A max-cut approach to heterogeneity in cryo-electron microscopy

TL;DR

This paper introduces a mathematically rigorous algorithm for classifying heterogeneous cryo-electron microscopy data, providing stability bounds and demonstrating improved performance over existing methods on simulated datasets.

Contribution

It presents the first rigorous mathematical analysis of heterogeneity classification in cryo-EM and proposes an extended algorithm combining classification and reconstruction.

Findings

Proves accuracy and stability bounds for the proposed algorithm

Demonstrates improved performance on simulated data

Extends the algorithm to combine classification and reconstruction

Abstract

The field of cryo-electron microscopy has made astounding advancements in the past few years, mainly due to advancements in electron detectors' technology. Yet, one of the key open challenges of the field remains the processing of heterogeneous data sets, produced from samples containing particles at several different conformational states. For such data sets, the algorithms must include some classification procedure to identify homogeneous groups within the data, so that the images in each group correspond to the same underlying structure. The fundamental importance of the heterogeneity problem in cryo-electron microscopy has drawn many research efforts, and resulted in significant progress in classification algorithms for heterogeneous data sets. While these algorithms are extremely useful and effective in practice, they lack rigorous mathematical analysis and performance guarantees. In this paper, we attempt to make the first steps towards rigorous mathematical analysis of the heterogeneity problem in cryo-electron microscopy. To that end, we present an algorithm for processing heterogeneous data sets, and prove accuracy and stability bounds for it. We also suggest an extension of this algorithm that combines the classification and reconstruction steps. We demonstrate it on simulated data, and compare its performance to the state-of-the-art algorithm in RELION.