A source reconstruction method in two dimensional radiative transport using boundary data measured on an arc

TL;DR

This paper presents a novel method for reconstructing sources in 2D radiative transport using boundary measurements on an arc, leveraging A-analytic maps and demonstrating robustness through numerical experiments.

Contribution

It introduces a new approach for inverse source reconstruction in 2D radiative transport with partial boundary data, extending previous methods to this specific case.

Findings

Successful source reconstruction with finite Fourier scattering kernels.

Method demonstrated to be robust through numerical experiments.

Extension of previous work to partial boundary data case.

Abstract

We consider an inverse source problem in the stationary radiating transport through a two dimensional absorbing and scattering medium. Of specific interest, the exiting radiation is measured on an arc. The attenuation and scattering properties of the medium are assumed known. For scattering kernels of finite Fourier content in the angular variable, we show how to quantitatively recover the part of the isotropic sources restricted to the convex hull of the measurement arc. The approach is based on the Cauchy problem with partial data for a Beltrami-like equation associated with $A$-analytic maps in the sense of Bukhgeim, and extends authors' previous work to this specific partial data case. The robustness of the method is demonstrated by the results of several numerical experiments.