Fast Reconstruction Method for Diffraction Imaging

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We present a fast image reconstruction method for two- and three-dimensional diffraction imaging. Provided that very little information about the phase is available, the method demonstrates convergence rates that are several orders of magnitude faster than current reconstruction techniques. Unlike current methods, our approach is based on convex optimization. Besides fast convergence, our method allows great deal of flexibility in choosing most appropriate objective function as well as introducing additional information about the sought signal, e.g., smoothness. Benefits of good choice of the objective function are demonstrated by reconstructing an image from noisy data.