A Representation Theory Perspective on Simultaneous Alignment and Classification

TL;DR

This paper introduces a novel representation theoretic framework based on Non-Unique Games for simultaneous alignment and classification in Cryo-EM, addressing heterogeneity and noise issues with convex relaxations.

Contribution

It extends the Non-Unique Games framework to handle joint alignment and classification, including continuous heterogeneity, in Cryo-EM image analysis.

Findings

Provides a convex relaxation approach for joint alignment and classification.

Addresses heterogeneity in Cryo-EM with a representation theoretic method.

Potential extension to continuous heterogeneity scenarios.

Abstract

One of the difficulties in 3D reconstruction of molecules from images in single particle Cryo-Electron Microscopy (Cryo-EM), in addition to high levels of noise and unknown image orientations, is heterogeneity in samples: in many cases, the samples contain a mixture of molecules, or multiple conformations of one molecule. Many algorithms for the reconstruction of molecules from images in heterogeneous Cryo-EM experiments are based on iterative approximations of the molecules in a non-convex optimization that is prone to reaching suboptimal local minima. Other algorithms require an alignment in order to perform classification, or vice versa. The recently introduced Non-Unique Games framework provides a representation theoretic approach to studying problems of alignment over compact groups, and offers convex relaxations for alignment problems which are formulated as semidefinite programs (SDPs) with certificates of global optimality under certain circumstances. In this manuscript, we propose to extend Non-Unique Games to the problem of simultaneous alignment and classification with the goal of simultaneously classifying Cryo-EM images and aligning them within their respective classes. Our proposed approach can also be extended to the case of continuous heterogeneity.