Fully-connected tensor network decomposition with gradient factors regularization for robust tensor completion

Bin Xiao, Heng-Chao Li, Rui Wang, Yu-Bang Zheng

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.