Two-dimensional multi-target detection: an autocorrelation analysis approach

TL;DR

This paper introduces an autocorrelation analysis method for recovering 2D target images from noisy measurements with multiple, randomly oriented and translated copies, inspired by cryo-electron microscopy, effective in high noise conditions.

Contribution

The paper presents a novel autocorrelation-based framework for 2D multi-target detection that bypasses the need for estimating individual image locations and orientations.

Findings

Successful image recovery in highly noisy environments

Framework applicable to arbitrary spacing distributions of image occurrences

Extensive numerical validation demonstrating robustness

Abstract

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.