  The photoacoustic tomography (PAT) is a hybrid modality that combines the
optics and acoustics to obtain high resolution and high contrast imaging of
heterogeneous media. In this work, our objective is to study the inverse
problem in the quantitative step of PAT which aims to reconstruct the optical
coefficients of the governing radiative transport equation from the ultrasound
measurements. In our analysis, we take the simplified $P_N$ approximation of
the radiative transport equation as the physical model and then show the
uniqueness and stability for this modified inverse problem. Numerical
simulations based on synthetic data are presented to validate our analysis.
