On generalizations of the nonwindowed scattering transform

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Applied and Computational Harmonic Analysis Pub Date : 2023-09-09 DOI:10.1016/j.acha.2023.101597

Albert Chua , Matthew Hirn , Anna Little

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引用次数: 0

Abstract

In this paper, we generalize finite depth wavelet scattering transforms, which we formulate as $L^{q} (R^{n})$ 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 $R \in SO (n)$ and an operator that is equivariant to the action of rotations of $R \in SO (n)$ .

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关于无窗散射变换的推广。

在本文中，我们推广了有限深度小波散射变换，我们将其公式化为Lq(ℝn）连续小波变换（或二进小波变换）和压缩非线性的级联的范数。然后我们给出了这些算子的范数，证明了这些算子是定义明确的，并且在特定情况下对C2微分同胚的作用是Lipschitz连续的。最后，我们将我们的结果推广到公式化一个对旋转作用R∈SO（n）不变的算子和一个对R∈SO（n）的旋转作用等变的算子。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied and Computational Harmonic Analysis 物理-物理：数学物理

CiteScore

5.40

自引率

4.00%

发文量

审稿时长

22.9 weeks

期刊介绍： Applied and Computational Harmonic Analysis (ACHA) is an interdisciplinary journal that publishes high-quality papers in all areas of mathematical sciences related to the applied and computational aspects of harmonic analysis, with special emphasis on innovative theoretical development, methods, and algorithms, for information processing, manipulation, understanding, and so forth. The objectives of the journal are to chronicle the important publications in the rapidly growing field of data representation and analysis, to stimulate research in relevant interdisciplinary areas, and to provide a common link among mathematical, physical, and life scientists, as well as engineers.