  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.
