Learning the Inverse Weighted Radon Transform

X-ray phase-contrast imaging enhances soft-tissue contrast. The measured differential phase signal strength in a Talbot-Lau interferometer is dependent on the object's position within the setup. For large objects, this affects the tomographic reconstruction and leads to artifacts and perturbed phase values. In this paper, we propose a pipeline to learn a filter and additional weights to invert the weighted forward projection. We train and validate the method with a synthetic dataset. We tested our pipeline on the Shepp-Logan phantom, and found that our method suppresses the artifacts and the reconstructed image slices are close to the actual phase values quantitatively and qualitatively. In an ablation study we showed the superiority of our fully optimized pipeline.