Hyperspectral Super-Resolution via Global–Local Low-Rank Matrix Estimation
Hyperspectral super-resolution (HSR) is a problem that aims to estimate an image of high spectral and spatial resolutions from a pair of coregistered multispectral (MS) and hyperspectral (HS) images, which have coarser spectral and spatial resolutions, respectively. In this article, we pursue a low-rank matrix estimation approach for HSR. We assume that the spectral–spatial matrices associated with the whole image and the local areas of the image have low-rank structures. The local low-rank assumption, in particular, has the aim of providing a more flexible model for accounting for local variation effects due to endmember variability. We formulate the HSR problem as a global–local rank-regularized least-squares problem. By leveraging on the recent advances in nonconvex large-scale optimization, namely the smooth Schatten- $p$ approximation and the accelerated majorization–minimization method, we develop an efficient algorithm for the global–local low-rank problem. Numerical experiments on synthetic, semi-real, and real data show that the proposed algorithm outperforms a number of benchmark algorithms in terms of recovery performance.