An approximate expectation-maximization for two-dimensional multi-target detection

TL;DR

This paper introduces an approximate expectation-maximization method for two-dimensional multi-target detection, effectively reconstructing images from noisy measurements with multiple rotated and translated copies, relevant to cryo-electron microscopy.

Contribution

The study develops a novel EM framework that maximizes an approximate likelihood, improving image recovery in high-noise scenarios compared to previous autocorrelation methods.

Findings

Successful image recovery in high noise environments

Outperforms autocorrelation analysis across various parameters

Demonstrates robustness in multi-target detection

Abstract

We consider the two-dimensional multi-target detection (MTD) problem of estimating a target image from a noisy measurement that contains multiple copies of the image, each randomly rotated and translated. The MTD model serves as a mathematical abstraction of the structure reconstruction problem in single-particle cryo-electron microscopy, the chief motivation of this study. We focus on high noise regimes, where accurate detection of image occurrences within a measurement is impossible. To estimate the image, we develop an expectation-maximization framework that aims to maximize an approximation of the likelihood function. We demonstrate image recovery in highly noisy environments, and show that our framework outperforms the previously studied autocorrelation analysis in a wide range of parameters.