Because of the Heisenberg uncertainty theorem, there is no intrinsic definition of the instantaneous frequencies of a finite energy signal.
The structure of the time frequency tiling achieved by the atoms of a time frequency transform determines its time frequency resolution.
To detect the instantaneous frequencies of a signal, an adapted time frequency transform must be used.
Adapting the transforms is one of the reasons why time frequency localized transforms have been generalized to more general time frequency tilings.
Wavelet packets and local cosine transforms are such generalizations. They are explained in chapter 8 of the book, but are not described here.
These transforms correspond to families of bases which can be represented as a maximal tree of time frequency refinements.
This structure is suited to the search for an "optimal" orthogonal basis using a dynamic programming algorithm within the tree.
If non orthogonal bases are allowed, the additivity of the cost is lost. Basis and matching pursuits are example of methods for a "best" basis selection.
These best basis selections are explained in chapter 9 of the book.
While this leads theoretically to a compact representation of the signal, the cost of the basis coding has to be taken into account. Moreover, too much relaxation on the basis requirements may lead to a representation whithout any structure information, because the basis is too much taylored on the signal.