Numerical Reconstruction of Radiative Sources from Partial 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. Numerical examples presented show the effectiveness of the proposed method.