Orientation Determination from Cryo-EM images Using Least Unsquared Deviation

TL;DR

This paper presents a robust method for determining orientations in cryo-EM images by improving global self-consistency error minimization through semidefinite relaxation and spectral norm regularization, especially effective in noisy conditions.

Contribution

It introduces a new robust optimization framework for orientation estimation in cryo-EM that outperforms existing methods under high noise levels.

Findings

Significantly reduces orientation estimation error in noisy cryo-EM images.

Effective in low common-line detection scenarios.

Uses semidefinite relaxation with spectral norm regularization.

Abstract

A major challenge in single particle reconstruction from cryo-electron microscopy is to establish a reliable ab-initio three-dimensional model using two-dimensional projection images with unknown orientations. Common-lines based methods estimate the orientations without additional geometric information. However, such methods fail when the detection rate of common-lines is too low due to the high level of noise in the images. An approximation to the least squares global self consistency error was obtained using convex relaxation by semidefinite programming. In this paper we introduce a more robust global self consistency error and show that the corresponding optimization problem can be solved via semidefinite relaxation. In order to prevent artificial clustering of the estimated viewing directions, we further introduce a spectral norm term that is added as a constraint or as a regularization term to the relaxed minimization problem. The resulted problems are solved by using either the alternating direction method of multipliers or an iteratively reweighted least squares procedure. Numerical experiments with both simulated and real images demonstrate that the proposed methods significantly reduce the orientation estimation error when the detection rate of common-lines is low.