Scattering Theory for Orthogonal Wavelets

Construction of Compactly Supported Nonseparable Orthogonal Wavelets of L^2(R^n)

Oblique and Biorthogonal Multi-wavelet Bases with Fast-Filtering Algorithms

We construct oblique multi-wavelets bases which encompass the orthogonal multi-wavelets and the biorthogonal uni-wavelets of Cohen, Deaubechies and Feauveau. These oblique multi-wavelets preserve the advantages of orthogonal and biorthogonal wavelets and enhance the flexibility of wavelet theory to accommodate a wider variety of wavelet shapes and properties. Moreover, oblique multi-wavelets ca...

5-refinement Wavelets with 4-fold Symmetry

Recently √ 5-refinement hierarchical sampling has been studied and √ 5-refinement has been used for surface subdivision. Compared with other refinements such as the dyadic or quincunx refinement, √ 5-refinement has a special property that the nodes in a refined lattice form groups of five nodes with these five nodes having different x and y coordinates. This special property has been shown to b...

Multiresolution analysis and orthogonal wavelets associated with fractional wavelet transform

The fractional wavelet transform (FRWT), which generalizes the classical wavelet transform, has been shown to be potentially useful for signal processing. Many fundamental results of this transform are already known, but the theory of multiresolution analysis and orthogonal wavelets is still missing. In this paper, we first develop multiresolution analysis associated with the FRWT and then deri...

2 Ronald a . Devore And

The subject of “wavelets” is expanding at such a tremendous rate that it is impossible to give, within these few pages, a complete introduction to all aspects of its theory. We hope, however, to allow the reader to become sufficiently acquainted with the subject to understand, in part, the enthusiasm of its proponents toward its potential application to various numerical problems. Furthermore, ...