Analysis of time-frequency scattering transforms
Analysis of time-frequency scattering transforms
复制标题
时频散射变换分析
DOI：
10.1016/j.acha.2017.08.005
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发表时间：
2016
影响因子：
2.5
通讯作者：
Weilin Li
中科院分区：
文献类型：
--
作者：
W. Czaja;Weilin Li
在本文中，我们解决的问题，构建一个特征提取相结合的Mallat的散射变换框架的时间-频率（Gabor）表示。为了做到这一点，我们引入了一类框架，称为均匀覆盖框架，其中包括各种半离散的Gabor系统。用神经网络结构表示均匀覆盖框架，得到傅里叶散射变换SF和截断傅里叶散射变换。我们证明了SF传播的能量沿着频率递减的路径和它的能量衰减指数作为深度的函数。这些定量的估计是基本的，在显示SF满足典型的散射变换特性，并在控制由于宽度和深度截断的信息损失。介绍了快速傅里叶散射变换算法，并举例说明了该算法的性能。本文中开发的时间-频率覆盖技术是灵活的，并深入分析散射变换。
In this paper we address the problem of constructing a feature extractor which combines Mallat's scattering transform framework with time-frequency (Gabor) representations. To do this, we introduce a class of frames, called uniform covering frames, which includes a variety of semi-discrete Gabor systems. Incorporating a uniform covering frame with a neural network structure yields the Fourier scattering transform S F and the truncated Fourier scattering transform. We prove that S F propagates energy along frequency decreasing paths and its energy decays exponentially as a function of the depth. These quantitative estimates are fundamental in showing that S F satisfies the typical scattering transform properties, and in controlling the information loss due to width and depth truncation. We introduce the fast Fourier scattering transform algorithm, and illustrate the algorithm's performance. The time-frequency covering techniques developed in this paper are flexible and give insight into the analysis of scattering transforms.
影响因子：
5.4
作者：
W. B. Pennebaker;Joan L. Mitchell
通讯作者：
W. B. Pennebaker;Joan L. Mitchell