# Is There Any Recovery Guarantee with Coupled Structured Matrix Factorization for Hyperspectral Super-Resolution?

## TL;DR

This paper investigates the theoretical recovery guarantees of coupled structured matrix factorization (CoSMF) in hyperspectral super-resolution, revealing conditions under which it guarantees accurate recovery in noiseless scenarios.

## Contribution

It provides the first theoretical analysis of CoSMF's recovery guarantees, highlighting the roles of sparsity and separability conditions.

## Key findings

- Sufficient conditions for global optimality and recovery accuracy are established.
- Sparsity and pure-pixel conditions are crucial for effective CoSMF performance.
- Guarantees are shown under noiseless assumptions.

## Abstract

Coupled structured matrix factorization (CoSMF) for hyperspectral super-resolution (HSR) has recently drawn significant interest in hyperspectral imaging for remote sensing. Presently there is very few work that studies the theoretical recovery guarantees of CoSMF. This paper makes one such endeavor by considering the CoSMF formulation by Wei et al., which, simply speaking, is similar to coupled non-negative matrix factorization. Assuming no noise, we show sufficient conditions under which the globably optimal solution to the CoSMF problem is guaranteed to deliver certain recovery accuracies. Our analysis suggests that sparsity and the pure-pixel (or separability) condition play a hidden role in enabling CoSMF to achieve some good recovery characteristics.