Framelets: MRA-based constructions of wavelet frames
type: Item
instance of: scholarly article
title: Framelets: MRA-based constructions of wavelet frames
zbMATH Open document ID: 1035.42031
DOI: 10.1016/S1063-5203(02)00511-0
author: Ingrid Daubechies
author: Bin Han
author: A. Ron
author: Zuowei Shen
published in: Applied and Computational Harmonic Analysis
publication date: 2003-05-27T00:00:00Z
review text: A wavelet system is a collection of the form \(X(\Psi) = \{ \psi_{j,k} = 2^{jd/2} \psi(2^jy-k): \psi \in \Psi, j \in Z, k \in Z^d \} \subset L^2(R^d)\). A wavelet is said to be MRA-based if there exists a multiresolution analysis such that \(\Psi \subset V_1\). If \(X(\Psi)\) is a frame, we call its elements {framelets}. The authors present the unitary extension principle and the oblique extension principle to facilitate constructions of MRA-based tight wavelet frames. Approximation orders and vanishing moments of MRA-based wavelet systems are studied in order to construct framelets with higher approximation orders. The scaling functions of these framelets are pseudo-splines, i.e., square roots of \(\cos^{2m}(x/2) \sum_{i=0}^l \binom{m+l}{i} \sin^{2i}(x/2) \cos^{2(l-i)}(x/2)\). Fast implementation algorithms are also provided.
reviewed by: Wojciech Czaja
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 42C15
zbMATH DE Number: 1917882
zbMATH Keywords: unitary extension principle
zbMATH Keywords: oblique extension principle
zbMATH Keywords: framelets
zbMATH Keywords: pseudo-splines
zbMATH Keywords: frames
zbMATH Keywords: tight frames
zbMATH Keywords: fast frame transform
zbMATH Keywords: multiresolution analysis
zbMATH Keywords: wavelets
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1917882