  Quantum gas microscopes, which image the atomic occupations in an optical
lattice, have opened a new avenue to the exploration of many-body lattice
systems. Imaging trapped systems after freezing the density distribution by
ramping up a pinning lattice leads, however, to a distortion of the original
density distribution, especially when its structures are on the scale of the
pinning lattice spacing. We show that this dynamics can be described by a
filter, which we call in analogy to classical optics a quantum point spread
function. Using a machine learning approach, we demonstrate via several
experimentally relevant setups that a suitable deconvolution allows for the
reconstruction of the original density distribution. These findings are both of
fundamental interest for the theory of imaging and of immediate importance for
current quantum gas experiments.
