  Single-shot images are the standard readout of experiments with ultracold
atoms -- the tarnished looking glass into their many-body physics. The
efficient extraction of observables from single-shot images is thus crucial.
Here, we demonstrate how artificial neural networks can optimize this
extraction. In contrast to standard averaging approaches, machine learning
allows both one- and two-particle densities to be accurately obtained from a
drastically reduced number of single-shot images. Quantum fluctuations and
correlations are directly harnessed to obtain physical observables for bosons
in a tilted double-well potential at an unprecedented accuracy. Strikingly,
machine learning also enables a reliable extraction of momentum-space
observables from real-space single-shot images and vice versa. This obviates
the need for a reconfiguration of the experimental setup between in-situ and
time-of-flight imaging, thus potentially granting an outstanding reduction in
resources.
