Multi-target detection with rotations

TL;DR

This paper presents a method using autocorrelation analysis to recover a target image from noisy measurements containing many randomly rotated and translated copies, inspired by cryo-electron microscopy.

Contribution

It introduces a novel autocorrelation-based approach for multi-target detection that works effectively in low signal-to-noise conditions.

Findings

Method successfully recovers target images at high noise levels

Autocorrelation features are invariant to rotations and translations

Approach is effective given sufficiently large measurement data

Abstract

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.