Nonlinear quantitative photoacoustic tomography with two-photon absorption

TL;DR

This paper develops a mathematical framework for reconstructing two-photon absorption properties in tissue using photoacoustic measurements, providing theoretical guarantees and numerical validation for the inverse problem.

Contribution

It introduces a novel inverse problem analysis for quantitative TP-PAT, including uniqueness, stability, and numerical reconstruction methods for optical coefficients.

Findings

Proved uniqueness of the optical coefficient reconstruction.

Established stability estimates for the inverse problem.

Demonstrated numerical reconstructions with synthetic data.

Abstract

Two-photon photoacoustic tomography (TP-PAT) is a non-invasive optical molecular imaging modality that aims at inferring two-photon absorption property of heterogeneous media from photoacoustic measurements. In this work, we analyze an inverse problem in quantitative TP-PAT where we intend to reconstruct optical coefficients in a semilinear elliptic PDE, the mathematical model for the propagation of near infra-red photons in tissue-like optical media with two-photon absorption, from the internal absorbed energy data. We derive uniqueness and stability results on the reconstructions of single and multiple optical coefficients, and present some numerical reconstruction results based on synthetic data to complement the theoretical analysis.