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Fully-connected tensor network decomposition with gradient factors regularization for robust tensor completion
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DOI：10.1016/j.sigpro.2025.109933.png)
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Abstract
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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.
Keywords:
Robust tensor completion
Local continuity
Proximal alternating minimization
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