Reconstruction algorithm for single-particle diffraction imaging experiments

Abstract

We introduce the EMC algorithm for reconstructing a particle's 3D diffraction intensity from very many photon shot-noise limited 2D measurements, when the particle orientation in each measurement is unknown. The algorithm combines a maximization step (M) of the intensity's likelihood function, with expansion (E) and compression (C) steps that map the 3D intensity model to a redundant tomographic representation and back again. After a few iterations of the EMC update rule, the reconstructed intensity is given to the differencemap algorithm for reconstruction of the particle contrast. We demonstrate reconstructions with simulated data and investigate the effects of particle complexity, number of measurements, and the number of photons per measurement. The relatively transparent scaling behavior of our algorithm provides a first estimate of the data processing resources required for future single-particle imaging experiments.

A minimal view of single-particle imaging with X-ray lasers

“…Among numerous reconstruction algorithms designed for this task [21][22][23][24], this paper focuses on the EMC algorithm 1 [25][26][27], which is based on the expectation maximization principle [28]. EMC succeeds even with extremely noisy patterns and additional unmeasured parameters besides orientations [29].…”

In-plane rotation classification for coherent X-ray imaging of single biomolecules

“…Because of the extremely low signal-to-noise level, this method is not applicable in current x-ray diffraction experiments. Current classification work on X-ray diffraction data [21,22] is primarily focused on the direct 2D diffraction patterns. We propose to compress the diffraction data by radial and azimuthal integrals, so that the orientation information can…”

“…If we can relax the requirement on the sensitivity of the classification, we can achieve 92% accuracy for the class size of 3 • and 97% accuracy for 5 • . In this way we can break the data set into smaller groups and use more sophisticated algorithms such as described in [21] or [22] to find additional information. Research in this direction is underway.…”

“…Thus the classification schemes based on large-angle-scattering-data are not currently practical. Recently there are two interesting developments where ExpectationMaximization algorithms is utilized for classification [21,22]. The signal level for successful classifications is much reduced.…”

“…As we have shown in Section 2, we can use the simple difference measure as described in Section 4 and 5 for classification of in-plane rotations. We can also use more elaborate methods for a complete orientation classification, such as [21,22], with the advantage of improved SNR.…”