Complete Source Trajectories for C-Arm Systems and a Method for Coping with Truncated Cone-Beam Projections

1 Introduction A C-arm system, such as the one shown in Figure 1, may be used to acquire X-ray cone-beam projections of a patient's three-dimensional (3D) region of interest (ROI) while the X-ray source moves along some trajectory around the ROI. Then, a 3D image of the X-ray attenuation coefficient within the ROI may be reconstructed from the acquired cone-beam projections. In fact, C-arm systems are being used in this way, see e.g. [1, 2]. Typically, the source moves along a circular arc spanning an angle of 180 • –200 • , and the image is reconstructed by a variant of the algorithm of Feldkamp, Davis, and Kress [3]. As the cone-beam does not cover the whole patient, the projections are truncated. This is usually handled by extending the projections in a simple manner parallel to the plane containing the source trajectory. In practice, the true trajectory differs slightly from its ideal, but this deviation can be measured [5, 6] and taken into account during the reconstruction. The reconstructed image is subjected to a surface or volume rendering process designed to extract and visualize only the high contrast structures of the object under examination. The reconstructed image itself is usually cluttered by severe artifacts. Nevertheless, the high contrast structures, such as bones or blood vessels filled with intraarterially injected contrast agents, are well recovered. This is because such structures stand out well against the background and are also reconstructed at the correct geometric locations. Accurate images of medium contrast structures, such as blood vessels filled with intravenously injected contrast agents, or low contrast structures, such as soft tissue organs, are not obtained in this way. If this is to be improved upon, the following conditions will have to be met: First, the data acquired by the C-arm system must provide (after some preprocessing) accurate, though sampled, cone-beam projections of the object function (the X-ray attenuation coefficient). Second, the sampling density along the trajectory and on the detector surface must be sufficiently high. Third, the source trajectory must be complete in the sense that every plane that intersects the ROI contains a source point. Fourth, the cone beam projections must not be truncated. Under these conditions, any standard exact cone-beam reconstruction algorithm will produce an accurate estimate of the object function within the ROI. It has been tacitly assumed that the object function varies only spatially. Imaging moving parts of the …