Low-rank tensors have received more attention in hyperspectral image (HSI) recovery. Minimizing the tensor nuclear norm, as a low-rank approximation method, often leads to modeling bias. To achieve an unbiased approximation and improve the robustness, this paper develops a non-convex relaxation approach for low-rank tensor approximation. Firstly, a non-convex approximation of tensor nuclear norm (NCTNN) is introduced to the low-rank tensor completion. Secondly, a non-convex tensor robust principal component analysis (NCTRPCA) method is proposed, which aims at exactly recovering a low-rank tensor corrupted by mixed-noise. The two proposed models are solved efficiently by the alternating direction method of multipliers (ADMM). Three HSI datasets are employed to exhibit the superiority of the proposed model over the low rank penalization method in terms of accuracy and robustness.

Hyperspectral image (HSI) super-resolution aims at improving the spatial resolution of HSI by fusing a high spatial resolution multispectral image (MSI). To preserve local submanifold structures in HSI super-resolution, a novel superpixel graph-based super-resolution method is proposed. Firstly, the MSI is segmented into superpixel blocks to form two-directional feature tensors, then two graphs are created using spectral–spatial distance between the unfolded feature tensors. Secondly, two graph Laplacian terms involving underlying BTD factors of high-resolution HSI are developed, which ensures the inheritance of the spatial geometric structures. Finally, by incorporating graph Laplacian priors with the coupled BTD degradation model, a HSI super-resolution model is established. Experimental results demonstrate that the proposed method achieves better fused results compared with other advanced super-resolution methods, especially on the improvement of the spatial structure.

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