Title : ( An inversion formula for the transport equation in ℝ3 using complex analysis in several variables )
Authors: Seyed Majid Saberi Fathi ,
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Abstract
In this paper, the stationary photon transport equation has been extended by analytical continuation from R3 to C3. A solution to the inverse problem posed by this equation is obtained on a hyper-sphere and a hyper-cylinder as X-ray and Radon transforms, respectively. We show that these results can be transformed into each other, and they agree with known results. Numerical reconstructions of a three-dimensional Shepp–Logan head phantom using the obtained inverse formula illustrate the analytical results obtained in this manuscript.
Keywords
, Transport equation; complex analysis in several variables; inversion formula; Radon transform; X, ray/cone beam transform
@article{paperid:1071954,
author = {Saberi Fathi, Seyed Majid},
title = {An inversion formula for the transport equation in ℝ3 using complex analysis in several variables},
journal = {Journal of Inverse and Ill-Posed Problems},
year = {2018},
month = {October},
issn = {0928-0219},
keywords = {Transport equation; complex analysis in several variables; inversion formula; Radon transform; X-ray/cone beam transform},
}
%0 Journal Article
%T An inversion formula for the transport equation in ℝ3 using complex analysis in several variables
%A Saberi Fathi, Seyed Majid
%J Journal of Inverse and Ill-Posed Problems
%@ 0928-0219
%D 2018
