Noise Limits on Reconstructing Diffraction Signals From Random Tomographs

An information theoretic criterion for the feasibility of reconstructing diffraction signals from noisy tomographs, when the positions of the tomographs within the signal are unknown, is derived. For shot-noise limited data, the number of detected photons per tomograph for successful reconstruction is much smaller than previously believed necessary, growing only logarithmically with the number of contrast elements of the diffracting object. Reconstruction up to the theoretic criterion is demonstrated on simulated data with an algorithm that combines the expectation-maximization (EM) principle with constraints arising from the band-limited nature of the signal.