  Incorporating computed tomography (CT) reconstruction operators into
differentiable pipelines has proven beneficial in many applications. Such
approaches usually focus on the projection data and keep the acquisition
geometry fixed. However, precise knowledge of the acquisition geometry is
essential for high quality reconstruction results. In this paper, the
differentiable formulation of fan-beam CT reconstruction is extended to the
acquisition geometry. This allows to propagate gradient information from a loss
function on the reconstructed image into the geometry parameters. As a
proof-of-concept experiment, this idea is applied to rigid motion compensation.
The cost function is parameterized by a trained neural network which regresses
an image quality metric from the motion affected reconstruction alone. Using
the proposed method, we are the first to optimize such an autofocus-inspired
algorithm based on analytical gradients. The algorithm achieves a reduction in
MSE by 35.5 % and an improvement in SSIM by 12.6 % over the motion affected
reconstruction. Next to motion compensation, we see further use cases of our
differentiable method for scanner calibration or hybrid techniques employing
deep models.
