Gradient-based Filter Design for the Dual-tree Wavelet Transform
This work addresses filter design for improved wavelet-based representations in neural networks, but it is incremental as it builds directly on prior methods.
The authors tackled the problem of designing filters for the dual-tree wavelet transform by extending a previous method to learn directional filters, showing that minimal modifications enable leveraging the transform's properties.
The wavelet transform has seen success when incorporated into neural network architectures, such as in wavelet scattering networks. More recently, it has been shown that the dual-tree complex wavelet transform can provide better representations than the standard transform. With this in mind, we extend our previous method for learning filters for the 1D and 2D wavelet transforms into the dual-tree domain. We show that with few modifications to our original model, we can learn directional filters that leverage the properties of the dual-tree wavelet transform.