# Robust Time Series Denoising with Learnable Wavelet Packet Transform

arXiv: https://arxiv.org/abs/2206.06126 · HTML: https://mlsanity.com/paper/2206.06126/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 77 references that are in the map.
- First posted on arXiv 13 Jun 2022.

## Builds on (most cited first, 21 of 21)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [Speaker Recognition from Raw Waveform with SincNet](https://mlsanity.com/paper/1808.00158/) (2018)
- [A multi-device dataset for urban acoustic scene classification](https://mlsanity.com/paper/1807.09840/) (2018)
- [Potential, Challenges and Future Directions for Deep Learning in Prognostics and Health Management Applications](https://mlsanity.com/paper/2005.02144/) (2020)
- [Multilevel Wavelet Decomposition Network for Interpretable Time Series Analysis](https://mlsanity.com/paper/1806.08946/) (2018)
- [WINNet: Wavelet-inspired Invertible Network for Image Denoising](https://mlsanity.com/paper/2109.06381/) (2021)
- [Adaptive wavelet distillation from neural networks through interpretations](https://mlsanity.com/paper/2107.09145/) (2021)
- [General-purpose Tagging of Freesound Audio with AudioSet Labels: Task Description, Dataset, and Baseline](https://mlsanity.com/paper/1807.09902/) (2018)
- [Fully Learnable Deep Wavelet Transform for Unsupervised Monitoring of High-Frequency Time Series](https://mlsanity.com/paper/2105.00899/) (2021)
- [Raw Waveform-based Speech Enhancement by Fully Convolutional Networks](https://mlsanity.com/paper/1703.02205/) (2017)
- [Blind Denoising Autoencoder](https://mlsanity.com/paper/1912.07358/) (2019)
- [Sound Event Detection and Time-Frequency Segmentation from Weakly Labelled Data](https://mlsanity.com/paper/1804.04715/) (2018)
- [Learning Sparse Wavelet Representations](https://mlsanity.com/paper/1802.02961/) (2018)
- [Dynamic Feature Acquisition Using Denoising Autoencoders](https://mlsanity.com/paper/1811.01249/) (2018)
- [LINN: Lifting Inspired Invertible Neural Network for Image Denoising](https://mlsanity.com/paper/2105.03303/) (2021)
- [NN3A: Neural Network supported Acoustic Echo Cancellation, Noise Suppression and Automatic Gain Control for Real-Time Communications](https://mlsanity.com/paper/2110.08437/) (2021)
- [Learnable Wavelet Packet Transform for Data-Adapted Spectrograms](https://mlsanity.com/paper/2201.11069/) (2022)
- [Canonical Polyadic Decomposition and Deep Learning for Machine Fault Detection](https://mlsanity.com/paper/2107.09519/) (2021)
- [Acceleration-guided Acoustic Signal Denoising Framework Based on Learnable Wavelet Transform Applied to Slab Track Condition Monitoring](https://mlsanity.com/paper/2205.05365/) (2022)

## Built on by (most cited first, 10 of 10)

- [Unsupervised Deep Learning for IoT Time Series](https://mlsanity.com/paper/2302.03284/) (2023)
- [A Co-training Approach for Noisy Time Series Learning](https://mlsanity.com/paper/2308.12551/) (2023)
- [WaveFormer: A Lightweight Transformer Model for sEMG-based Gesture Recognition](https://mlsanity.com/paper/2506.11168/) (2025)
- [WDMIR: Wavelet-Driven Multimodal Intent Recognition](https://mlsanity.com/paper/2506.10011/) (2025)
- [DeepExtractor: Time-domain reconstruction of signals and glitches in gravitational wave data with deep learning](https://mlsanity.com/paper/2501.18423/) (2025)
- [RINS-T: Robust Implicit Neural Solvers for Time Series Linear Inverse Problems](https://mlsanity.com/paper/2510.17396/) (2025)
- [WaveletInception Networks for on-board Vibration-Based Infrastructure Health Monitoring](https://mlsanity.com/paper/2507.12969/) (2025)
- [A self-supervised learning approach for denoising autoregressive models with additive noise: finite and infinite variance cases](https://mlsanity.com/paper/2508.12970/) (2025)
- [Dilated CNNs for Periodic Signal Processing: A Low-Complexity Approach](https://mlsanity.com/paper/2604.21651/) (2026)
- [Machine Learning Integrated in Wavelet Shrinkage (MLShrink)](https://mlsanity.com/paper/2606.19580/) (2026)

## Abstract (arXiv)

Signal denoising is a key preprocessing step for many applications, as the performance of a learning task is closely related to the quality of the input data. In this paper, we apply a signal processing based deep neural network architecture, a learnable extension of the wavelet packet transform. As main advantages, this model has few parameters, an intuitive initialization and strong learning capabilities. Moreover, we show that it is possible to easily modify the parameters of the model after the training step to tailor to different noise intensities. Two case studies are conducted to compare this model with the state of the art and commonly used denoising procedures. The first experiment uses standard signals to study denoising properties of the algorithms. The second experiment is a real application with the objective to remove audio background noises. We show that the learnable wavelet packet transform has the learning capabilities of deep learning methods while maintaining the robustness of standard signal processing approaches. More specifically, we demonstrate that our approach maintains excellent denoising performances on signal classes separate from those used during the training step. Moreover, the learnable wavelet packet transform was found to be robust when different noise intensities, noise varieties and artifacts are considered.