Master thesis: Curvelet sparse regularization for differential phase-contrast X-ray imaging

Abstract

Advances in imaging hardware have enabled differential phase contrast imaging (DPCI) with conventional X-ray tube sources. So far, iterative series expansion methods have been applied in a weighted maximum likelihood framework to reconstruct absorption and phase contrast data using the pixel basis functions. This work aims at using the curvelet frame, which provides an optimal sparse representation of C2-functions with singularities along C2-curves. We will integrate and evaluate different curvelet sparse regularization based reconstruction techniques, including multiple discretization methods. We will show, that curvelets further provide a suitable data representation for DPCI tomography while supporting an analytical formula for the forward model for both, X-ray absorption and DPCI. In contrast to the pixel basis functions, this enables discretization free formulation of the forward model. Within the scope of this thesis, the mathematical theory for curvelet based phase-contrast X-ray reconstruction will be derived and methods for sparse regularization will be applied. Finally, we will apply our method to X-ray absorption and DPCI data from both phantom and real data.