Well-posedness for Photoacoustic Tomography with Fabry-Perot Sensors

In the mathematical analysis of photoacoustic imaging, it is usually assumed that the acoustic pressure (Dirichlet data) is measured on a detection surface. However, actual ultrasound detectors gather data of a different type. In this paper, we propose a more realistic mathematical model of ultrasound measurements acquired by the Fabry--Perot sensor. This modeling incorporates directional response of such sensors. We study the solvability of the resulting photoacoustic tomography problem, concluding that the problem is well-posed under certain assumptions. Numerical reconstructions are implemented using the Landweber iterations, after discretization of the governing equations using the finite element method

A Hybrid Reconstruction Approach for Absorption Coefficient by Fluorescence Photoacoustic Tomography

In this paper, we propose a hybrid method to reconstruct the absorption coefficient by fluorescence photoacoustic tomography (FPAT), which combines a squeeze iterative method (SIM) and a nonlinear optimization method. The SIM is to use two monotonic sequences to squeeze the exact coefficient, and it quickly locates near the exact coefficient. The nonlinear optimization method is utilized to attain a higher accuracy. The hybrid method inherits the advantages of each method with higher accuracy and faster convergence. The hybrid reconstruction method is also suitable for multi-measurement. Numerical experiments show that the hybrid method converges faster than the optimization method in multi-measurement case, and that the accuracy is also higher in one-measurement case.Comment: 25 pages, 9 figures, 1 tabl

Unique determination of absorption coefficients in a semilinear transport equation

Motivated by applications in quantitative photoacoustic imaging, we study inverse problems to a semilinear radiative transport equation (RTE) where we intend to reconstruct absorption coefficients in the equation from single and multiple internal data sets. We derive uniqueness and stability results for the inverse transport problem in the absence of scattering (in which case we also derive some explicit reconstruction methods) and in the presence of known scattering.Comment: 30 page