An efficient algorithm to compute the X-ray transform
文献类型：期刊论文
| 作者 | Chen, Chong1; Wang, Runqian2; Bajaj, Chandrajit3; Oktem, Ozan4 |
| 刊名 | INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
 |
| 出版日期 | 2021-08-31 |
| 页码 | 19 |
| 关键词 | X-ray transform intersection length projection matrix non-vanishing intersectability ambiguity and flexibility tomographic image reconstruction |
| ISSN号 | 0020-7160 |
| DOI | 10.1080/00207160.2021.1969017 |
| 英文摘要 | We propose a new algorithm to compute the X-ray transform of an image represented by unit (pixel/voxel) basis functions. The fundamental task is equivalently calculating the intersection lengths of the ray with associated units. For the given ray, we derive the sufficient and necessary condition for non-vanishing intersectability. By this condition, we can distinguish the units that produce valid intersections with the ray. Only for those units, we calculate the intersection lengths by the obtained analytic formula. The proposed algorithm is adapted to various two-dimensional (2D)/three-dimensional (3D) scanning geometries, and its several issues are also discussed, including the intrinsic ambiguity, flexibility, computational cost and parallelization. The proposed method is fast and easy to implement, more complete and flexible than the existing alternatives with respect to different scanning geometries and different basis functions. Finally, we validate the correctness of the algorithm. |
| 资助项目 | Beijing Natural Science Foundation[Z180002] ; Swedish Foundation of Strategic Research[AM13-0049] |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000690307600001 |
| 出版者 | TAYLOR & FRANCIS LTD |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/59180]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Chen, Chong |
| 作者单位 | 1.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China 2.Princeton Int Sch Math & Sci, Princeton, NJ USA 3.Univ Texas Austin, Dept Comp Sci, Oden Inst Computat Engn & Sci, Austin, TX 78712 USA 4.KTH Royal Inst Technol, Dept Math, Stockholm, Sweden |
| 推荐引用方式 GB/T 7714 | Chen, Chong,Wang, Runqian,Bajaj, Chandrajit,et al. An efficient algorithm to compute the X-ray transform[J]. INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS,2021:19. |
| APA | Chen, Chong,Wang, Runqian,Bajaj, Chandrajit,&Oktem, Ozan.(2021).An efficient algorithm to compute the X-ray transform.INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS,19. |
| MLA | Chen, Chong,et al."An efficient algorithm to compute the X-ray transform".INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS (2021):19. |
入库方式： OAI收割
来源：数学与系统科学研究院
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