A general fan-beam reconstruction algorithm for free-form trajectories  

作　　者：LILiang CHENZhi-Qiang WANGGe KANGKe-Jun 

机构地区：[1]DepartmentofEngineeringPhysics,TsinghuaUniversity,Beijing100084.China [2]DepartmentofBiomedicalEngineering,UniversityofIowa,IowaCity,Iowa,USA

出　　处：《Nuclear Science and Techniques》2005年第3期171-176,共6页核技术（英文）

基　　金：Supported by a grant from the Ph.D. Programs Foundation of Ministry of Education of China (No.20030003074) and the National Natural Science Foundation of China (No.10135040).

摘　　要：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.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.

关 键 词：扫描成象 扇形波束 图像重构 优化算法 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构] R814.42[自动化与计算机技术—计算机科学与技术]