  We consider the multi-target detection problem of estimating a
two-dimensional target image from a large noisy measurement image that contains
many randomly rotated and translated copies of the target image. Motivated by
single-particle cryo-electron microscopy, we focus on the low signal-to-noise
regime, where it is difficult to estimate the locations and orientations of the
target images in the measurement. Our approach uses autocorrelation analysis to
estimate rotationally and translationally invariant features of the target
image. We demonstrate that, regardless of the level of noise, our technique can
be used to recover the target image when the measurement is sufficiently large.
