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, Guangdong, China

Received:2023-11-30 Revised:2024-02-02 Accepted:2024-02-04 Online:2024-07-08 Published:2024-07-08
Contact: Xiao-Fei Peng,E-mail:pxf6628@m.scnu.edu.cn E-mail:pxf6628@m.scnu.edu.cn

摘要/Abstract

摘要： Recently, the tensor robust principal component analysis (TRPCA), aiming to recover the true low-rank tensor from noisy data, has attracted considerable attention. In this paper, we solve the TRPCA problem under the framework of the tensor singular value decomposition (t-SVD). Since the convex relaxation approaches have some limitations, we establish a new non-convex TRPCA model by introducing the non-convex tensor rank approximation based on the Laplace function via the weighted l_p-norm regularization. An efficient algorithm based on the alternating direction method of multipliers (ADMM) is developed to solve the proposed model. We further prove that the constructed sequence converges to the desirable Karush-Kuhn-Tucker point. Experimental results show that the proposed approach outperforms various latest approaches in the literature.

关键词: Tensor robust principal component analysis (TRPCA), Laplace function, Weighted l_p-norm, Alternating direction method of multipliers (ADMM), Tensor singular value decomposition (t-SVD)

Abstract: Recently, the tensor robust principal component analysis (TRPCA), aiming to recover the true low-rank tensor from noisy data, has attracted considerable attention. In this paper, we solve the TRPCA problem under the framework of the tensor singular value decomposition (t-SVD). Since the convex relaxation approaches have some limitations, we establish a new non-convex TRPCA model by introducing the non-convex tensor rank approximation based on the Laplace function via the weighted l_p-norm regularization. An efficient algorithm based on the alternating direction method of multipliers (ADMM) is developed to solve the proposed model. We further prove that the constructed sequence converges to the desirable Karush-Kuhn-Tucker point. Experimental results show that the proposed approach outperforms various latest approaches in the literature.

Key words: Tensor robust principal component analysis (TRPCA), Laplace function, Weighted l_p-norm, Alternating direction method of multipliers (ADMM), Tensor singular value decomposition (t-SVD)

Hai-Fei Zeng, Xiao-Fei Peng, Wen Li. Tensor Robust Principal Component Analysis via Non-convex Low-Rank Approximation Based on the Laplace Function[J]. Communications on Applied Mathematics and Computation, 2025, 7(5): 1684-1703.

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Tensor Robust Principal Component Analysis via Non-convex Low-Rank Approximation Based on the Laplace Function

Tensor Robust Principal Component Analysis via Non-convex Low-Rank Approximation Based on the Laplace Function

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