An inversion formula for the transport equation in ℝ3 using complex analysis in several variables-Reference-Cited by-同舟云学术

An inversion formula for the transport equation in ℝ3 using complex analysis in several variables

Published:2018-10-30 Issue:3 Volume:27 Page:341-352
ISSN:1569-3945
Container-title:Journal of Inverse and Ill-posed Problems
language:en
Short-container-title:

Author:

Saberi Fathi Seyed Majid¹^ORCID

Affiliation:

1. Department of Physics , Faculty of Science , Ferdowsi University of Mashhad , Mashhad , Iran

Abstract

Abstract In this paper, the stationary photon transport equation has been extended by analytical continuation from ℝ 3

{\mathbb{R}^{3}}

to ℂ 3

{\mathbb{C}^{3}}

. 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.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/jiip-2018-0015/pdf

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