{"title":"Fully-connected tensor network decomposition with gradient factors regularization for robust tensor completion","authors":"Bin Xiao, Heng-Chao Li, Rui Wang, Yu-Bang Zheng","doi":"10.1016/j.sigpro.2025.109933","DOIUrl":null,"url":null,"abstract":"<div><div>The robust tensor completion (RTC) problem focuses on recovering both a low-rank and a sparse component from noisy and incomplete observational data. The fully-connected tensor network (FCTN) decomposition has demonstrated remarkable effectiveness in capturing the global low-rank structure in high-dimensional data. However, prior research utilizing FCTN decomposition has predominantly considered global data correlations, which may lead to suboptimal recovery by ignoring local continuity. In this study, we present a model leveraging factor-regularized FCTN decomposition to tackle the RTC problem. Specifically, the global low-rank property is captured via FCTN decomposition, while the local continuity is enforced through constraints on the FCTN factors. Furthermore, to solve the proposed model, we develop a proximal alternating minimization (PAM) algorithm and prove its convergence theoretically. Finally, the effectiveness of the proposed method is validated through numerical experiments conducted on both color and hyperspectral video data.</div></div>","PeriodicalId":49523,"journal":{"name":"Signal Processing","volume":"233 ","pages":"Article 109933"},"PeriodicalIF":3.4000,"publicationDate":"2025-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Signal Processing","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0165168425000489","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ENGINEERING, ELECTRICAL & ELECTRONIC","Score":null,"Total":0}
引用次数: 0
Abstract
The robust tensor completion (RTC) problem focuses on recovering both a low-rank and a sparse component from noisy and incomplete observational data. The fully-connected tensor network (FCTN) decomposition has demonstrated remarkable effectiveness in capturing the global low-rank structure in high-dimensional data. However, prior research utilizing FCTN decomposition has predominantly considered global data correlations, which may lead to suboptimal recovery by ignoring local continuity. In this study, we present a model leveraging factor-regularized FCTN decomposition to tackle the RTC problem. Specifically, the global low-rank property is captured via FCTN decomposition, while the local continuity is enforced through constraints on the FCTN factors. Furthermore, to solve the proposed model, we develop a proximal alternating minimization (PAM) algorithm and prove its convergence theoretically. Finally, the effectiveness of the proposed method is validated through numerical experiments conducted on both color and hyperspectral video data.
期刊介绍:
Signal Processing incorporates all aspects of the theory and practice of signal processing. It features original research work, tutorial and review articles, and accounts of practical developments. It is intended for a rapid dissemination of knowledge and experience to engineers and scientists working in the research, development or practical application of signal processing.
Subject areas covered by the journal include: Signal Theory; Stochastic Processes; Detection and Estimation; Spectral Analysis; Filtering; Signal Processing Systems; Software Developments; Image Processing; Pattern Recognition; Optical Signal Processing; Digital Signal Processing; Multi-dimensional Signal Processing; Communication Signal Processing; Biomedical Signal Processing; Geophysical and Astrophysical Signal Processing; Earth Resources Signal Processing; Acoustic and Vibration Signal Processing; Data Processing; Remote Sensing; Signal Processing Technology; Radar Signal Processing; Sonar Signal Processing; Industrial Applications; New Applications.