Robust Low-Rank Tensor Recovery Using a Self-Adaptive Learnable Weighted Tensor Total Variation Method

doi:10.1002/nla.70013

	Robust Low-Rank Tensor Recovery Using a Self-Adaptive Learnable Weighted Tensor Total Variation Method
	Yang, Fanyin 1; Zheng, Bing 1; Zhao, Ruijuan2 ; Liu, Guimin 1
	2025-04
发表期刊	NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS
卷号	32 期号:2
摘要	Tensor robust principal component analysis (TRPCA) is a fundamental technique for recovering low-rank and sparse components from multidimensional data corrupted by noise or outliers. Recently, a method based on tensor-correlated total variation (t-CTV) was introduced, where t-CTV serves as a regularizer to simultaneously encode both the low-rank structure and local smoothness of the tensor, eliminating the need for parameter tuning. However, this method may introduce bias when encoding the low-rank structure of the data, which limits its recovery performance. To address this limitation, we propose a novel weighted t-CTV pseudo-norm that more accurately captures both the low-rank structure and local smoothness of a tensor. Building on this, we introduce the self-adaptive learnable weighted t-CTV (SALW-CTV) method for TRPCA. In contrast to traditional TRPCA methods that use the suboptimal & ell;(1)-norm for noise filtering, our method incorporates an improved weighted & ell;(1)-norm to further enhance recovery performance. Additionally, we design a data-driven, self-adaptive learnable weight selection scheme that dynamically determines the optimal weights for both the weighted t-CTV and the weighted & ell;(1)-norm. To solve the resulting optimization problem, we develop an efficient algorithm and analyze its computational complexity and convergence. Extensive numerical experiments on various datasets validate the superior performance of our proposed method compared to existing state-of-the-art approaches.
关键词	local smoothness low-rank prior self-adaptive learnable weight selection scheme tensor robust principal component analysis weighted & ell (1)-norm weighted t-CTV
DOI	10.1002/nla.70013
收录类别	SCIE
ISSN	1070-5325
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:001447842500001
出版者	WILEY
原始文献类型	Article
EISSN	1099-1506
文献类型	期刊论文
条目标识符	http://ir.lzufe.edu.cn/handle/39EH0E1M/38932
专题	信息工程与人工智能学院
通讯作者	Zheng, Bing
作者单位	1.Lanzhou Univ, Sch Math & Stat, Lanzhou, Gansu, Peoples R China; 2.Lanzhou Univ Finance & Econ, Sch Informat Engn & Artificial Intelligence, Lanzhou, Gansu, Peoples R China
推荐引用方式 GB/T 7714	Yang, Fanyin,Zheng, Bing,Zhao, Ruijuan,et al. Robust Low-Rank Tensor Recovery Using a Self-Adaptive Learnable Weighted Tensor Total Variation Method[J]. NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS,2025,32(2).
APA	Yang, Fanyin,Zheng, Bing,Zhao, Ruijuan,&Liu, Guimin.(2025).Robust Low-Rank Tensor Recovery Using a Self-Adaptive Learnable Weighted Tensor Total Variation Method.NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS,32(2).
MLA	Yang, Fanyin,et al."Robust Low-Rank Tensor Recovery Using a Self-Adaptive Learnable Weighted Tensor Total Variation Method".NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS 32.2(2025).