In sparse X-ray Computed Tomography, the radiation dose to the patient is lowered by measuring fewer projection views compared to a standard protocol. In this work we investigate a hybrid approach combining shearlet representation with deep learning for reconstruction of sparse-view X-ray computed tomography. The proposed method is hybrid in that it reconstructs the parts that can provably be retrieved by utilizing a model-based approach, and it in-paints the parts that provably cannot through a learning-based approach. In doing so, we attempt to benefit from the best aspects of model- and learning-based methods. We demonstrate first promising results on publicly available data.
Anisotropic X-ray Dark-field Tomography (AXDT) is a novel imaging modality aimed at the reconstruction of spherical scattering functions in every three-dimensional volume element, based on the directional X-ray dark-field contrast as measured by an X-ray grating interferometer. In this work, we re-derive a detectability index for the AXDT forward model directly using the spherical function formulation, and use it to compute optimized acquisition trajectories using a greedy algorithm. The results demonstrate that the optimized trajectories can represent task-specific features in AXDT accurately using only a fraction of the data.