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 reconstruction from transverse truncated projections of fan-beam scans. This paper introduced and reformulated 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 transverse 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 implications of ROI reconstruction from truncated data are discussed, which suggests that the BPF algorithm can be used in the ROI reconstruction from truncated projections.
