Image reconstruction in quantitative photoacoustic tomography with the simplified $P_2$ approximation

TL;DR

This paper explores using the simplified P2 equations as a new light propagation model in photoacoustic tomography, demonstrating its feasibility and providing theoretical stability analysis.

Contribution

It introduces the simplified P2 approximation for PAT, offering a potentially more accurate model than classical diffusion and transport equations.

Findings

Numerical evidence supports the feasibility of the simplified P2 model in PAT.

Stability results are derived for the proposed model.

The approach offers an alternative to existing light propagation models in PAT.

Abstract

Photoacoustic tomography (PAT) is a hybrid imaging modality that intends to construct high-resolution images of optical properties of heterogeneous media from measured acoustic data generated by the photoacoustic effect. To date, most of the model-based quantitative image reconstructions in PAT are performed with either the radiative transport equation or its classical diffusion approximation as the model of light propagation. In this work, we study quantitative image reconstructions in PAT using the simplified $P_2$ equations as the light propagation model. We provide numerical evidences on the feasibility of this approach and derive some stability results as theoretical justifications.