Pairs of dual wavelet frames from any two refinable functions
type: Item
instance of: scholarly article
title: Pairs of dual wavelet frames from any two refinable functions
zbMATH Open document ID: 1055.42025
author: Ingrid Daubechies
author: Bin Han
published in: Constructive Approximation
publication date: 2004-10-28T00:00:00Z
review text: A function \(\phi\in L^2(R)\) is \(d\)-refinable if \(\phi= \sum_{k\in Z} a_k\phi(d \cdot -k)\) for some (finite) scalar sequence \(\{a_k\}\). Given two compactly supported \(d\)-refinable functions, it is shown how to construct \(2d\) compactly supported functions \(\{\psi_1, \dots, \psi_d\}\) and \(\{\tilde{\psi}_1, \dots, \tilde{\psi}_d\}\) generating a pair of dual wavelet frames for \(L^2(R)\), with the maximal number of vanishing moments. The functions \(\psi_j,\tilde{\psi}_j\) are finite linear combinations of the translates \(\phi(d \cdot -k), k\in Z\). The results are applied to construct pairs of dual frames generated from B-splines.
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 42C15
Mathematics Subject Classification ID: 41A15
zbMATH DE Number: 2111589
zbMATH Keywords: dual wavelet frames
zbMATH Keywords: refinable function
zbMATH Keywords: wavelet frames
zbMATH Keywords: B-splines
MaRDI profile type: Publication
full work available at URL: s00365-004-0567-4
OpenAlex ID: W2028582172
DOI: 10.1007/S00365-004-0567-4
description: scientific article; zbMATH DE number 2111589