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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 reparametrize $u$ and $\xi$ in terms of $j$ and $k$, and then compute the various wavelet transforms with varying combinations of $j$ and $k$?