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 is an element of SO(n) and an operator that is equivariant to the action of rotations of R is an element of SO(n).(c) 2023 Elsevier Inc. All rights reserved.

Automated summary

In this paper, we generalize and study finite depth wavelet scattering transforms. We provide norms for these operators and prove their continuity and invariance under specific conditions.