Inverse transport problems in quantitative PAT for molecular imaging

TL;DR

This paper investigates inverse problems in fluorescence photoacoustic tomography, focusing on reconstructing physical coefficients from ultrasound data, with theoretical guarantees and algorithms validated through numerical simulations.

Contribution

It provides new uniqueness and stability results for inverse radiative transport problems in fPAT and develops efficient reconstruction algorithms.

Findings

Proved uniqueness and stability of inverse problems in fPAT.

Developed algorithms validated by synthetic data simulations.

Complemented previous work in the diffusive regime with results in the radiative transport regime.

Abstract

Fluorescence photoacoustic tomography (fPAT) is a molecular imaging modality that combines photoacoustic tomography (PAT) with fluorescence imaging to obtain high-resolution imaging of fluorescence distributions inside heterogeneous media. The objective of this work is to study inverse problems in the quantitative step of fPAT where we intend to reconstruct physical coefficients in a coupled system of radiative transport equations using internal data recovered from ultrasound measurements. We derive uniqueness and stability results on the inverse problems and develop some efficient algorithms for image reconstructions. Numerical simulations based on synthetic data are presented to validate the theoretical analysis. The results we present here complement these in [Ren-Zhao, SIAM J. Imag. Sci., 2013] on the same problem but in the diffusive regime.