Fully-Connected Tensor Network Decomposition for Robust Tensor Completion Problem

• URL: http://arxiv.org/abs/2110.08754v1
• Date: Sun, 17 Oct 2021 08:12:50 GMT
• Title: Fully-Connected Tensor Network Decomposition for Robust Tensor Completion Problem
• Authors: Yun-Yang Liu, Xi-Le Zhao, Guang-Jing Song, Yu-Bang Zheng, Ting-Zhu Huang
• Abstract summary: We propose a $textbfFCTN$-based $textbfr$obust $textbfc$onvex optimization model (RC-FCTN) for the RTC problem. For solving the constrained optimization model RC-FCTN, we develop an alternating direction method of multipliers (ADMM)-based algorithm. A proximal alternating minimization (PAM)-based algorithm is developed to solve the proposed RNC-FCTN.
• Score: 9.580645211308557
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The robust tensor completion (RTC) problem, which aims to reconstruct a low-rank tensor from partially observed tensor contaminated by a sparse tensor, has received increasing attention. In this paper, by leveraging the superior expression of the fully-connected tensor network (FCTN) decomposition, we propose a $\textbf{FCTN}$-based $\textbf{r}$obust $\textbf{c}$onvex optimization model (RC-FCTN) for the RTC problem. Then, we rigorously establish the exact recovery guarantee for the RC-FCTN. For solving the constrained optimization model RC-FCTN, we develop an alternating direction method of multipliers (ADMM)-based algorithm, which enjoys the global convergence guarantee. Moreover, we suggest a $\textbf{FCTN}$-based $\textbf{r}$obust $\textbf{n}$on$\textbf{c}$onvex optimization model (RNC-FCTN) for the RTC problem. A proximal alternating minimization (PAM)-based algorithm is developed to solve the proposed RNC-FCTN. Meanwhile, we theoretically derive the convergence of the PAM-based algorithm. Comprehensive numerical experiments in several applications, such as video completion and video background subtraction, demonstrate that proposed methods are superior to several state-of-the-art methods.

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