Abstract
Practical CT reconstruction algorithms incorporate assumptions concerning the X-ray source trajectory, and the detectors rotate in a circular trajectory. However, in order to reduce the scanning time or to reconstruct objects that move during projection acquisition, a free-form X-ray source trajectory is needed. In this paper, we present the derivation of a general reconstruction formula for a free-form trajectory from fan-beam projection data. Furthermore, we have rewritten the reconstruction formula using both equal-angle rays and equally spaced collinear detectors for practical implementation and application. As in any reconstruction processing, it is necessary to address the redundant projection data problem. We propose a plus-minus weighting scheme that avoids the need to calculate the number of intersection points between each X-ray line and trajectory. A numerical study was conducted using a standard Shepp-Logan phantom to verify the proposed algorithm.
