由投影重建图象的样条拟合法  

A Spline Fitting Method for Image Reconstruction from Projections

作　　者：李岳生[1] 胡日章[1] 

机构地区：[1]中山大学

出　　处：《计算数学》1992年第3期379-384,共6页Mathematica Numerica Sinica

摘　　要：曾获得诺贝尔医学奖的CT(计算机断层扫描)技术,其应用范围已从医学扩展到地质勘探、工业无损探伤等许多工程和科技领域.它的理论基础就是由投影重建图象这样一个数学问题,即已知某函数(在屏幕上表现为图象)沿低维流形(二维情形为直线或曲线,三维情形为平面或曲面)的积分值,反求函数(图象)本身.拉当早在1 916年就提出并研究了这一问题,一般称为拉当变换及其反演.目前已有很多实用算法,如代数重建法,卷积反投影法等田.而CT技术应用范围不断扩大。In this paper the problem of image reconstruction is considered as a constrained minimiza-tion problem of the functional where constraint conditions are volues of the integral on somemanifolds. Thus, a new method for image reconstruction from projections is developed. The co-mputational algorithms are constructed and the existence and the uniqueness of the solution as aspline function are proved. Some examples are given to illustrate the effectiveness of the method.

关 键 词：投影重建图象 样条拟合 CT技术 

分 类 号：R814.42[医药卫生—影像医学与核医学]