Bohmian trajectories and quantum phase space distributions
  We prove that most quasi-distributions can be written in a form similar to that of the de Broglie-Bohm distribution, except that ordinary products are replaced by some suitable non-commutative star product. In doing so, we show that the Hamilton-Jacobi trajectories and the concept of "classical pure state" are common features to all phase space formulations of quantum mechanics. Furthermore, these results provide an explicit quantization prescription for classical distributions. 
Nuno Costa Dias, Joao Nuno Prata