I've come across the following claim in a [paper][1] of Mallat:

"High frequency instabilities [of a signal representation] to deformations can be avoided by grouping frequencies into dyadic packets in $\mathbb{R}^d$, with a wavelet transform."

I know what the wavelet packet decomposition is and I know what stability to deformations is (in the case of $C^2$ diffeomorphisms), but I don't understand why the quoted statement is true. 

Perhaps I missed the explanation in the paper, but could someone provide a reference, an explanation or both? I assume it has something to do with the fact that a wavelet is localized. 


  [1]: http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=3&ved=0CD0QFjAC&url=http%3A%2F%2Fwww.cmap.polytechnique.fr%2F~mallat%2Fpapiers%2FScatCPAM.pdf&ei=I8IlVNmoH4S2yQTX8IHYAQ&usg=AFQjCNGPB2MnmRzmpcSApltPK4MQqicPCw&sig2=r7dPlmBfWmSs7WZ8bqdetA&bvm=bv.76247554,d.aWw