Generalized Logarithmic Tensor Nuclear Norm for Hyperspectral-Multispectral Image Fusion via Tensor Ring Decomposition

The fusion of a low-spatial-resolution hyperspectral image (LR-HSI) and a high-spatial-resolution multispectral image (HR-MSI) is an effective way to generate a high-resolution hyperspectral image (HR-HSI). In recent years, methods based on tensor ring (TR) decomposition have received widespread attention due to their superior performance in approximating high-dimensional data. However, these methods often neglect the intrinsic low-rank property of TR factors. More importantly, even with low-rank consideration, their effectiveness remains severely limited by both the restrictive low-rank tensor definition and high sensitivity to the permutation of tensor modes, ultimately degrading their performance. To address these issues, we propose a new HSI–MSI fusion model based on the generalized logarithmic tensor nuclear norm (GLTNN) under the TR decomposition framework. Specifically, we extend the traditional LTNN based on the third pattern to any pattern and define the generalized LTNN, where the Fourier transform is conducted on arbitrary mode. This method can not only capture the correlations comprehensively for tensor modes, but also effectively avoid the influence of the permutation of tensor modes on the fusion results. In addition, we design a proximal alternating minimization algorithm to efficiently solve the proposed model. The experimental results on four public datasets show that our method outperforms existing approaches in both numerical metrics and visual quality, validating its effectiveness and superiority.