Numerical reconstruction of radiative sources in an absorbing and non-diffusing scattering medium in two dimensions

TL;DR

This paper presents a numerical method for reconstructing radiative sources within a two-dimensional absorbing and scattering medium, demonstrating its effectiveness through simulations relevant to optical molecular imaging.

Contribution

The paper introduces a numerical implementation of a new reconstruction method for anisotropic scattering media where diffusion approximation fails.

Findings

Solution is exact for finite Fourier content scattering kernels

Numerical experiments confirm the method's feasibility

Applicable to optical molecular imaging scenarios

Abstract

We consider the two dimensional quantitative imaging problem of recovering a radiative source inside an absorbing and scattering medium from knowledge of the outgoing radiation measured at the boundary. The medium has an anisotropic scattering property that is neither negligible nor large enough for the diffusion approximation to hold. We present the numerical realization of the authors' recently proposed reconstruction method. For scattering kernels of finite Fourier content in the angular variable, the solution is exact. The feasibility of the proposed algorithms is demonstrated in several numerical experiments, including simulated scenarios for parameters meaningful in optical molecular imaging.