We introduce a variational framework for indirect image registration where a template is registered against a target that is known only through indirect noisy observations, such as in tomographic imaging. The registration uses diffeomorphisms that transform the template through a (group) action. These diffeomorphisms are generated using the large deformation diffeomorphic metric mapping framework, i.e., they are given as solutions of a flow equation that is defined by a velocity field. We prove existence of solutions to this indirect image registration procedure and provide examples of its performance on 2D tomography with very sparse and/or highly noisy data.
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