Nonlinear quantitative photoacoustic tomography with two-photon absorption
For researchers in photoacoustic imaging, this work provides theoretical foundations for quantitative TP-PAT, though it is incremental as it extends existing analysis to a semilinear model.
The paper addresses the inverse problem of reconstructing optical coefficients in two-photon photoacoustic tomography (TP-PAT) from internal absorbed energy data, deriving uniqueness and stability results and presenting numerical reconstructions with synthetic data.
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.