Uniqueness and Non-uniqueness in inverse radiative transfer

TL;DR

This paper investigates the inverse problem in stationary radiative transfer, revealing gauge equivalence classes of solutions and conditions for unique media recovery, especially when absorption depends on travel direction.

Contribution

It characterizes non-uniqueness via gauge equivalence and establishes conditions for unique determination of media properties in inverse radiative transfer problems.

Findings

Gauge equivalent pairs produce identical albedo operators.

Unique recovery of media when absorption depends on travel direction.

Extension of previous results to directional dependent absorption.

Abstract

We characterize the non-uniqueness in the inverse problem for the stationary transport model, in which the absorption "a" and the scattering coefficient "k" are to be recovered from the albedo operator. We show that "gauge equivalent" pairs (a,k) yield the same albedo operator, and that we can recover uniquely the class of gauge equivalent pairs. We apply this result to show unique determination of the media when the absorption "a" depends on the line of travel through each point while scattering "k" obeys a symmetry property. Previously known results concerned directional independent absorption.