Phase retrieval is the numerical procedure of recovering a complex-valued
signal from knowledge about its amplitude and some additional information.
Here, an indirect registration procedure, based on the large deformation
diffeomorphic metric mapping (LDDMM) formalism, is investigated as a phase
retrieval method for coherent diffractive imaging. The method attempts to find
a deformation which transforms an initial, template image to match an unknown
target image by comparing the diffraction pattern to the data. The exterior
calculus framework is used to treat different types of deformations in a
unified and coordinate-free way. The algorithm performance with respect to
measurement noise, image topology, and particular action are explored through
numerical examples