| A general fan-beam reconstruction algorithm for free-form trajectories |
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| 引用本文： | LILiang CHENZhi-Qiang WANGGe KANGKe-Jun. A general fan-beam reconstruction algorithm for free-form trajectories[J]. 核技术(英文版), 2005, 16(3): 171-176 |
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| 作者姓名： | LILiang CHENZhi-Qiang WANGGe KANGKe-Jun |
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| 作者单位： | [1]DepartmentofEngineeringPhysics,TsinghuaUniversity,Beijing100084.China [2]DepartmentofBiomedicalEngineering,UniversityofIowa,IowaCity,Iowa,USA |
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| 基金项目： | 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). |
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| 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 condition 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.
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| 关 键 词： | 扫描成象 扇形波束 图像重构 优化算法 |
A general fan-beam reconstruction algorithm for free-form trajectories |
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| LI Liang,CHEN Zhi-Qiang,WANG Ge,KANG Ke-jun. A general fan-beam reconstruction algorithm for free-form trajectories[J]. , 2005, 16(3): 171-176 |
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| Authors: | LI Liang CHEN Zhi-Qiang WANG Ge KANG Ke-jun |
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| Affiliation: | 1. Department of Engineering Physics, Tsinghua University, Beijing 100084, China
2. Department of Biomedical Engineering, University of Iowa, Iowa City, Iowa, USA |
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| Abstract: | 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. |
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| Keywords: | Tomography Fan-beam Image reconstruction Region of Interest (ROI) |
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