Matrix splitting with symmetry and dyadic framelet filter banks over algebraic number fields
type: Item
instance of: scholarly article
title: Matrix splitting with symmetry and dyadic framelet filter banks over algebraic number fields
zbMATH Open document ID: 1258.42037
author: Qun Mo
author: Xiaosheng Zhuang
published in: Linear Algebra and its Applications
publication date: 2012-11-09T00:00:00Z
review text: Tight wavelet frames have many applications, for example, in signal denoising and image processing. One of the most important topics in wavelet analysis is the study of tight wavelet frames and how to construct them with desirable properties. This paper addresses the important problem of how to design tight framelet filter banks with symmetry over algebraic number fields, which are of particular importance in both theory and application. To achieve this goal, the authors investigate the matrix splitting problem, that is, how to split a \(2\times 2\) matrix of Laurent polynomials with symmetry. They obtain a necessary and sufficient condition in Theorem 1 and a step-by-step algorithm in Algorithm 1 on the matrix splitting problem with symmetry. As an application, the authors develop an interesting result in Theorem 2 to construct tight framelet filter banks with symmetry over algebraic number fields. Many convincing and interesting examples are provided in Section 4 to illustrate the results and algorithms developed in this paper.
reviewed by: Bin Han
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 42C15
Mathematics Subject Classification ID: 65T60
zbMATH DE Number: 6104564
zbMATH Keywords: matrix splitting
zbMATH Keywords: algebraic number fields
zbMATH Keywords: symmetric wavelets
zbMATH Keywords: framelet filter banks
MaRDI profile type: Publication
full work available at URL: j.laa.2012.06.039
OpenAlex ID: W1990032047
cites work: Compactly supported tight frames associated with refinable functions
cites work: Compactly supported tight and sibling frames with maximum vanishing moments
cites work: Ten Lectures on Wavelets
cites work: Framelets: MRA-based constructions of wavelet frames
cites work: On dual wavelet tight frames
cites work: Symmetric orthonormal scaling functions and wavelets with dilation factor 4
cites work: Vector cascade algorithms and refinable function vectors in Sobolev spaces
cites work: Compactly supported tight wavelet frames and orthonormal wavelets of exponential decay with a general dilation matrix
cites work: Matrix extension with symmetry and Applications to Symmetric orthonormal complex \(M\)-wavelets
cites work: Symmetric orthogonal filters and wavelets with linear-phase moments
cites work: Tight wavelet frames generated by three symmetric $B$-spline functions with high vanishing moments
cites work: Splitting a Matrix of Laurent Polynomials with Symmetry and itsApplication to Symmetric Framelet Filter Banks
cites work: Matrix Extension with Symmetry and Its Application to Symmetric Orthonormal Multiwavelets
cites work: Algorithms for matrix extension and orthogonal wavelet filter banks over algebraic number fields
cites work: The matrix-valued Riesz lemma and local orthonormal bases in shift-invariant spaces
cites work: Parameterizations of masks for tight affine frames with two symmetric/antisymmetric generators
cites work: Symmetric tight wavelet frames with rational coefficients
cites work: Symmetric framelets
cites work: Construction of symmetric orthogonal bases of wavelets and tight wavelet frames with integer dilation factor
cites work: Affine systems in \(L_ 2(\mathbb{R}^d)\): The analysis of the analysis operator
cites work: Smooth wavelet tight frames with zero moments
cites work: Symmetric wavelet tight frames with two generators
cites work: Complex wavelets and framelets from pseudo splines
cites work: Q3096719
cites work: Q3138779
cites work: Matrix Extension with Symmetry and Its Applications
DOI: 10.1016/J.LAA.2012.06.039
description: scientific article; zbMATH DE number 6104564