Global Lipschitz Stability in Determining Coefficients of the Radiative Transport Equation

TL;DR

This paper establishes Lipschitz stability estimates for inverse problems in the radiative transport equation, enabling the determination of scattering or attenuation coefficients from boundary data with optimal bounds.

Contribution

It provides the first Lipschitz stability results for these inverse problems, using Carleman estimates to achieve optimal bounds and reverse inequalities.

Findings

Lipschitz stability estimates for inverse coefficients

Optimal bounds proven via reverse inequalities

Method based on Carleman estimates with linear weight

Abstract

In this article, for the radiative transport equation, we study inverse problems of determining a time independent scattering coefficient or total attenuation by boundary data on the complementary sub-boundary after making one time input of a pair of a positive initial value and boundary data on a suitable sub-boundary. The main results are Lipschitz stability estimates. We can also prove the reverse inequality, which means that our estimates for the inverse problems are the best possible. The proof is based on a Carleman estimate with a linear weight function.