Multiwavelet frames from refinable function vectors
type: Item
instance of: scholarly article
title: Multiwavelet frames from refinable function vectors
zbMATH Open document ID: 1059.42030
DOI: 10.1023/A:1021360312348
author: Bin Han
author: Qun Mo
published in: Advances in Computational Mathematics
publication date: 2003-04-10T00:00:00Z
review text: A \(d\)-refinable function vector \(\phi = (\phi_1, \ldots, \phi_r)^T\) satisfies the refinement equation \[ \phi = | d| \sum_{k \in {\mathbb Z}} a_k \phi(d\cdot - k), \] where \(r\) is the multiplicity, \(d\) the dilation factor, and \(a\) is the finitely supported sequence of \(r\times r\) matrices. Such a vector generates a wavelet function vector by \[ \widehat \psi^l (d \xi) = b^l(\xi) \widehat \phi(\xi), \] where \(l=1, \ldots, L\) and \(b^l\) are periodic trigonometric polynomials. The paper under review studies the properties of dual wavelet frames and of wavelet frames generated by refinable function vectors. In particular, algorithms for constructing dual wavelet frames with maximum vanishing moments are given. Moreover, symmetry/antisymmetry properties of wavelets are examined and examples are provided.
reviewed by: Wojciech Czaja
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 42C15
zbMATH DE Number: 1896703
zbMATH Keywords: dual wavelet frames
zbMATH Keywords: wavelet frames
zbMATH Keywords: refinable function vectors
zbMATH Keywords: multiwavelets
zbMATH Keywords: refinable Hermite interpolants
zbMATH Keywords: sum rules
zbMATH Keywords: vanishing moments
zbMATH Keywords: symmetry
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1896703