Hyperspectral-Multispectral Image Fusion via Tensor Ring and Subspace Decompositions

Fusion from a spatially low resolution hyperspectral image (LR-HSI) and a spectrally low resolution multispectral image (MSI) to produce a high spatial-spectral HSI (HR-HSI), known as hyperspectral super resolution, has risen to a preferred topic for reinforcing the spatial-spectral resolution of HSI in recent years. In this work, we propose a new model, namely, low-rank tensor ring decomposition based on tensor nuclear norm (LRTRTNN), for HSI-MSI fusion. Specifically, for each spectrally subspace cube, similar patches are grouped to exploit both the global low-rank property of LR-HSI and the nonlocal similarity of HR-MSI. Afterward, a joint optimization of all groups via the presented LRTRTNN approximation is implemented in a unified cost function. With the introduced tensor nuclear norm (TNN) constraint, all 3D tensor ring factors are no longer unfolded to suit the matrix nuclear norm used in conventional methods, and the internal tensor structure can be naturally retained. The alternating direction method of multipliers is introduced for coefficients update. Numerical and visual experiments on real data show that our LRTRTNN method outperforms most state-of-the-art algorithms in terms of fusing performance.