The canonical dual frame of a wavelet frame
type: Item
instance of: scholarly article
title: The canonical dual frame of a wavelet frame
zbMATH Open document ID: 1013.42023
author: Ingrid Daubechies
author: Bin Han
published in: Applied and Computational Harmonic Analysis
publication date: 2002-11-28T00:00:00Z
review text: It is well known that there exist wavelet frames \(\{2^{j/2}\psi(2^jx-k)\}_{j,k\in Z}\) for which the canonical dual frame does not have wavelet structure. In this paper the authors find such a frame with the additional property that other duals, which have the wavelet structure, exist; in fact, infinitely many such duals exist. Similar constructions are possible for wavelet frames \(\{2^{j/2}\psi_l(2^jx-k)\}_{j,k\in Z, l=1,\dots,r}\) generated by \(r\) functions. For such a frame, equivalent conditions for the canonical dual frame to be generated by \(2^Jr\) functions (for some \(J=0,1,2,\dots\)) are given.
Mathematics Subject Classification ID: 42C40
zbMATH DE Number: 1836814
zbMATH Keywords: wavelet frame
zbMATH Keywords: dual frame
zbMATH Keywords: canonical dual
MaRDI profile type: Publication
OpenAlex ID: W2076198220
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DOI: 10.1006/ACHA.2002.0381
description: scientific article; zbMATH DE number 1836814