Rational Gaussian wavelets and corresponding model driven neural networks

2025-02-03

AI Summary

To address the challenges of sparsely and accurately representing complex morphological features in medical signals (e.g., ECG) and the limited interpretability of deep learning models, this paper proposes rational Gaussian wavelets: a learnable rational function—parameterized by trainable zeros and poles—is embedded into the Gaussian mother wavelet to enable adaptive morphological modulation. Furthermore, a differentiable wavelet transform layer based on variational projection operators is designed to explicitly incorporate continuous-wavelet-domain priors into neural networks. This work pioneers zero-pole-driven structural learnability of wavelets, establishing a synergistic, interpretable feature extraction paradigm that integrates model-driven priors with data-driven learning. Evaluated on real-world ECG data, the method achieves high-accuracy ventricular ectopic beat (VEB) detection using only a small number of wavelet coefficients, significantly enhancing diagnostic interpretability and cross-device generalizability.

Technology Category

Machine Learning: Multimodal LearningComputer Vision: Multi-modal VisionKnowledge Representation and Reasoning: Diagnosis and Abductive Reasoning

Application Category

Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphsUser Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalizationSemantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

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.

Problem

• Complex Signal Representation
• Neural Network Feature Extraction
• Medical Signal Processing

Innovation

• Rational Gaussian Wavelets
• Continuous Wavelet Transform
• Neural Network Application