  Hyperspectral super-resolution (HSR) is a problem that aims to estimate an
image of high spectral and spatial resolutions from a pair of co-registered
multispectral (MS) and hyperspectral (HS) images, which have coarser spectral
and spatial resolutions, respectively. In this paper 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
non-convex 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.
