  Estimating the travel time of ultrasound in an inhomogeneous medium is
crucial for high-quality imaging, as with an accurate estimate of the
distribution of speed of sound, phase aberration, which is normally viewed as
one of the reasons for image degradation, can be corrected by multiple methods.
In order to estimate the ultrasound travel time in an inhomogeneous medium, the
approach using solutions to the eikonal equation is attractive, since it can be
easily integrated into a conventional delay-and-sum beamformer. In our
manuscript, we first propose employing the finite element method to solve the
eikonal equation in ultrasound imaging, which is easy to extend to a high-order
numerical scheme and potentially runs faster on GPU. Through a series of
in-silicon experiments, our results are comparable to those of fast marching
methods.
