Multi-target detection with rotations
This addresses the multi-target detection challenge in applications like cryo-electron microscopy, where noise complicates localization and orientation estimation.
The paper tackles the problem of estimating a 2D target image from a noisy measurement containing many randomly rotated and translated copies, focusing on low signal-to-noise regimes. It demonstrates that using autocorrelation analysis to estimate invariant features allows recovery of the target image regardless of noise level, given a sufficiently large measurement.
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.