Multimode Low-Rank Relaxation and Manifold Regularization for Hyperspectral Image Super-Resolution

Hyperspectral imagery typically exhibits high spectral resolution but low spatial resolution due to limitations in imaging sensors. This limitation results in a large quantity of mixed pixels especially in noisy environments. Hyperspectral image super-resolution aims to enhance spatial resolution and reduce redundant interference, but it is often an ill-posed inverse problem. So far, the classical NMF-based method needs to unfold the remotely sensed cubic data into matrix form, resulting in the loss of 3-D structure knowledge. Also, the deep-learning-based algorithms suffer from massive hyperparameter tuning and weak interpretability. Furthermore, the tensor-based models also poses a lot of challenges, such as the uncertainty of exact rank and high complexity. To address the aforementioned issues, this article reformulates a novel tensor-based super-resolution model that incorporates multimode low-rank and graph-based manifold regularization (M-LGMR) for performance enhancement of reconstruction images. First, the low-rank relaxation is redefined to eliminate the nonuniqueness of tensor rank and suppress minor components. Next, owing to local similarity in hyperspectral cubic data, Laplace embedding-based manifold regularization is imposed on both spatial and spectral components to denoise and preserve the spatial-spectral structure. In the end, using matrix-vector operators, we also develop a set of efficient solvers to reduce the computational load. The simulation and experimental results on several real datasets demonstrate that the proposed method enhances the spatial resolution of reconstruction images effectively and also greatly improves the classification accuracy in practical applications of hyperspectral images.