A Truncated Matrix Decomposition for Hyperspectral Image Super-Resolution

Abstract

Hyperspectral image super-resolution addresses the problem of fusing a low-resolution hyperspectral image (LR-HSI) and a high-resolution multispectral image (HR-MSI) to produce a high-resolution hyperspectral image (HR-HSI). In this paper, we propose a novel fusion approach for hyperspectral image super-resolution by exploiting the specific properties of matrix decomposition, which consists of four main steps. First, an endmember extraction algorithm is used to extract an initial spectral matrix from LR-HSI. Then, with the initial spectral matrix, we estimate the spatial matrix, i.e., the spatial-contextual information, from the degraded observations of HR-HSI. Third, the spatial matrix is further utilized to estimate the spectral matrix from LR-HSI by solving a least squares (LS)-based problem. Finally, the target HR-HSI is constructed by combing the estimated spectral and spatial matrixes. In particular, two models are proposed to estimate the spatial matrix. One is a simple case that involves a LS-based problem, and the other is an elaborate case that consists of two fidelity terms and a spatial regularizer, where the spatial regularizer aiming to restrain the range of solutions is achieved by exploiting the superpixel-level low-rank characteristics of HR-HSI. Experiment results conducted on both synthetic and real data sets demonstrate the effectiveness of the proposed approach as compared to other hyperspectral image super-resolution methods.