一类R^n空间上旋转椭球面簇的广义Radon变换

Generalized Radon Transformation along a Family of Rotating Ellipsoids in R^n

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。

Based on the principles of bistatic radar imaging,this paper deals with themathematical problem of bistatic radar imaging.For an image function f(x)in R(?),giventhe integral values of,f(x)over a family of rotating ellipsoids,the generalized Radontransformation 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 harmonicfunction 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.