In this article we introduce an exact backprojection filtered (BPF) type reconstruction algorithm for cone-beam scans based on Zou and Pan’s work. The algorithm can reconstruct images using only the projection data passing through the parallel PI-line segments in reduced scans. Computer simulations and practical experiments are carried out to evaluate this algorithm. The BPF algorithm has a higher computational efficiency than the famous FDK algorithm. The BPF algorithm is evaluated using the practical CT projection data on a 450 keV X-ray CT system with a flat-panel detector (FPD). From the practical experiments, we get the spatial resolution of this CT system. The algo- rithm could achieve the spatial resolution of 2.4 lp/mm and satisfies the practical applications in industrial CT inspec- tion.
In this paper we develop a general exact fan-beam reconstruction algorithm for free-form trajectories not only closed but also unclosed,based on the fan-beam reconstruction formula recently developed by Noo et al.. A mathematical proof is then provided with the geometrical explanation of equi-spatial detectors. With this algorithm we can obtain exact region of interest (ROI) reconstruction if and only if every projecting line passing through the ROI intersects the free-form source trajectory,when the projections are not truncated. Furthermore,under the condi- tion that the source-to-detectors distance changes slowly enough relative to the length itself,we obtain a very good approximate reconstruction algorithm,which is the same as the algorithm of the circular trajectory except that the source-to-detectors distance is a function of the rotation angle. Then the algorithms are tested using the Shepp-Logan phantom and the experiment shows that the algorithms can get perfect numerical results.
Some novel reconstruction algorithms have recently been proposed to solve the problem of re-construction from transverse truncated projections of fan-beam scans. This paper introduced and reformu-lated the exact backprojection-filtration (BPF)-type reconstruction algorithm for fan-beam scans based on Zou and Pan's work. Subsequently, a legible and implementary BPF algorithm for region-of-interest (ROI) reconstruction is presented using projection data truncated not only in angle-scanning but also in the trans-verse direction. The algorithm can be widely used for fan-beam full-scans, short-scans, or super-short-scans. The algorithm uses less projection data than the preceding super-short-scan. The algorithm is implemented using the Shepp-Logan phantom and some primary results are presented. Some new discoveries and impli-cations of ROI reconstruction from truncated data are discussed, which suggests that the BPF algorithm can be used in the ROI reconstruction from truncated projections.
