Bayesian Fully-Connected Tensor Network for Hyperspectral-Multispectral Image Fusion

Tensor decomposition is a powerful tool for data analysis and has been extensively employed in the field of hyperspectral-multispectral image fusion (HMF). Existing tensor decomposition-based fusion methods typically rely on disruptive data vectorization/reshaping or impose rigid constraints on the arrangement of factor tensors, hindering the preservation of spatial-spectral structures and the modeling of cross-dimensional correlations. Although recent advances utilizing the Fully-Connected Tensor Network (FCTN) decomposition have partially alleviated these limitations, the process of reorganizing data into higher-order tensors still disrupts the intrinsic spatial-spectral structure. Furthermore, these methods necessitate extensive manual parameter tuning and exhibit limited robustness against noise and spatial degradation. To alleviate these issues, we propose the Bayesian FCTN (BFCTN) method. Within this probabilistic framework, a hierarchical sparse prior that characterizing the sparsity of physical elements, establishes connections between the factor tensors. This framework explicitly models the intrinsic physical coupling among spatial structures, spectral signatures, and local scene homogeneity. For model learning, we develop a parameter estimation method based on Variational Bayesian inference (VB) and the Expectation-Maximization (EM) algorithm, which significantly reduces the need for regularization parameter tuning. Extensive experiments demonstrate that BFCTN not only achieves state-of-the-art fusion accuracy and strong robustness but also exhibits practical applicability in complex real-world scenarios. The source code is available at: https://github.com/LinsongShan/BFCTN.