Regularising orientation estimation in Cryo-EM 3D map refinement through measure-based lifting over Riemannian manifolds

TL;DR

This paper introduces a measure-based lifting scheme called ESL for regularising orientation estimation in Cryo-EM 3D map refinement, improving robustness and accuracy in noisy data scenarios.

Contribution

The paper develops a novel measure-based lifting method over Riemannian manifolds and integrates it into a joint reconstruction and rotation estimation algorithm for Cryo-EM.

Findings

ESL improves rotation estimation accuracy in noisy Cryo-EM data.

Theoretical analysis confirms well-posedness and bias bounds of the method.

Numerical experiments demonstrate better ground-truth proximity of estimated rotations.

Abstract

Motivated by the trade-off between noise-robustness and data-consistency for joint 3D map reconstruction and rotation estimation in single particle cryogenic-electron microscopy (Cryo-EM), we propose ellipsoidal support lifting (ESL), a measure-based lifting scheme for regularising and approximating the global minimiser of a smooth function over a Riemannian manifold. Under a uniqueness assumption on the minimiser we show several theoretical results, in particular well-posedness of the method and an error bound due to the induced bias with respect to the global minimiser. Additionally, we use the developed theory to integrate the measure-based lifting scheme into an alternating update method for joint homogeneous 3D map reconstruction and rotation estimation, where typically tens of thousands of manifold-valued minimisation problems have to be solved and where regularisation is necessary because of the high noise levels in the data. The joint recovery method is used to test both the theoretical predictions and algorithmic performance through numerical experiments with Cryo-EM data. In particular, the induced bias due to the regularising effect of ESL empirically estimates better rotations, i.e., rotations closer to the ground truth, than global optimisation would.