Nonlocal Patch Tensor Sparse Representation for Hyperspectral Image Super-Resolution.

This paper presents a hypserspectral image (HSI) super-resolution method which fuses a low-resolution hyperspectral image (LR-HSI) with a high-resolution multispectral image (HR-MSI) to get high-resolution HSI (HR-HSI). The proposed method first extracts the nonlocal similar patches to form a nonlocal patch tensor (NPT). A novel tensor-tensor product (t-product) based tensor sparse representation is proposed to model the extracted NPTs. Through the tensor sparse representation, both the spectral and spatial similarities between the nonlocal similar patches are well preserved. Then, the relationship between the HR-HSI and LR-HSI is built using t-product which allows us to design a unified objective function to incorporate the nonlocal similarity, tensor dictionary learning, and tensor sparse coding together. Finally, Alternating Direction Method of Multipliers (ADMM) is used to solve the optimization problem. Experimental results on three data sets and one real data set demonstrate that the proposed method substantially outperforms the existing state-of-the-art HSI super-resolution methods.