非均匀衰减Radon变换的反演问题

Inversion of non-uniform attenuation Radon transform

本文主要利用傅里叶变换,Riesz位势,积分变换和广义中心切片定理将Natterer的结果推广到了非均匀衰减的情形,构建了衰减Radon变换的精确重建公式.同时,通过该公式研究了衰减Radon变换的值域,从而将Rigaud和Lakhal的Sobolev估计结果推广到了n维空间.

In this paper,the results of Natterer are generalized to non-uniform attenuation using Fourier transform,Riesz potential,integral transform and generalized central slice theorem,and the exact reconstruction formula of attenuated Radon transform is constructed.Meanwhile,through the stated formula,the range of attenuated Radon transform is studied,then the Sobolev estimation results of Rigaud and Lakhal are extended to n-dimensional space.