# Learning Sparse Wavelet Representations

arXiv: https://arxiv.org/abs/1802.02961 · HTML: https://mlsanity.com/paper/1802.02961/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Feb 2018.

## Built on by (most cited first, 6 of 6)

- [Adaptive wavelet distillation from neural networks through interpretations](https://mlsanity.com/paper/2107.09145/) (2021)
- [Robust Time Series Denoising with Learnable Wavelet Packet Transform](https://mlsanity.com/paper/2206.06126/) (2022)
- [Learnable Wavelet Packet Transform for Data-Adapted Spectrograms](https://mlsanity.com/paper/2201.11069/) (2022)
- [Learning sparsity-promoting regularizers for linear inverse problems](https://mlsanity.com/paper/2412.16031/) (2024)
- [Interpreting and improving deep-learning models with reality checks](https://mlsanity.com/paper/2108.06847/) (2021)
- [Wavelet Flow Matching for Time Series](https://mlsanity.com/paper/2609.39374/) (2026)

## Abstract (arXiv)

In this work we propose a method for learning wavelet filters directly from data. We accomplish this by framing the discrete wavelet transform as a modified convolutional neural network. We introduce an autoencoder wavelet transform network that is trained using gradient descent. We show that the model is capable of learning structured wavelet filters from synthetic and real data. The learned wavelets are shown to be similar to traditional wavelets that are derived using Fourier methods. Our method is simple to implement and easily incorporated into neural network architectures. A major advantage to our model is that we can learn from raw audio data.