I've come across the following claim in a paper:

"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.

Could someone provide a reference, an explanation or both?