Known Operator Learning Enables Constrained Projection Geometry Conversion: Parallel to Cone-Beam for Hybrid MR/X-Ray Imaging.

X-ray imaging is a wide-spread real-time imaging technique. Magnetic Resonance Imaging (MRI) offers a multitude of contrasts that offer improved guidance to interventionalists. As such simultaneous real-time acquisition and overlay would be highly favorable for image-guided interventions, e.g., in stroke therapy. One major obstacle in this setting is the fundamentally different acquisition geometry. MRI k -space sampling is associated with parallel projection geometry, while the X-ray acquisition results in perspective distorted projections. The classical rebinning methods to overcome this limitation inherently suffers from a loss of resolution. To counter this problem, we present a novel rebinning algorithm for parallel to cone-beam conversion. We derive a rebinning formula that is then used to find an appropriate deep neural network architecture. Following the known operator learning paradigm, the novel algorithm is mapped to a neural network with differentiable projection operators enabling data-driven learning of the remaining unknown operators. The evaluation aims in two directions: First, we give a profound analysis of the different hypotheses to the unknown operator and investigate the influence of numerical training data. Second, we evaluate the performance of the proposed method against the classical rebinning approach. We demonstrate that the derived network achieves better results than the baseline method and that such operators can be trained with simulated data without losing their generality making them applicable to real data without the need for retraining or transfer learning.