On Generalizations of the Nonwindowed Scattering Transform.

In this paper, we generalize finite depth wavelet scattering transforms, which we formulate as Lq(ℝn) 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 C2 diffeomorphisms in specific cases. Lastly, we extend our results to formulate an operator invariant to the action of rotations R∈SO(n) and an operator that is equivariant to the action of rotations of R∈SO(n).