Well-posedness for Photoacoustic Tomography with Fabry-Perot Sensors
arXiv:1906.01090 · doi:10.1137/19M1248297
Abstract
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.
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