The exponential Radon transform, a generalization of the Radon transform, is defined and studied as a mapping of function spaces. It is represented in terms of Fourier transform of its domain and range, and this leads...The exponential Radon transform, a generalization of the Radon transform, is defined and studied as a mapping of function spaces. It is represented in terms of Fourier transform of its domain and range, and this leads to the harmonic decomposition reconstruction. The results are similar results of Tretiak and Metz.展开更多
The present work is devoted to the development of the extension of FRT (Finite Radon Transform) to the tridimensional case. One simple formulation is proposed and it is shown that it is the exact discretization of the...The present work is devoted to the development of the extension of FRT (Finite Radon Transform) to the tridimensional case. One simple formulation is proposed and it is shown that it is the exact discretization of the continuous Discrete Radon Transform. More precisely this is the case when the sampling is given on a regular grid i.e. the continuous function is filtered by the mean of the box function. Relation of this transform with the Discrete Fourier one is given and is for some help in numerical implementation.展开更多
基金Supported by the National Natural Science F oundation of China( No.199710 6 4) ,Key Project of Science and Tech-nology of Hubei Province Education Com mittee
文摘The exponential Radon transform, a generalization of the Radon transform, is defined and studied as a mapping of function spaces. It is represented in terms of Fourier transform of its domain and range, and this leads to the harmonic decomposition reconstruction. The results are similar results of Tretiak and Metz.
文摘The present work is devoted to the development of the extension of FRT (Finite Radon Transform) to the tridimensional case. One simple formulation is proposed and it is shown that it is the exact discretization of the continuous Discrete Radon Transform. More precisely this is the case when the sampling is given on a regular grid i.e. the continuous function is filtered by the mean of the box function. Relation of this transform with the Discrete Fourier one is given and is for some help in numerical implementation.
