An Inverse Source Problem in Radiative Transfer with Partial Data

TL;DR

This paper investigates the inverse source problem in radiative transfer with partial data, demonstrating conditions under which sources and their wave front sets can be recovered in certain regions, extending previous full data results.

Contribution

It extends the inverse source problem analysis to partial data scenarios, showing recoverability of sources and wave front sets under smoothness conditions.

Findings

Recovery of sources supported in the visible set.

Recovery of wave front set components supported in the microlocally visible set.

Extension of full data results to partial data case.

Abstract

The inverse source problem for the radiative transfer equation is considered, with partial data. Here it is shown that under certain smoothness conditions on the scattering and absorption coefficients, one can recover sources supported in a certain subset of the domain, which we call the visible set. Furthermore, it is shown for an open dense set of $C^{\infty}$ absorption and scattering coefficients that one can recover the part of the wave front set of the source that is supported in the microlocally visible set, modulo a function in the Sobolev space $H^{k}$ for $k$ arbitrarily large. This is an extension to the full data case, which is considered in \cite{inversesource}.