For telescopes operating at optical wavelengths, the turbulence of the atmosphere limits the resolution of space objects to about one second of arc, although the diffraction limit of the largest telescopes is many times as fine. We discuss an image processing technique that uses interferometer data (the modulus of the Fourier transform) to reconstruct diffraction limited images. Data from a stellar speckle interferometer or from an amplitude interferometer can be used. The processing technique is an iterative method that finds a real, non-negative object that agrees with the Fourier modulus data. For complicated two-dimensional objects, the solutions found by this technique are surprisingly unique. New results are shown for simulated speckle interferometer data having realistic noise present.