MATRICIAL FILTERS AND CRYSTALLOGRAPHIC COMPOSITE DILATION WAVELETS 1.
Introduction Composite dilation wavelets (CDW) represent a Page 1 MATHEMATICS OF …

Abstract (Γ, a)-crystallographic multiwavelets are a finite set of functions Ψ={ψ^i\}_i=1^L,
which generate an orthonormal basis, a Riesz basis or a Parseval frame for L 2 (ℝ d), under …

We shall introduce a novel methodology for data reconstruction and recovery, based on
composite wavelet representations. These representations include shearlets and …

Composite dilation wavelets are a class of wavelets that include additional dilations from a
countable subgroup of the invertible matrices. We consider the case when these additional …

Single wavelet sets, and thus single wavelets, are shown to exist for the actions of all
crystallographic groups on ℝ 2\mathbb R^ 2 under all integer dilations. Examples of such …

This is a preview paper on Crystallographic Groups of Ho¨ rmander Fields. We describe an
emerging picture in analysis of extended groups. In particular, we introduce and provide …

We characterize the scaling function of a crystal Multiresolution Analysis in terms of the
vector-scaling function for a Multiresolution Analysis associated to a lattice. We give …

We characterize the scaling function of a crystal Multiresolution Analysis in terms of the
vector-scaling function for a Multiresolution Analysis associated to a lattice. We give …

In many fields of science and technology, multiscale (or multiresolution) analysis is a useful
tool to study data via efficient representation at increasingly precise resolution. In this paper …

The invariance of the core subspace V 0 of a GMRA under the group Γ of unitary operators
implies the existence of a unitary representation of Γ on V 0, thus enabling the use of tools …