Reprojection Alignment for Trajectory Perturbation Estimation in Microtomography

For standard laboratory microtomography systems, acquired radiographs do not always adhere to the strict geometrical assumptions of the reconstruction algorithm. The consequence of this geometrical inconsistency is that the reconstructed tomogram contains
motion
artifacts, e.g., blurring, streaking, double-edges. To achieve a motion-artifact-free tomographic reconstruction, one must estimate, and subsequently correct for, the per-radiograph experimental geometry parameters. In this paper, we examine the use of
re-projection alignment
(RA) to estimate per-radiograph geometry. Our simulations evaluate how the convergence properties of RA vary with: motion-type (smooth versus random), trajectory (helical versus discrete-sampling `space-filling' trajectories) and tomogram resolution. The idealized simulations demonstrate for the space-filling trajectory that RA convergence rate and accuracy is invariant with regard to the motion-type and that the per-projection motions can be estimated to less than 0.25 pixel mean absolute error by performing a single quarter-resolution RA iteration followed by a single half-resolution RA iteration. The direct impact is that, for the space-filling trajectory, one can incorporate RA in an iterative multi-grid reconstruction scheme with only a single RA iteration per multi-grid resolution step. We also find that for either trajectory, slowly varying vertical errors cannot be reliably estimated by employing the RA method alone; such errors are indistinguishable from a trajectory of different pitch. This has minimal effect in practice because RA can be combined with reference frame correction which is effective for correcting low-frequency errors.