  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.
