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arXiv · 1610.07739

A classification of continuous wavelet transforms in dimension three

Bradley Currey·Hartmut Führ·Vignon Oussa
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Abstract

This paper presents a full catalogue, up to conjugacy and subgroups of finite index, of all matrix groups $H < {\rm GL}(3,\mathbb{R})$ that give rise to a continuous wavelet transform with associated irreducible quasi-regular representation. For each group in this class, coorbit theory allows to consistently define spaces of sparse signals, and to construct atomic decompositions converging simultaneously in a whole range of these spaces. As an application of the classification, we investigate the existence of compactly supported admissible vectors and atoms for the groups.

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Bradley Currey, Hartmut Führ, Vignon Oussa. 2016-10-25. A classification of continuous wavelet transforms in dimension three. https://arxiv.org/abs/1610.07739

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