The velocity and interface depth determination is one of the most important tasks of exploration seismology. However the process of velocity-depth determination suffers from non-uniqueness of the solution. Traditional methods for imposing uniqueness suffer from loss of resolution and damping of the solution. This work presents an improvement to travel time tomography by using a wavelet expansion of the model parameters combined with Cauchy regularization. By this method we achieve a stable high resolution tomography which produces geologically plausible solutions. The method is tested on synthetic and field data.