Learning Sparse Wavelet Representations
This provides a method for learning wavelets from data, which could benefit signal processing and neural network applications, but it is incremental as it adapts existing techniques.
The authors tackled the problem of learning wavelet filters directly from data by framing the discrete wavelet transform as a modified convolutional neural network, resulting in a model that learns structured wavelet filters similar to traditional ones from synthetic and real data, with the advantage of learning from raw audio.
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.