  In the past decades, Computed Tomography (CT) has established itself as one
of the most important imaging techniques in medicine. Today, the applicability
of CT is only limited by the deposited radiation dose, reduction of which
manifests in noisy or incomplete measurements. Thus, the need for robust
reconstruction algorithms arises. In this work, we learn a parametric
regularizer with a global receptive field by maximizing it's likelihood on
reference CT data. Due to this unsupervised learning strategy, our trained
regularizer truly represents higher-level domain statistics, which we
empirically demonstrate by synthesizing CT images. Moreover, this regularizer
can easily be applied to different CT reconstruction problems by embedding it
in a variational framework, which increases flexibility and interpretability
compared to feed-forward learning-based approaches. In addition, the
accompanying probabilistic perspective enables experts to explore the full
posterior distribution and may quantify uncertainty of the reconstruction
approach. We apply the regularizer to limited-angle and few-view CT
reconstruction problems, where it outperforms traditional reconstruction
algorithms by a large margin.
