Analysis of a cone beam x-ray tomographic system for different scanning modes

Cone beam x-ray tomography is based on the aquisition of two-dimensional projections for different positions of a cone beam x-ray source. Generally the x-ray source describes a single circle around the volume. We consider three different scanning modes: a sphere, a circle, and two orthogonal circles. We study the response of a cone beam reconstruction system defined as the weighted backprojection of the cone beam projections of an arbitrary impulse point. The spatial invariance of the system is discussed for the three acquisition geometries. Exact and approximate reconstruction methods based on three-dimensional convolution are then proposed. Some results obtained from both simulated and experimental data are presented and analyzed.