What is dyadic sampling in the context of a wavelet transform?

Math
Integral-Transforms
Wavelets
Author

Galen Seilis

Published

February 1, 2022

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Question

In Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges the authors introduce to the reader (page 24) the notion of wavelet transforms as a way of having multiscale representations (of a group, I suspect). Here is the relevant quote that prompted me to ask:

The translated and dilated filters are called wavelet atoms; their spatial position and ilation correspond to the coordinates \(u\) and \(\xi\) of the wavelet transform. These coordinates are usually sampled dyadically (\(\xi=2^{-j}\) and \(u=2^{-j}k\)), with \(j\) referred to as scale.

So is this to say that we often reparameterize \(u\) and \(\xi\) in terms of \(j\) and \(k\), and then compute the various wavelet transforms with varying combinations of \(j\) and \(k\)?