| 一类R~n空间上旋转椭球面簇的广义Radon变换 |
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| 引用本文： | 吴一刚,邱佩璋.一类R~n空间上旋转椭球面簇的广义Radon变换[J].CT理论与应用研究,1993(1). |
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| 作者姓名： | 吴一刚 邱佩璋 |
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| 作者单位： | 北京信息工程学院应用教学研究室 100101
(吴一刚)，北京信息工程学院应用教学研究室 100101(邱佩璋) |
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| 摘 要： | 本文基于二维雷达成像的原理研究了其数学问题,对R~n 空间中的图像函数f(x),已知其旋转椭球面簇上的积分值,应用广义Radon 变换来重建图像函数f(x)。利用球谐函数展开和Funk-Heck 定理证明了这种重建图像问题的存在、唯一性,并在一定的函数类中给出了它的反演解的数学表达式和推广了V.G.Romanov的工作。
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| 关 键 词： | 广义Radon变换 球谐函数 旋转椭球面 |
Generalized Radon Transformation along a Family of Rotating Ellipsoids in R~n |
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| Wu Yigang Qiu Penzhang.Generalized Radon Transformation along a Family of Rotating Ellipsoids in R~n[J].Computerized Tomography Theory and Applications,1993(1). |
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| Authors: | Wu Yigang Qiu Penzhang |
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| Abstract: | Based on the principles of bistatic radar imaging,this paper deals with the
mathematical problem of bistatic radar imaging.For an image function f(x)in R(?),given
the integral values of,f(x)over a family of rotating ellipsoids,the generalized Radon
transformation is used to reconstruct the image function,f(x).The existence and unique-
ness of the image function have been proved with the expanison of spherical harmonic
function and the theorem of Furk-Heck.The mathematical formula of the inversion solu-
tion is given in certain classes of functions,and the work of Romanov's is extended. |
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| Keywords: | Generalized Radon transformation Spherical harmonic function Rotating ellipsoid |
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