Learning Sparse Wavelet Representations

TL;DR

This paper introduces a neural network-based method to learn wavelet filters directly from data, enabling adaptive wavelet representations from raw audio, which are comparable to traditional Fourier-derived wavelets.

Contribution

It presents a novel autoencoder approach to learn structured wavelet filters from data within a neural network framework.

Findings

Learned wavelets resemble traditional wavelets.

Method works on synthetic and real data.

Easily integrated into neural architectures.

Abstract

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.