An efficient algorithm to compute the X-ray transform

doi:10.1080/00207160.2021.1969017

	An efficient algorithm to compute the X-ray transform
	Chen, Chong 2; Wang, Runqian 3; Bajaj, Chandrajit 4; Oktem, Ozan 1
刊名	INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
	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
出版者	TAYLOR & FRANCIS LTD
WOS记录号	WOS:000690307600001
内容类型	期刊论文
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.KTH Royal Inst Technol, Dept Math, Stockholm, Sweden 2.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China 3.Princeton Int Sch Math & Sci, Princeton, NJ USA 4.Univ Texas Austin, Dept Comp Sci, Oden Inst Computat Engn & Sci, Austin, TX 78712 USA
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.