Hyperspectral Image High-resolution via Subspace-Based Non-Convex Arctangent-Rank Regularization

In this paper, we focus on improving the spatial resolution of hyperspectral images. The combination of low spatial resolution hyperspectral image (LR-HSI) and high spatial resolution multispectral image (HR-MSI) into high spatial resolution hyperspectral image (HR-HSI) has been attracting significant research interest in recent years. The traditional nuclear norm approximation adds all singular values together directly, which may depend heavily on the magnitudes of singular values. However, tensor arctangent rank is a tighter approximation to the rank function. The rank of tensor is obtained by adding the constraint of arctangent to the rank of each frontal slice of the tensor. We propose a novel subspace-based low tensor arctangent rank regularization method for this fusion. In this process, it makes full use of spectral correlation and non-local similarity in the HR-HSI. Firstly, we learn subspace from LR-HSI. In this step, we use the prior condition that the spectral vector usually exists in the low dimensional subspace. Secondly, we use K-means algorithm to cluster HR-MSI, and the coefficient is also grouped according to the clustering. Finally, the coefficient is estimated by low tensor arctangent rank prior. Extensive experiments on two public HSI datasets show that the proposed method outperfoms the state-of-the-art methods.