On Generalizations of the Nonwindowed Scattering Transform.

In this paper, we generalize finite depth wavelet scattering transforms, which we formulate as norms of a cascade of continuous wavelet transforms (or dyadic wavelet transforms) and contractive nonlinearities. We then provide norms for these operators, prove that these operators are well-defined, and are Lipschitz continuous to the action of diffeomorphisms in specific cases. Lastly, we extend our results to formulate an operator invariant to the action of rotations and an operator that is equivariant to the action of rotations of .