On the inversion of the Radon transform on a generalized Cormack-type class of curves
On the inversion of the Radon transform on a generalized Cormack-type class of curves
复制标题
关于广义 Cormack 型曲线类的 Radon 变换的反演
DOI：
10.1088/0266-5611/29/11/115010
复制
发表时间：
2013
期刊：
影响因子：
2.1
通讯作者：
G. Rigaud
中科院分区：
文献类型：
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作者：
G. Rigaud
1981年，Cormack研究了定义在一族曲线族上的Radon变换，并通过它们的圆调和展开式展示了它们的逆。在本文中，我们建议将这一性质推广到由一阶非线性微分方程定义的更一般的曲线族。特别地，我们重点研究了这一族的一个子类，它可以推广Cormack在1964年所证明的奇异值分解。由于定义在其三种曲线上的Radon变换可以用来模拟三种不同的康普顿散射层析成像模式，因此基于这一子类的应用清晰可见。利用解析反演法和切比雪夫/泽尼克展开法对这三种Radon变换进行了仿真，结果表明了该方法的有效性和有效性。
In 1981 Cormack studied the Radon transform defined on a family of curves and showed their inversion through their circular harmonic expansions. In this paper we propose to extend this property to a more general family of curves which are defined by a nonlinear-first-order differential equation. In particular we focus on a subclass of this family for which the singular value decomposition shown by Cormack in 1964 can be generalized. Applications based on this subclass clearly appear since the Radon transform defined on three kinds of its curves may serve to model three different Compton scattering tomography modalities. Simulation results using analytical inversions and Chebyshev/Zernike expansions for these three Radon transform show the strength and the validation of proposed inversion methods.
DOI：
10.1088/1751-8113/46/25/254015
发表时间：
2013-06
期刊：
Journal of Physics A: Mathematical and Theoretical
影响因子：
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作者：
Hong-liu Yang;G. Radons
通讯作者：
Hong-liu Yang;G. Radons