Expansion-maximization-compression algorithm with spherical harmonics for single particle imaging with x-ray lasers.
In three-dimensional (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 angular 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 avenues to improve computational efficiency and speed of convergence, which are critically important considering the very large datasets expected from experiment.
Univ. Lille, Centre National de la Recherche Scientifique, Centrale Lille, UMR 9189, CRIStAL, Centre de Recherche en Informatique Signal et Automatique de Lille, 59000 Lille, France.
Julien
J
Flamant
Centre National de la Recherche Scientifique, GIPSA Laboratory, 11 Rue des Mathématiques, Domaine Universitaire, BP 46, 38402 Saint Martin d'Heres Cedex, France.
Nicolas
N
Le Bihan
ARC Centre of Excellence for Advanced Molecular Imaging, School of Physics, The University of Melbourne, Victoria 3010, Australia.
Andrew V
AV
Martin
Department of Electrical and Electronic Engineering, The University of Melbourne, Victoria 3010, Australia.
Jonathan H
JH
Manton