A Truncated Matrix Decomposition for Hyperspectral Image Super-Resolution

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.

I. Introduction

Hyperspectral images (HSIs) contain hundreds of contiguous and narrow spectral bands, with spectral coverage ranging from the visible to infrared spectrum. This high spectral resolution of HSIs has proved useful for object detection [1], tracking [2], face recognition [3], [4] and land-cover classification [5]–[8]. Due to the limit of imaging sensors, there is always a tradeoff between the spectral resolution and spatial resolution of images [9]. For HSIs, the spectral resolution is required to be high, and thus the spatial resolution is sacrificed. Conversely, with the loss of much spectral information, conventional panchromatic or multispectral images (MSIs) achieve high spatial resolution. To obtain a high-resolution HSI (HR-HSI), an economical solution is to instead record a low-resolution HSI (LR-HSI) and a conventional high-resolution image, and to fuse them into a product that should be high in both spectral and spatial resolutions.