  Quantum-gas microscopes are used to study ultracold atoms in optical lattices
at the single particle level. In these system atoms are localised on lattice
sites with separations close to or below the diffraction limit. To determine
the lattice occupation with high fidelity, a deconvolution of the images is
often required. We compare three different techniques, a local iterative
deconvolution algorithm, Wiener deconvolution and the Lucy-Richardson
algorithm, using simulated microscope images. We investigate how the
reconstruction fidelity scales with varying signal-to-noise ratio, lattice
filling fraction, varying fluorescence levels per atom, and imaging resolution.
The results of this study identify the limits of singe-atom detection and
provide quantitative fidelities which are applicable for different atomic
species and quantum-gas microscope setups.
