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Phase retrieval is the numerical procedure of recovering a complex-valuedsignal from knowledge about its amplitude and some additional information.Here, an indirect registration procedure, based on the large deformationdiffeomorphic metric mapping (LDDMM) formalism, is investigated as a phaseretrieval method for coherent diffractive imaging. The method attempts to finda deformation which transforms an initial, template image to match an unknowntarget image by comparing the diffraction pattern to the data. The exteriorcalculus framework is used to treat different types of deformations in aunified and coordinate-free way. The algorithm performance with respect tomeasurement noise, image topology, and particular action are explored throughnumerical examples.

Phase retrieval via non-rigid image registration