As for any other traveltime method that involves computations in the ray domain, the interpolation to a Cartesian grid remains the major problem. In the current implementation, the interpolation is about one order of magnitude more expensive than the traveltime computation itself.
A possible direction for future work is to modify HWT to a grid-adaptive finite-difference method. HWT requires computing derivatives along the wavefronts. As the distance between adjacent points on the wavefront increases, the accuracy of those derivatives decreases. One possible way to increase the accuracy is to adapt the sampling of the wavefront in the ray domain, as done with finite-difference methods in the physical domain Symes et al. (1999).