  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.
