Gradient-based Filter Design for the Dual-tree Wavelet Transform

TL;DR

This paper introduces a method to learn directional filters for the dual-tree wavelet transform, enhancing neural network representations by leveraging the transform's properties with minimal modifications to existing models.

Contribution

It extends previous filter learning methods to the dual-tree wavelet domain, enabling the design of directional filters that improve wavelet-based neural network features.

Findings

Successfully learned directional filters for dual-tree wavelet transform

Enhanced wavelet representations in neural networks

Minimal modifications needed for existing models

Abstract

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.