关于非窗口散射变换的推广
On Generalizations of the Nonwindowed Scattering Transform
AI总结：
本文推广了有限深度小波散射变换，证明了其算子的良定义性与 Lipschitz 连续性，并构造了对旋转作用不变与等变的新算子。
摘要：
本文推广了有限深度小波散射变换，将其表述为连续小波变换（或二进小波变换）与收缩非线性级联的 $\Lb^q(\mathbb{R}^n)$ 范数。随后，我们给出了这些算子的范数，证明其是良定义的，且在特定情形下对 $C^2$ 微分同胚的作用是 Lipschitz 连续的。最后，我们扩展结果，构造了一个对旋转 $R \in \text{SO}(n)$ 作用不变的算子，以及一个对旋转 $R \in \text{SO}(n)$ 作用等变的算子。
英文摘要：
In this paper, we generalize finite depth wavelet scattering transforms, which we formulate as $\Lb^q(\mathbb{R}^n)$ 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 $C^2$ diffeomorphisms in specific cases. Lastly, we extend our results to formulate an operator invariant to the action of rotations $R \in \text{SO}(n)$ and an operator that is equivariant to the action of rotations of $R \in \text{SO}(n)$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
