An inversion formula for the transport equation in ℝ3 using complex analysis in several variables
2019 ◽
Vol 27
(3)
◽
pp. 341-352
Keyword(s):
X Ray
◽
Abstract In this paper, the stationary photon transport equation has been extended by analytical continuation from {\mathbb{R}^{3}} to {\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.