  Computed tomography (CT) relies on precise patient immobilization during
image acquisition. Nevertheless, motion artifacts in the reconstructed images
can persist. Motion compensation methods aim to correct such artifacts
post-acquisition, often incorporating temporal smoothness constraints on the
estimated motion patterns. This study analyzes the influence of a spline-based
motion model within an existing rigid motion compensation algorithm for
cone-beam CT on the recoverable motion frequencies. Results demonstrate that
the choice of motion model crucially influences recoverable frequencies. The
optimization-based motion compensation algorithm is able to accurately fit the
spline nodes for frequencies almost up to the node-dependent theoretical limit
according to the Nyquist-Shannon theorem. Notably, a higher node count does not
compromise reconstruction performance for slow motion patterns, but can extend
the range of recoverable high frequencies for the investigated algorithm.
Eventually, the optimal motion model is dependent on the imaged anatomy,
clinical use case, and scanning protocol and should be tailored carefully to
the expected motion frequency spectrum to ensure accurate motion compensation.
