Comparison of two three-dimensional x-ray cone-beam-reconstruction algorithms with circular source trajectories

Abstract

We compare two algorithms of three-dimensional (3D) cone-beam tomography: a 3D backprojection algorithm and a Radon algorithm, with a circular source trajectory. We recall the principle of these algorithms and show that when the source trajectory is circular, an exact reconstruction cannot be performed. We evaluate structures that cannot be detected and show that, for each algorithm, assumptions must be made about the object to estimate the missing information. Using simulated data, we measured the modulation transfer function of the two algorithms, evaluated the density resolution, and measured the artifacts due to missing information. We show that the 3D backprojection algorithm has good geometrical resolution along the axis of rotation and that, from the standpoint of density resolution, its useful limit is ±3°. We also show that it is sensitive to the lack of information in the horizontal planes. The useful aperture of the Radon algorithm is ±12°; for apertures lower than this limit, the algorithm is much less sensitive to the lack of information in the horizontal planes than the 3D backprojection algorithm. We present two examples of reconstructions that illustrate the limitations of these algorithms when applied to realistic samples and discuss the limits of using each algorithm when the source trajectory is circular.