# Rational Gaussian wavelets and corresponding model driven neural networks

arXiv: https://arxiv.org/abs/2502.01282 · HTML: https://mlsanity.com/paper/2502.01282/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 70 references that are in the map.
- First posted on arXiv 3 Feb 2025.

## Builds on (most cited first, 12 of 12)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Recent Advances in Convolutional Neural Networks](https://mlsanity.com/paper/1512.07108/) (2015)
- [Training Spiking Neural Networks Using Lessons From Deep Learning](https://mlsanity.com/paper/2109.12894/) (2021)
- [Model-Based Deep Learning](https://mlsanity.com/paper/2012.08405/) (2020)
- [Physics-Driven Deep Learning for Computational Magnetic Resonance Imaging](https://mlsanity.com/paper/2203.12215/) (2022)
- [Multi-stage image denoising with the wavelet transform](https://mlsanity.com/paper/2209.12394/) (2022)
- [WaveletKernelNet: An Interpretable Deep Neural Network for Industrial Intelligent Diagnosis](https://mlsanity.com/paper/1911.07925/) (2019)
- [Analysis of a Deep Learning Model for 12-Lead ECG Classification Reveals Learned Features Similar to Diagnostic Criteria](https://mlsanity.com/paper/2211.01738/) (2022)
- [Empirical wavelet transform](https://mlsanity.com/paper/2410.23534/) (2024)
- [VPNet: Variable Projection Networks](https://mlsanity.com/paper/2006.15590/) (2020)
- [Generalized Rational Variable Projection With Application in ECG Compression](https://mlsanity.com/paper/2003.00058/) (2020)
- [Abnormal Road Surface Detection Using Wheel Sensor Data](https://mlsanity.com/paper/2108.09162/) (2021)

## Built on by (most cited first, 1 of 1)

- [Classification and detection of multiple UAVs using rational Gaussian wavelet neural networks](https://mlsanity.com/paper/2605.26310/) (2026)

## Abstract (arXiv)

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.