Noise limits in the assembly of diffraction data

We obtain an information theoretic criterion for the feasibility of assembling diffraction signals from noisy tomographs when the positions of the tomographs within the signal are unknown. For shot-noise limited data, the minimum number of detected photons per tomograph for successful assembly is much smaller than previously believed necessary, growing only logarithmically with the number of resolution elements of the diffracting object. We also demonstrate assembly up to the information theoretic limit with a constraint-based algorithm.