  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.
