  Single-particle imaging experiments of biomolecules at x-ray free-electron
lasers (XFELs) require processing of hundreds of thousands (or more) of images
that contain very few x-rays. Each low-flux image of the diffraction pattern is
produced by a single, randomly oriented particle, such as a protein. We
demonstrate the feasibility of collecting data at these extremes, averaging
only 2.5 photons per frame, where it seems doubtful there could be information
about the state of rotation, let alone the image contrast. This is accomplished
with an expectation maximization algorithm that processes the low-flux data in
aggregate, and without any prior knowledge of the object or its orientation.
The versatility of the method promises, more generally, to redefine what
measurement scenarios can provide useful signal in the high-noise regime.
