  We consider the two-dimensional multi-target detection problem of recovering
a target image from a noisy measurement that contains multiple copies of the
image, each randomly rotated and translated. Motivated by the structure
reconstruction problem in single-particle cryo-electron microscopy, we focus on
the high noise regime, where the noise hampers accurate detection of the image
occurrences. We develop an autocorrelation analysis framework to estimate the
image directly from a measurement with an arbitrary spacing distribution of
image occurrences, bypassing the estimation of individual locations and
rotations. We conduct extensive numerical experiments, and demonstrate image
recovery in highly noisy environments. The code to reproduce all numerical
experiments is publicly available at https://github.com/krshay/MTD-2D.
