Propagation of boundary-induced discontinuity in stationary radiative transfer and its application to the optical tomography

TL;DR

This paper investigates how boundary conditions cause discontinuities in solutions to stationary radiative transfer equations and introduces a method to reconstruct attenuation coefficients from boundary measurement jumps.

Contribution

It provides new conditions for boundary-induced discontinuities and proposes a novel reconstruction method for attenuation coefficients in optical tomography.

Findings

Discontinuities are caused by boundary data in stationary radiative transfer.

Sufficient conditions for boundary-induced discontinuity are established.

A reconstruction method for attenuation coefficients from boundary jumps is proposed.

Abstract

We consider a boundary value problem of the stationary transport equation with the incoming boundary condition in two or three dimensional bounded convex domains. We discuss discontinuity of the solution to the boundary value problem arising from discontinuous incoming boundary data, which we call the boundary-induced discontinuity. In particular, we give two kinds of sufficient conditions on the incoming boundary data for the boundary-induced discontinuity. We propose a method to reconstruct attenuation coefficient from jumps in boundary measurements.