Referencing this article here https://arxiv.org/pdf/1203.1513.pdf
It states "A wavelet transform commutes with translations, and is therefore not translation invariant". Now I understand why it is a problem that the result is not translation invariant, however, I'm confused as to why it is.
What does it mean for a transform to commute with translation and why does the Wavelet transform commute with translations (i.e. why is the Wavelet transformation shift invariant)?.