Hilbert-Huang (or Huang-Hilbert) transform: Mathematical foundations

Hi!

As we know, the Hilbert-Huang transform is a powerfull tool in analysing
signals.
Nevertheless, some mathematical foundations concerning the Huang's
algorithm are needed if we want to know things like atomic decompositions
and N best-approximation theorems like Jackson type inequalities. 

Do someone try some connections with other subjects like evolutionary
PDE's, Chirplet transform and/or Nonlinear Fourier transform?


Thanks a lot