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Schemes for X-ray imaging single protein molecules using new x-ray sources,like x-ray free electron lasers (XFELs), require processing many frames of datathat are obtained by taking temporally short snapshots of identical molecules,each with a random and unknown orientation. Due to the small size of themolecules and short exposure times, average signal levels of much less than 1photon/pixel/frame are expected, much too low to be processed using standardmethods. One approach to process the data is to use statistical methodsdeveloped in the EMC algorithm (Loh & Elser, Phys. Rev. E, 2009) whichprocesses the data set as a whole. In this paper we apply this method to areal-space tomographic reconstruction using sparse frames of data (below$10^{-2}$ photons/pixel/frame) obtained by performing x-ray transmissionmeasurements of a low-contrast, randomly-oriented object. This extends the workby Philipp et al. (Optics Express, 2012) to three dimensions and is one stepcloser to the single molecule reconstruction problem.

Real-Space x-ray tomographic reconstruction of randomly oriented objects with sparse data frames