Speaker: Yimin Zhong (Auburn University)

 

Title: Photoacoustic Imaging with Multi-Photon Absorption

 

 

Abstract: In this talk, we discuss photoacoustic imaging with multi-photon absorption, where the quantitative part can be modeled as an inverse problem for a semilinear radiative transport model in which the absorption coefficient depends on the angular average of the transport solution. Our first result is a well-posedness theory for the transport model with general boundary data, significantly improving previous results for small boundary data. For the inverse problem of reconstructing the nonlinear absorption coefficient from internal data, we develop stability results for the reconstructions and unify a stability theory for both the diffusion and transport regimes by introducing a weighted norm that penalizes the contribution from the boundary region. The problems studied here are motivated by applications such as photoacoustic imaging of multi-photon absorption of heterogeneous media.