Fully-connected tensor network decomposition for robust tensor completion problem

The robust tensor completion (RTC) problem, which aims to reconstruct a low-rank from partially observed contaminated by sparse tensor, has received increasing attention. In this paper, leveraging the superior expression of fully-connected network (FCTN) decomposition, we propose $\textbf{FCTN}$-based $\textbf{r}$obust $\textbf{c}$onvex optimization model (RC-FCTN) for RTC problem. Then, rigorously establish exact recovery guarantee RC-FCTN. For solving constrained RC-FCTN, develop an alternating direction method multipliers (ADMM)-based algorithm, enjoys global convergence guarantee. Moreover, suggest $\textbf{n}$on$\textbf{c}$onvex (RNC-FCTN) A proximal minimization (PAM)-based algorithm is developed solve proposed RNC-FCTN. Meanwhile, theoretically derive PAM-based algorithm. Comprehensive numerical experiments in several applications, such as video and background subtraction, demonstrate that methods are state-of-the-art methods.