Acoustic nonlinearity parameter tomography as an inverse coefficient problem for a nonlinear wave equation

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RNTW02 - Rich and non-linear tomography in medical imaging, materials and non destructive testing

We consider an undetermined coefficient inverse problem for a nonlinear partial differential equation occuring in high intensity ultrasound propagation as used in acoustic tomography.   In particular, we investigate the recovery of the nonlinearity coefficient commonly labeled as $B/A$ in the literature, which is part of a space dependent coefficient $\kappa$ in the Westervelt equation governing nonlinear acoustics.   Corresponding to the typical measurement setup, the overposed data consists of time trace measurements on some zero or one dimensional set $\Sigma$ representing the receiving transducer array. In this talk, we will dwell on topics like modeling, uniqueness, numerical reconstruction schemes (in particular based on Newton type methods) as well as simultaneous reconstruction of $\kappa$ and the sound speed. If time permits, we will also show some recent results pertaining to the formulation of this problem in frequency domain and numerical reconstruction of piecewise constant coefficients in two space dimensions.   This is joint work with Bill Rundell, Texas A&M University.

This talk is part of the Isaac Newton Institute Seminar Series series.

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