Wavelet Toolbox    

Some Interesting Subtrees

Using wavelet packets requires tree-related actions and labeling. The implementation of the user interface is built around this consideration. For more information on the technical details, see the reference pages.

The complete binary tree of depth D corresponding to a wavelet packet decomposition tree developed at level D is denoted by WPT.

We have the following interesting subtrees:

Decomposition Tree
Subtree Such That the Set of Leaves Is a Basis
Wavelet packets decomposition tree
Complete binary tree: WPT of depth D
Wavelet packets optimal decomposition tree
Binary subtree of WPT
Wavelet packets best-level tree
Complete binary subtree of WPT
Wavelet decomposition tree
Left unilateral binary subtree of WPT of
depth D
Wavelet best-basis tree
Left unilateral binary subtree of WPT

We deduce the following definitions of optimal decompositions, with respect to an entropy criterion E.

Decompositions
Optimal Decomposition
Best-Level Decomposition
Wavelet packet decompositions
Search among 2D trees
Search among D trees
Wavelet decompositions
Search among D trees
Search among D trees

For any nonterminal node, we use the following basic step to find the optimal subtree with respect to a given entropy criterion E (where Eopt denotes the optimal entropy value).

Entropy Condition
Action on Tree and on Entropy Labeling














with the natural initial condition on the reference tree, Eopt(t) = E(t) for each terminal node t.


  Choosing the Optimal Decomposition Wavelet Packets 2-D Decomposition Structure