Comparison of motion-compensated reconstruction with FBP and BPF for circular X-ray tomography: A simulation study

We present two new approximate variants of motion compensated 3D back-projection filtration (MC-BPF) algorithms for circular cone-beam X-ray tomography in divergent beam geometry. The first one uses differentiation in a single projection (SD), while the second one is based on the Katsevich-type differentiation (KD) involving two neighboring projections. The BPF type algorithms are compared to an approximate 3D motion compensated filtered back-projection (MC-FDK) algorithm investigated earlier. This work is driven by the hypothesis that shading artifacts observed in the approximate 3D MC-FDK algorithm are mitigated by BPF-type algorithms due to a more local correction of the motion. The MC-BPF consists of three steps: (1) short range differentiation filter, (2) motion-compensated backprojection and (3) inverse Hilbert filtering of the DBP. The long range Hilbert filter is applied to the already motion-corrected DBP. In a simulation study using the Forbild thorax phantom with beating heart insert, a slow and a fast acquisition are investigated. The motion-compensated reconstructions for the fast acquisition show almost the same image quality as the reconstructions from the static reference. The motion-compensated reconstructions for the slow acquisition are capable to recover high and medium contrast objects, however artifacts remain especially at the transition edges towards the lungs. Only minor differences in the quality between the MC-FDK, MC-BPF-KD and MC-BPF-SD are observed.