A nonlinear high-order transformations-based method for high-order tensor completion

Luo, Linhong1; Tu, Zhihui1; Lu, Jian1,2,3; Wang, Chao2,4; Xu, Chen1,2

2024-12-01

10.1016/j.sigpro.2024.109514

SIGNAL PROCESSING   影响因子和分区

0165-1684

1872-7557

The high-order tensor nuclear norm model (HTNN) has recently shown promising results in tensor completion problems. The HTNN-based approaches rely on the low-rank structure of tensor slices during reversible transformations. However, under reversible transformations, the low-rank configuration within the slice- wise modality of the tensor's structure is not markedly pronounced. In order to more effectively describe the low-rank characteristics, we propose a model based on the nonlinear high-order transform-based tensor nuclear norm (NHTNN). Specifically, our framework consists of a linearly semi-orthogonal transformation along the high-dimensional modality and an element-wise nonlinear transformation. We introduce a model for tensor completion, grounded in the suggested measure of tensor low-rank, i.e., NHTNN. Utilizing this non-convex nonlinear model, we formulate a proximal alternating minimization (PAM) algorithm, establishing its convergence through a rigorous proof. In experiments on datasets such as hyperspectral videos (HSVs) and color videos (CVs), our approach demonstrates superior quantitative numerical results and qualitative visual effects compared to cutting-edge tensor completion techniques.

Nonlinear transform Sparsity measure High-order tensor nuclear norm Tensor completion

SCI ; EI

英语

其他

National Natural Science Foundation of China["U21A20455","12326619","61972265","62372302","11871348","12201286"] ; Natural Science Foundation of Guangdong Province of China["2020B1515310008","2023A1515011691","2024A1515011913"] ; Educational Commission of Guangdong Province of China[2019KZDZX1007] ; Shenzhen Science and Technology Program, China[20231115165836001] ; HKRGC, China[CityU11301120] ; National Key R&D Program of China[2023YFA1011400] ; Shenzhen Fundamental Research Program, China[JCYJ20220818100602005]

Engineering

Engineering, Electrical & Electronic

WOS:001274618800001

ELSEVIER

ENGINEERING

Web of Science

1.Shenzhen Univ, Sch Math Sci, Shenzhen Key Lab Adv Machine Learning & Applicat, Shenzhen 518060, Peoples R China
2.Natl Ctr Appl Math Shenzhen NCAMS, Shenzhen 518055, Peoples R China
3.Pazhou Lab, Guangzhou 510320, Peoples R China
4.Southern Univ Sci & Technol, Dept Stat & Data Sci, Shenzhen 518005, Peoples R China

Luo, Linhong,Tu, Zhihui,Lu, Jian,et al. A nonlinear high-order transformations-based method for high-order tensor completion[J]. SIGNAL PROCESSING,2024,225.

Luo, Linhong,Tu, Zhihui,Lu, Jian,Wang, Chao,&Xu, Chen.(2024).A nonlinear high-order transformations-based method for high-order tensor completion.SIGNAL PROCESSING,225.

Luo, Linhong,et al."A nonlinear high-order transformations-based method for high-order tensor completion".SIGNAL PROCESSING 225(2024).