Hyperspectral Image Fusion via Logarithmic Low-rank Tensor Ring Decomposition

Integrating a low-spatial-resolution hyperspectral image (LR-HSI) with a high-spatial-resolution multispectral image (HR-MSI) is recognized as a valid method for acquiring HR-HSI. Among the current fusion approaches, the tensor ring (TR) decomposition-based method has received growing attention owing to its superior performance on preserving the spatial-spectral correlation. Furthermore, the low-rank property in some TR factors has been exploited via the matrix nuclear norm regularization along mode-2. On the other hand, the tensor nuclear norm (TNN)-based approaches have recently demonstrated to be more efficient on keeping high-dimensional low-rank structures in tensor recovery. Here, we study the low-rankness of TR factors from the TNN perspective and consider the mode-2 logarithmic TNN (LTNN) on each TR factor. A novel fusion model is proposed by incorporating this LTNN regularization and the weighted total variation which is to promote the continuity of HR-HSI in the spatial-spectral domain. Meanwhile, we have devised a highly efficient proximal alternating minimization algorithm to solve the proposed model. The experimental results indicate that our method improves the visual quality and exceeds the existing state-of-the-art fusion approaches with respect to various quantitative metrics.