Nonlinear ultrasound imaging modeled by a Westervelt equation
Analysis of PDEs
2022-02-04 v3
Abstract
We consider the ultrasound imaging problem governed by a nonlinear wave equation of Westervelt type with variable wave speed. We show that the coefficient of nonlinearity can be recovered uniquely from knowledge of the Dirichlet-to-Neumann map. Our proof is based on a second order linearization and the use of Gaussian beam solutions to reduce the problem to the inversion of a weighted geodesic ray transform. We propose an inversion algorithm and report the results of a numerical implementation to solve the nonlinear ultrasound imaging problem in a transmission setting in the frequency domain.
Keywords
Cite
@article{arxiv.2105.05423,
title = {Nonlinear ultrasound imaging modeled by a Westervelt equation},
author = {Sebastian Acosta and Gunther Uhlmann and Jian Zhai},
journal= {arXiv preprint arXiv:2105.05423},
year = {2022}
}