# Hyperspectral Super-Resolution via Global-Local Low-Rank Matrix Estimation

## TL;DR

This paper introduces a novel low-rank matrix estimation method for hyperspectral super-resolution, leveraging global and local low-rank structures to improve image reconstruction from multispectral and hyperspectral data.

## Contribution

It proposes a global-local low-rank regularization framework and an efficient optimization algorithm for hyperspectral super-resolution, accounting for local spectral variations.

## Key findings

- Outperforms benchmark algorithms in recovery accuracy
- Effective in synthetic, semi-real, and real data scenarios
- Leverages recent non-convex optimization advances

## Abstract

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.