  Single-particle imaging with X-ray free-electron lasers depends crucially on
algorithms that merge large numbers of weak diffraction patterns despite
missing measurements of parameters such as particle orientations. The
Expand-Maximize-Compress (EMC) algorithm is highly effective at merging
single-particle diffraction patterns with missing orientation values, but most
implementations exhaustively sample the space of missing parameters and may
become computationally prohibitive as the number of degrees of freedom extend
beyond orientation angles. Here we describe how the EMC algorithm can be
modified to employ Metropolis Monte Carlo sampling rather than grid sampling,
which may be favorable for cases with more than three missing parameters. Using
simulated data, this variant is compared to the standard EMC algorithm. Higher
dimensional cases of mixed target species and variable x-ray fluence are also
explored.
