Dragonfly: an implementation of the expand–maximize–compress algorithm for single-particle imaging

Abstract

Single-particle imaging (SPI) with X-ray free-electron lasers has the potential to change fundamentally how biomacromolecules are imaged. The structure would be derived from millions of diffraction patterns, each from a different copy of the macromolecule before it is torn apart by radiation damage. The challenges posed by the resultant data stream are staggering: millions of incomplete, noisy and un-oriented patterns have to be computationally assembled into a threedimensional intensity map and then phase reconstructed. In this paper, the Dragonfly software package is described, based on a parallel implementation of the expand-maximize-compress reconstruction algorithm that is well suited for this task. Auxiliary modules to simulate SPI data streams are also included to assess the feasibility of proposed SPI experiments at the Linac Coherent Light Source, Stanford, California, USA.

Low-signal limit of X-ray single particle diffractive imaging

“…By sub-sampling the experimental data from PR772 viruses measured in Reddy et al [9], we show that the reconstruction quality is essentially same as from the full data set with as few as 135 relevant photons/pattern, corresponding to 0.087 photons/speckle at the detector corner. This approaches the limits of prior work using simulated data [1] [2] or proof-of-principle experiments under highly controlled conditions not realistic for single particle imaging [12] [14]. By way of contrast, the results here are based on data derived from experimental measurements on PR772 viruses incorporating particle variability and instrument background, demonstrating that the signal required for X-ray single particle imaging under realistic conditions is much lower than previously demonstrated especially in terms of the number of scattered photons required per frame.…”

CCP-FEL: a collection of computer programs for free-electron laser research

“…In the case of SPI, two packages are presented for determining structures from diffraction patterns. For imaging faint reproducible samples, the Dragonfly package (Ayyer, Lan et al, 2016) implements an expectation maximization recipe to recover the unmeasured orientations of very many singleparticle diffraction patterns. For non-reproducible samples, Ma & Liu (2016) studied the structure determination by harvesting information from angular correlations similar to that in small-angle X-ray scattering experiments performed at synchrotrons.…”

Experimental 3D coherent diffractive imaging from photon-sparse random projections

“…However, the important case of sparse diffraction from a 3D object has only been solved experimentally in a setting different from the classical CDI problem. For example, one of the methods of orientation recovery-a statistical technique based on expectation maximization, the Expand-Maximize-Compress (EMC) algorithm [18,34]has been applied successfully to real-space sparse radiographic data, in two [35] and three dimensions [36], to sparse crystallographic data limited to one [37] and two rotation axes [38], and very recently also to synchrotronbased serial protein crystallographic data for random crystal orientations [39].…”