# A Fourier approach to the inverse source problem in an absorbing and anisotropic scattering medium

## TL;DR

This paper introduces a non-iterative Fourier-based method for reconstructing an unknown isotropic source in a 2D absorbing, scattering medium, extending Bukhgeim's approach to complex media with practical optical tomography applications.

## Contribution

It develops a novel Fourier approach for inverse source problems in scattering media, generalizing previous non-scattering techniques to more realistic optical environments.

## Key findings

- Successful numerical demonstration with Henyey-Greenstein scattering kernel
- Extension of Bukhgeim's method to scattering media
- Feasibility shown for optical tomography scenarios

## 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.