A classification of continuous wavelet transforms in dimension three (Q2415400)

The construction of continuous wavelet transforms in dimension three departs from the choice of irreducibly admissible matrix groups $H < \mathrm{GL}(3, \mathbb R)$. In this paper, the authors classify all matrix groups $H$ that give rise to a continuous wavelet transform with irreducible quasi-regular representation. For each matrix group, coorbit theory allows to define spaces of sparse signals, and to construct atomic decompositions converging in a whole range of these spaces. For corresponding classification results of continuous wavelet transforms in dimension two, see [the second author, Rev. Cienc. Mat. 18, No. 2, 179--190 (2000; Zbl 1158.42308)].