An inverse source problem for linearly anisotropic radiative sources in absorbing and scattering medium

TL;DR

This paper addresses the inverse problem of recovering linearly anisotropic radiative sources in a 2D absorbing and scattering medium using boundary measurements, employing a novel approach based on Beltrami-like equations.

Contribution

It introduces a method to recover anisotropic sources in a complex medium without relying on diffusion approximation, using $A$-analytic maps and boundary data analysis.

Findings

Recovery of anisotropic sources from boundary data in finite Fourier content scenarios.

Conditions for data indistinguishability between different sources.

Application of Beltrami-like equations to inverse radiative transport problems.

Abstract

We consider in a two dimensional absorbing and scattering medium, an inverse source problem in the stationary radiative transport, where the source is linearly anisotropic. The medium has an anisotropic scattering property that is neither negligible nor large enough for the diffusion approximation to hold. The attenuating and scattering properties of the medium are assumed known. For scattering kernels of finite Fourier content in the angular variable, we show how to recover the anisotropic radiative sources from boundary measurements. The approach is based on the Cauchy problem for a Beltrami-like equation associated with $A$-analytic maps. As an application, we determine necessary and sufficient conditions for the data coming from two different sources to be mistaken for each other.