Stability estimates in stationary inverse transport

TL;DR

This paper establishes an $L^1$-stability estimate for reconstructing spatially dependent scattering and absorption coefficients in stationary linear transport equations from boundary measurements, extending previous uniqueness and stability results.

Contribution

It generalizes prior stability estimates to spatially dependent coefficients, providing a new $L^1$-stability result in higher dimensions.

Findings

Proves an $L^1$-stability estimate for the inverse problem.

Extends stability results to spatially dependent coefficients.

Builds on and generalizes previous uniqueness and partial stability results.

Abstract

We study the stability of the reconstruction of the scattering and absorption coefficients in a stationary linear transport equation from knowledge of the full albedo operator in dimension $n\geq3$. The albedo operator is defined as the mapping from the incoming boundary conditions to the outgoing transport solution at the boundary of a compact and convex domain. The uniqueness of the reconstruction was proved in [M. Choulli-P. Stefanov, 1996 and 1999] and partial stability estimates were obtained in [J.-N. Wang, 1999] for spatially independent scattering coefficients. We generalize these results and prove an $L^1$-stability estimate for spatially dependent scattering coefficients.