Rational Gaussian wavelets and corresponding model driven neural networks

TL;DR

This paper introduces a novel rational Gaussian wavelet transform with free parameters for signal approximation, and integrates it into neural networks for interpretable biomedical feature learning, demonstrated on ECG data.

Contribution

It proposes a new rational Gaussian wavelet construction with adjustable parameters and applies it within neural networks for interpretable biomedical signal analysis.

Findings

Effective approximation of complex signals with few wavelet coefficients

Admissibility of the proposed wavelets established

Successful detection of ventricular ectopic beats in ECG data

Abstract

In this paper we consider the 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 biomedical application, namely, the detection of ventricular ectopic beats (VEBs) in real ECG measurements.