  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 difference-map
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.
