Generalized autocorrelation analysis for multi-target detection

TL;DR

This paper introduces a generalized autocorrelation analysis method for multi-target detection in noisy measurements, improving signal recovery performance over previous least squares approaches, with applications inspired by cryo-electron microscopy.

Contribution

It develops a weighted autocorrelation analysis framework that adapts weights based on data, enhancing detection accuracy in high noise scenarios.

Findings

Outperforms traditional autocorrelation analysis in noisy conditions

Enables reliable signal recovery from highly noisy data

Provides a data-driven method for optimal weighting in autocorrelation analysis

Abstract

We study the multi-target detection problem of recovering a target signal from a noisy measurement that contains multiple copies of the signal at unknown locations. Motivated by the structure reconstruction problem in cryo-electron microscopy, we focus on the high noise regime, where noise hampers accurate detection of signal occurrences. Previous works proposed an autocorrelation analysis framework to estimate the signal directly from the measurement, without detecting signal occurrences. Specifically, autocorrelation analysis entails finding a signal that best matches the observable autocorrelations by minimizing a least squares objective. This paper extends this line of research by developing a generalized autocorrelation analysis framework that replaces the least squares by a weighted least squares. The optimal weights can be computed directly from the data and guarantee favorable statistical properties. We demonstrate signal recovery from highly noisy measurements, and show that the proposed framework outperforms autocorrelation analysis in a wide range of parameters.