Expansion-maximization-compression algorithm with spherical harmonics for single particle imaging with X-ray lasers

TL;DR

This paper introduces an advanced algorithm for 3D single particle imaging with X-ray lasers, leveraging spherical harmonics to improve efficiency and accuracy in reconstructing particle orientations from diffraction data.

Contribution

It extends the Expansion-Maximization-Compression algorithm with a shell-by-shell approach and adaptive angular bandwidth, enhancing computational efficiency and convergence speed.

Findings

Efficient separation of angular and radial data using harmonic analysis.

Determination of minimal patterns and rotation sampling for target resolutions.

Improved reconstruction speed suitable for large datasets.

Abstract

In 3D single particle imaging with X-ray free-electron lasers, particle orientation is not recorded during measurement but is instead recovered as a necessary step in the reconstruction of a 3D image from the diffraction data. Here we use harmonic analysis on the sphere to cleanly separate the angu- lar and radial degrees of freedom of this problem, providing new opportunities to efficiently use data and computational resources. We develop the Expansion-Maximization-Compression algorithm into a shell-by-shell approach and implement an angular bandwidth limit that can be gradually raised during the reconstruction. We study the minimum number of patterns and minimum rotation sampling required for a desired angular and radial resolution. These extensions provide new av- enues to improve computational efficiency and speed of convergence, which are critically important considering the very large datasets expected from experiment.