Bayesian Robust Fully-Connected Tensor Network Decomposition for Visual Data Denoising

Tensor Robust Principal Component Analysis (TRPCA) aims to recover low-rank and sparse components from the noisy tensor data, which has attracted significant attention in visual data denoising. However, existing CANDECOMP/PARAFAC (CP) and Tucker decomposition methods fail to fully exploit inter-dimensional correlations, thus exhibiting limited expressive power for complex multiway data. The tensor singular value decomposition (t-SVD) methods are constrained by their predefined fixed mode and are generally only applicable to third-order tensors. Tensor Train (TT) and Tensor Ring (TR) decompositions methods can partially capture higher-order interactions but are restricted by their linear chain structure in modeling intricate multiway relationships. Although recent studies leveraging Fully-Connected Tensor Network (FCTN) decomposition have mitigated these limitations, these methods still lack data adaptability, require extensive manual parameter tuning, and incur high computational costs. To mitigate these limitations, we propose the Bayesian Robust Fully-Connected Tensor Network called BRFCTN. Within this probabilistic framework, the interconnections between factor tensors are established through hierarchical sparse priors, thereby constructing a low FCTN-ranks learning model. For model estimation, an efficient variational Bayesian (VB) inference algorithm is developed that performs sequential parameter updates. Benefiting from the probabilistic modeling capabilities of the Bayesian framework, the proposed method learns low-rank structures in a data-driven manner. Extensive experiments across diverse visual datasets and multiple noise scenarios demonstrate that the proposed BRFCTN method outperforms state-of-the-art approaches in both effectiveness and robustness. The source code is released at https://github.com/hustlcl/BRFCTN.