论文标题
关于未窗散射变换的概括
On Generalizations of the Nonwindowed Scattering Transform
论文作者
论文摘要
在本文中，我们概括了有限的深度小波散射变换，我们将其作为$ \ lb^q（\ Mathbb {r}^n）$ cascade cascade连续小波变换（或二元小波变换）和合同非线性的规范。然后，我们为这些操作员提供规范，证明这些操作员的定义明确，并且在特定情况下是$ c^2 $ differemorlism的行动。最后，我们扩展了结果，以使操作员不变，以\ text {so}（n）$的旋转$ r \的动作和与$ r \ in \ in \ text {so}（so}（n）$的旋转作用的运算符。
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 $R \in \text{SO}(n)$.
