Cone-beam reconstruction by the use of Radon transform intermediate functions
Cone-beam reconstruction by the use of Radon transform intermediate functions
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使用 Radon 变换中间函数进行锥束重建
DOI：
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发表时间：
1994
期刊：
影响因子：
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通讯作者：
M. Defrise
中科院分区：
文献类型：
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作者：
R. Clack;M. Defrise
提出了一个锥束重建的数学框架，通过中间函数，涉及到三维Radon变换的对象被成像。用滤波器处理锥束投影数据以形成中间函数。滤波器是斜坡核h1（l）和导数泛函h2（l）的线性组合ah 1（l）+bh 2（l）。根据中间函数，利用卷积和反投影完成重建，其中卷积滤波器是服从限制ac + bd = 1的另一线性组合ch 1（l）+dh 2（l）。该公式统一和推广了Tuy [ SIAM J.Appl.Math.43，546（1983）]、Smith [ IEEE Trans. Med. ImagingMI-4，14（1985）]和Grangeat [ Ph.D.论文（Ecole Nationale Telecommunications，巴黎，1987年）]。导出了这些方法的a、B、c、d的适当值。
A mathematical framework is presented for cone-beam reconstruction by intermediate functions that are related to the three-dimensional Radon transform of the object being imaged. Cone-beam projection data are processed with a filter to form an intermediate function. The filter is a linear combination ah1(l) + bh2(l) of the ramp kernel h1(l) and the derivative functional h2(l). From the intermediate function, the reconstruction is completed with a convolution and backprojection, where the convolution filter is another linear combination ch1(l) + dh2(l) subject to the restriction ac + bd = 1. This formulation unifies and generalizes the important cone-beam formulas of Tuy [ SIAM J. Appl. Math.43, 546 ( 1983)], Smith [ IEEE Trans. Med. ImagingMI-4, 14 ( 1985)], and Grangeat [ Ph.D. dissertation ( Ecole Nationale Superieure des Telecommunications, Paris, 1987)]. The appropriate values of a, b, c, d for these methods are derived.