Incorporation of a Deformation Prior in Image Reconstruction

This article presents a method to incorporate a deformation prior in image reconstruction via the formalism of deformation modules. The framework of deformation modules allows to build diffeomorphic deformations that satisfy a given structure. The idea is to register a template image against the indirectly observed data via a modular deformation, incorporating this way the deformation prior in the reconstruction method. We show that this is a well-defined regularisation method (proving existence, stability and convergence) and present numerical examples of reconstruction from 2-D tomographic simulations and partially observed images.