Inverse transport and diffusion problems in photoacoustic imaging with nonlinear absorption

TL;DR

This paper investigates inverse problems in photoacoustic imaging involving nonlinear optical absorption, establishing uniqueness and stability results for reconstructing absorption coefficients from internal data, using linearization techniques.

Contribution

It introduces novel inverse problem analysis for nonlinear radiative transport equations and their diffusion approximations in photoacoustic imaging, with stability results for absorption coefficient reconstruction.

Findings

Proved uniqueness of the inverse problem solutions.

Established stability estimates for coefficient reconstruction.

Analyzed the impact of scattering coefficient variations on absorption recovery.

Abstract

Motivated by applications in imaging nonlinear optical absorption by photoacoustic tomography (PAT), we study in this work inverse coefficient problems for a semilinear radiative transport equation and its diffusion approximation with internal data that are functionals of the coefficients and the solutions to the equations. Based on the techniques of first- and second-order linearization, we derive uniqueness and stability results for the inverse problems. For uncertainty quantification purpose, we also establish the stability of the reconstruction of the absorption coefficients with respect to the change in the scattering coefficient.