Title: Assessing Uncertainties in X-ray Single-particle Three-dimensional reconstructions,
Abstract: Modern technology for producing extremely bright and coherent X-ray laser
pulses provides the possibility to acquire a large number of diffraction
patterns from individual biological nanoparticles, including proteins, viruses,
and DNA. These two-dimensional diffraction patterns can be practically
reconstructed and retrieved down to a resolution of a few \angstrom. In
principle, a sufficiently large collection of diffraction patterns will contain
the required information for a full three-dimensional reconstruction of the
biomolecule. The computational methodology for this reconstruction task is
still under development and highly resolved reconstructions have not yet been
produced.
We analyze the Expansion-Maximization-Compression scheme, the current state
of the art approach for this very challenging application, by isolating
different sources of uncertainty. Through numerical experiments on synthetic
data we evaluate their respective impact. We reach conclusions of relevance for
handling actual experimental data, as well as pointing out certain improvements
to the underlying estimation algorithm.
We also introduce a practically applicable computational methodology in the
form of bootstrap procedures for assessing reconstruction uncertainty in the
real data case. We evaluate the sharpness of this approach and argue that this
type of procedure will be critical in the near future when handling the
increasing amount of data.