A new weighted tensor nuclear norm for hyperspectral image super-resolution via tensor ring decomposition

Hyperspectral images (HSIs) are characterized by their rich spectral information but often suffer from low spatial resolution. To address this limitation, we propose a novel super-resolution method based on tensor ring (TR) decomposition. The core innovation of our approach is the introduction of a mode-2 weighted tensor nuclear norm (WTNN) to impose low-rank constraints on the TR factors. Unlike the conventional tensor nuclear norm that treats all singular values equally, our WTNN assigns adaptive weights to different singular values, thereby providing a more accurate and unbiased estimation of the tensor’s low-rank structure and better preserving essential information. Furthermore, we incorporate a weighted total variation regularization term to exploit the spatial-spectral smoothness prior inherent in HSIs. To efficiently solve the resulting optimization model, we develop an algorithm under the proximal alternating minimization framework, which leverages the alternating direction method of multipliers to handle subproblems and employs a weighted singular value thresholding technique. Experimental results on two benchmark datasets demonstrate that the proposed method outperforms several state-of-the-art approaches in terms of both numerical metrics and visual quality, validating its effectiveness for HSI super-resolution.