Numerical reconstruction of radiative sources from partial boundary measurements

TL;DR

This paper presents a numerical method for reconstructing radiative sources within a medium using boundary measurements, addressing stability issues in the inverse problem.

Contribution

It introduces a stable numerical algorithm for inverse source reconstruction in radiative transport, handling the instability of operator inversion.

Findings

The discretized inverse operator's continuity constant grows at most linearly with discretization.

The proposed method stabilizes the inverse problem despite inherent instability.

Numerical results demonstrate effective source reconstruction within the convex hull of boundary measurements.

Abstract

We consider an inverse source problem in the stationary radiative transport through an absorbing and scattering medium in two dimensions. Using the angularly resolved radiation measured on an arc of the boundary, we propose a numerical algorithm to recover the source in the convex hull of this arc. The method involves an unstable step of inverting a bounded operator whose range is not closed. We show that the continuity constant of the discretized inverse grows at most linearly with the discretization step, thus stabilizing the problem.