This paper presents a method to reconstruct moving objects from cone beam X-ray projections acquired during a single rotational run using a given motion vector field. The method is applicable to voxel driven cone-beam filtered back-projection reconstruction approaches. Here, a formulation based on the algorithm of Feldkamp, Davis, and Kress (FDK) is presented. The motion correction is applied during the back-projection step by shifting the voxel to be reconstructed according to the motion vector field. The method is applied to three-dimensional (3-D) rotational X-ray angiography. Projections from a beating coronary heart phantom are simulated. Motion-compensated reconstructions with varying accuracy of the applied motion field are carried out for a late diastolic heart phase and compared to the reconstruction obtained with the standard FDK-method from projections of the corresponding motion-free model in the same heart phase. Furthermore, gated reconstructions are calculated by weighting the projections according to their cardiac phase without using a motion vector field. Different gating window widths are applied, and the reconstructions are compared. Using the correct motion field with the motion-compensated reconstruction, the image quality of the standard reconstruction from the corresponding motion-free coronary model can almost be recovered. The reconstructed image quality stays acceptable if the accuracy of the motion field sampling points is better than 1 mm. The gated reconstructions with a window width of 15%-20% of the cardiac cycle lead to superior results compared to nearest neighbor gating, especially for histogram based visualization and analysis. The motion-compensated reconstructions provide sharp images of the coronaries far surpassing the image quality of gated reconstructions.
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