Rational Gaussian Wavelets and Corresponding Model Driven Neural Networks

IF 5.8 2区 工程技术 Q1 ENGINEERING, ELECTRICAL & ELECTRONIC
Attila Miklós Ámon;Kristian Fenech;Péter Kovács;Tamás Dózsa
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引用次数: 0

Abstract

In this paper we introduce a highly adaptive continuous wavelet transform using Gaussian wavelets multiplied by an appropriate rational term. The zeros and poles of this rational modifier act as free parameters and their choice highly influences the shape of the mother wavelet. This allows the proposed construction to approximate signals with complex morphology using only a few wavelet coefficients. We show that the proposed rational Gaussian wavelets are admissible and provide numerical approximations of the wavelet coefficients using variable projection operators. In addition, we show how the proposed variable projection based rational Gaussian wavelet transform can be used in neural networks to obtain a highly interpretable feature learning layer. We demonstrate the effectiveness of the proposed scheme through a number of numerical experiments including biomedical applications, and the detection of abnormal road surface based on tire sensor signals.
有理高斯小波和相应的模型驱动神经网络*
本文介绍了一种高自适应连续小波变换,它是用高斯小波乘以一个适当的有理项来实现的。该有理修饰语的零点和极点作为自由参数,它们的选择对母小波的形状有很大影响。这使得所提出的结构近似信号与复杂的形态只使用几个小波系数。我们证明了所提出的有理高斯小波是可接受的,并利用变投影算子给出了小波系数的数值逼近。此外,我们还展示了如何将所提出的基于变量投影的有理高斯小波变换用于神经网络以获得高度可解释的特征学习层。我们通过一系列数值实验证明了该方案的有效性,包括生物医学应用,以及基于轮胎传感器信号的异常路面检测。
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
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing 工程技术-工程:电子与电气
CiteScore
11.20
自引率
9.30%
发文量
310
审稿时长
3.0 months
期刊介绍: The IEEE Transactions on Signal Processing covers novel theory, algorithms, performance analyses and applications of techniques for the processing, understanding, learning, retrieval, mining, and extraction of information from signals. The term “signal” includes, among others, audio, video, speech, image, communication, geophysical, sonar, radar, medical and musical signals. Examples of topics of interest include, but are not limited to, information processing and the theory and application of filtering, coding, transmitting, estimating, detecting, analyzing, recognizing, synthesizing, recording, and reproducing signals.
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