A FACTORIZATION METHOD FOR THE 3D X-RAY TRANSFORM
A FACTORIZATION METHOD FOR THE 3D X-RAY TRANSFORM
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DOI：
10.1088/0266-5611/11/5/003
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发表时间：
1995-10-01
期刊：
影响因子：
2.1
通讯作者：
DEFRISE, M
中科院分区：
文献类型：
--
作者：
DEFRISE, M
我们考虑的三维（3D）X射线变换的反演与有限的数据集包含线积分，其中有两个交叉点与圆柱形探测器的侧表面。通常解决这一问题的方法是基于三维滤波反投影，但这种方法速度较慢。本文提出了一种新的算法，该算法的因素的三维重建问题的一组独立的二维Radon变换的堆叠的平行切片。然后使用标准2D滤波反投影重建每个切片。该算法基于对数据的2D傅立叶变换的静止相位近似的应用，并且是Edholm等人针对2D Radon变换导出的频率-距离关系的三维扩展。误差估计也得到了。
We consider the inversion of the three-dimensional (3D) x-ray transform with a limited data set containing the line integrals which have two intersections with the lateral surface of a cylindrical detector. The usual solution to this problem ids based on 3D filtered-backprojection, but this method is slow. This paper presents a new algorithm which factors the 3D reconstruction problem into a set of independent 2D radon transforms for a stack of parallel slices. Each slice is then reconstructed using standard 2D filtered-backprojection. the algorithm is based on the application of the stationary-phase approximation to the 2D Fourier transform of the data, and is an extension to three dimensions of the frequency-distance relation derived by Edholm et al for the 2D radon transform. Error estimates are also obtained.