  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.
