Super-resolving star clusters with sheaves

TL;DR

This paper introduces an optimization-based method for accurately counting and localizing stars in small clusters using photon counts, leveraging sheaf theory for a general and robust approach.

Contribution

It presents a novel, general framework based on sheaf theory for star cluster analysis, capable of handling various array configurations and low photon counts.

Findings

Accurate star localization when separation exceeds 0.2 Rayleigh radii.

Low photon count requirements ensure convergence.

Method is robust to array arrangements.

Abstract

This article explains an optimization-based approach for counting and localizing stars within a small cluster, based on photon counts in a focal plane array. The array need not be arranged in any particular way, and relatively small numbers of photons are required in order to ensure convergence. The stars can be located close to one another, as the location and brightness errors were found to be low when the separation was larger than $0.2$ Rayleigh radii. To ensure generality of our approach, it was constructed as a special case of a general theory built upon topological signal processing using the mathematics of sheaves.