三维Radon变换的一种快速解析方法

3D Radon变换及其反变换是X-CT三维图像重建理论的核心,它在其他许多学科领域也有广泛应用。3D Radon变换的表达式是一个三重积分,按照定义直接计算相当费时。为此,研究一种新的快速的方法实现3D Radon变换,对X-CT图像重建理论及相关领域的发展有重要意义。本文以算法仿真常用椭球模型为基础,通过求解椭球模型与空间任意平面的面积,实现了用解析的方法快速得到模型的Radon变换,进一步比较了它与传统方法的优缺点,最后根据Radon反变换重建出原物体模型;计算机仿真结果验证了这种方法的正确。

Fast Computation of 3D Radon Transform Via a Geometrical Method

Exact three-dimensional reconstruction algorithms are usually based on the three-dimensional Radon transform which is also widely used in other related fields.However,Radon transform consists of all Radon values placed at the corresponding points.Each value is defined as a plane integral in the object domain.So,the computation of Radon value is rather time expensive using direct integral method.New applications based on it may become convenient if a fast and efficient transformation algorithm is adopted.Therefore,an analytical method is proposed to compute the 3D Radon transform in this paper that is based on 3D S-L phantom including spheres and further compare it with the traditional algorithms of their advantages and disadvantages.Finally,the origin object reconstructed by 3D inverse Radon transform has been proved right by the result from computer simulation.