A Fourier approach to the inverse source problem in an absorbing and anisotropic scattering medium
Analysis of PDEs
2020-01-29 v1 Complex Variables
Abstract
We revisit the inverse source problem in a two dimensional absorbing and scattering medium and present a non-iterative reconstruction method using measurements of the radiating flux at the boundary. The attenuation and scattering coefficients are known and the unknown source is isotropic. The approach is based on the Cauchy problem for a Beltrami-like equation for the sequence valued maps, and extends the original ideas of A. Bukhgeim from the non-scattering to scattering media. We demonstrate the feasibility of the method in a numerical experiment in which the scattering is modeled by the two dimensional Henyey-Greenstein kernel with parameters meaningful in Optical Tomography.
Keywords
Cite
@article{arxiv.1907.07423,
title = {A Fourier approach to the inverse source problem in an absorbing and anisotropic scattering medium},
author = {Hiroshi Fujiwara and Kamran Sadiq and Alexandru Tamasan},
journal= {arXiv preprint arXiv:1907.07423},
year = {2020}
}