Learning Sparse Wavelet Representations.

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