  Cone-beam computed tomography (CBCT) systems, with their portability, present
a promising avenue for direct point-of-care medical imaging, particularly in
critical scenarios such as acute stroke assessment. However, the integration of
CBCT into clinical workflows faces challenges, primarily linked to long scan
duration resulting in patient motion during scanning and leading to image
quality degradation in the reconstructed volumes. This paper introduces a novel
approach to CBCT motion estimation using a gradient-based optimization
algorithm, which leverages generalized derivatives of the backprojection
operator for cone-beam CT geometries. Building on that, a fully differentiable
target function is formulated which grades the quality of the current motion
estimate in reconstruction space. We drastically accelerate motion estimation
yielding a 19-fold speed-up compared to existing methods. Additionally, we
investigate the architecture of networks used for quality metric regression and
propose predicting voxel-wise quality maps, favoring autoencoder-like
architectures over contracting ones. This modification improves gradient flow,
leading to more accurate motion estimation. The presented method is evaluated
through realistic experiments on head anatomy. It achieves a reduction in
reprojection error from an initial average of 3mm to 0.61mm after motion
compensation and consistently demonstrates superior performance compared to
existing approaches. The analytic Jacobian for the backprojection operation,
which is at the core of the proposed method, is made publicly available. In
summary, this paper contributes to the advancement of CBCT integration into
clinical workflows by proposing a robust motion estimation approach that
enhances efficiency and accuracy, addressing critical challenges in
time-sensitive scenarios.
