Two-Dimensional Multi-Target Detection: An Autocorrelation Analysis Approach

We consider thetwo-dimensional multi-target detection problem of recovering a target image from noisy measurement that contains multiple copies the image, each randomly rotated and translated. Motivated by structure reconstruction in single-particle cryo-electron microscopy, we focus on high noise regime, where hampers accurate occurrences. develop an autocorrelation analysis framework to estimate directly with arbitrary spacing distribution occurrences, bypassing estimation individual locations rotations. conduct extensive numerical experiments, demonstrate recovery highly environments. 1