Learning optimal wavelet bases using a neural network approach
This provides a novel method for signal representation in domains like physics, though it appears incremental as it adapts existing neural network techniques to wavelet learning.
The paper tackles the problem of learning optimal orthonormal wavelet bases for 1D and 2D signals by proposing a 'wavenet' method that combines wavelet transforms with neural networks, using stochastic gradient descent to learn filter coefficients with quadratic regularization for orthonormality. It demonstrates that an optimal solution is found even in high-dimensional search spaces, applied to high-energy physics collision events for QCD processes.
A novel method for learning optimal, orthonormal wavelet bases for representing 1- and 2D signals, based on parallels between the wavelet transform and fully connected artificial neural networks, is described. The structural similarities between these two concepts are reviewed and combined to a "wavenet", allowing for the direct learning of optimal wavelet filter coefficient through stochastic gradient descent with back-propagation over ensembles of training inputs, where conditions on the filter coefficients for constituting orthonormal wavelet bases are cast as quadratic regularisations terms. We describe the practical implementation of this method, and study its performance for high-energy physics collision events for QCD $2 \to 2$ processes. It is shown that an optimal solution is found, even in a high-dimensional search space, and the implications of the result are discussed.