  We demonstrate improved detection of small trapped atomic ensembles through
advanced post-processing and optimal analysis of absorption images. A fringe
removal algorithm reduces imaging noise to the fundamental photon-shot-noise
level and proves beneficial even in the absence of fringes. A
maximum-likelihood estimator is then derived for optimal atom-number estimation
and is applied to real experimental data to measure the population differences
and intrinsic atom shot-noise between spatially separated ensembles each
comprising between 10 and 2000 atoms. The combined techniques improve our
signal-to-noise by a factor of 3, to a minimum resolvable population difference
of 17 atoms, close to our ultimate detection limit.
