二维Radon变换在图像重建中的重要性质及定理  

Important Properties and Theorems of Two-dimensional Radon Transform in Image Reconstruction

作　　者：李静[1] 

机构地区：[1]周口师范学院数学与统计学院,河南周口466001

出　　处：《河南教育学院学报（自然科学版）》2015年第4期21-23,共3页Journal of Henan Institute of Education(Natural Science Edition)

基　　金：周口师范学院青年科研基金项目(ZKNUB315209)

摘　　要：Radon变换及其逆变换作为图像重建的数学基础,在图像重建中有着特殊的意义.首先介绍了二维Radon变换定义的几种形式,然后总结了二维Radon变换的基本性质:线性、带线性、对称性、周期性、位移性等,最后给出了中心切片定理和二维Radon逆变换公式并给予证明.The Radon transform and its inverse transform have special significance as the mathematical foundation of the image reconstruction. First,several forms of the definition of two-dimension Radon transform are introduced,and then the basic properties of two-dimensional Radon transform are summarized： linear,linear,symmetry,periodic,displacement and so on. Finally,the center section theorem and a two-dimensional Radon inverse transform formula are given and proved.

关 键 词：RADON变换 逆变换 傅里叶变换 图像重构 卷积 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]