Abstract
In recent years, image reconstruction methods for cone-beam computed tomography (CT) have been widely discussed with default setting of geometry that the normal vector of the detector plane passing the X ray source crosses the rotation axis. However, this may not be true in reality. In this paper, we defined a cone beam CT with freedom in the arrangement of an X ray source and detector. A circular trajectory scan is studied. An FDK-type reconstruction is derived for this kind of CT geometry. The reconstruction formulae are similar to the well-known FDK. The implementation is simple and straightforward. It reduces to the original FDK if the default setting of geometry for traditional circular CT is applied. Hence, one can adapt our method directly to current applications and allow more flexibility in system arrangement. A computer-simulation study is performed to validate the reconstruction algorithm and demonstrate its performance. The proposed algorithm for a free-geometry cone beam CT can reconstruct the exact mid-plane image of the object and a volume within a reasonable cone angle with very small error like FDK for traditional CT.