An inverse boundary value problem arising in nonlinear acoustics

TL;DR

This paper addresses an inverse problem in nonlinear ultrasound imaging, demonstrating that boundary measurements can uniquely determine the medium's nonlinearity through a quasilinear wave model.

Contribution

It establishes the theoretical link between boundary data and the nonlinearity in a quasilinear wave equation used in nonlinear acoustics.

Findings

Boundary measurements determine the nonlinearity uniquely.

The inverse problem is well-posed under the given model.

The approach applies to nonlinear ultrasound imaging scenarios.

Abstract

We consider an inverse problem arising in nonlinear ultrasound imaging. The propagation of ultrasound waves is modeled by a quasilinear wave equation. We make measurements at the boundary of the medium encoded in the Dirichlet-to-Neumann map, and we show that these measurements determine the nonlinearity.