A characterization of the higher dimensional groups associated with continuous wavelets

By Richard S. Laugesen, N. Weaver, Guido L. Weiss, E. Wilson. 2002

110 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computer Vision and Pattern Recognition, Geophysics

View Paper: https://www.semanticscholar.org/paper/027f99e1c18b129d4b4f6133fda77cb616988e48

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In Applied Mathematics

In Computer Vision and Pattern Recognition

In Geophysics

Citations in the corpus

Coorbit spaces and wavelet coefficient decay over general dilation groups (2012, background): “Moreover, recent investigations of wavelet inversion formulae (such as [20,22,27]) and of coorbit theory [3–5] beyond the irreducible setting indicate that irreducibility may not be essential for the development of coorbit space theory.”
Resolution of the wavefront set using continuous shearlets (2006, unknown): “We refer to [23, 29] for more details.”
Reproducing formulas for generalized translation invariant systems on locally compact abelian groups (2014, background): “Higher dimensional versions of Calderón’s admissibility condition are obtained similarly, see also [20, 40].”
Wavelet Coorbit Spaces viewed as Decomposition Spaces (2014, background): “A rather general class of constructions follows the initial inception of the continuous wavelet transform in [20] and uses the language of group representations [25, 1, 15, 23]: Picking a suitable matrix group H ≤ GL ( R ) , the so-called dilation group, one defines the associated semidirect product”
Diffusion Wavelets (2004, background): “, [30,31] and references therein), but an efficient discretization of such transforms seems in many respects still an open problem.”
Wavelets with composite dilations and their MRA properties (2006, background): “By a trivial extension of an argument in [16], one shows that Ψ satisfies (4) if and only if it satisfies the Calderòn equation:”
A unified characterization of reproducing systems generated by a finite family, II (2002, result): “This result follows by an argument similar to one presented in [25], where continuous wavelets are studied.”