Minimum-energy multiwavelet frames with arbitrary integer dilation factor
type: Item
instance of: scholarly article
title: Minimum-energy multiwavelet frames with arbitrary integer dilation factor
zbMATH Open document ID: 1264.65224
DOI: 10.1155/2012/640789
author: Yongdong Huang
author: Qiufu Li
author: Ming Li
published in: Mathematical Problems in Engineering
publication date: 2013-06-11T00:00:00Z
review text: Summary: In order to organically combine the minimum-energy frame with the significant properties of multiwavelets, minimum-energy multiwavelet frames with arbitrary integer dilation factor are studied. Firstly, we define the concept of minimum-energy multiwavelet frame with arbitrary dilation factor and present its equivalent characterizations. Secondly, some necessary conditions and sufficient conditions for minimum-energy multiwavelet frame are given. Thirdly, the decomposition and reconstruction formulas of minimum-energy multiwavelet frame with arbitrary integer dilation factor are deduced. Finally, we give several numerical examples based on B-spline functions.
Mathematics Subject Classification ID: 65T60
Mathematics Subject Classification ID: 42C15
zbMATH DE Number: 6173453
Wikidata QID: Q58912378
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/640789
OpenAlex ID: W2062702596
cites work: Q4321676
cites work: Fractal functions and wavelet expansions based on several scaling functions
cites work: A study of orthonormal multi-wavelets
cites work: Construction of Multiscaling Functions with Approximation and Symmetry
cites work: An algorithm for matrix extension and wavelet construction
cites work: Symmetric paraunitary matrix extension and parametrization of symmetric orthogonal multifilter banks
cites work: Multiwavelets on the interval
cites work: Painless nonorthogonal expansions
cites work: The theory of multiresolution analysis frames and applications to filter banks
cites work: Orthonormal wavelets and tight frames with arbitrary real dilations
cites work: Compactly supported tight frames associated with refinable functions
cites work: An introduction to frames and Riesz bases
cites work: Riesz multiwavelet bases
cites work: Parameterizations of univariate wavelet tight frames with short support
cites work: Minimum-energy frames associated with refinable function of arbitrary integer dilation factor
cites work: Tight wavelet frames for irregular multiresolution analysis
cites work: Q3533340
cites work: Minimum-energy wavelet frame on the interval
cites work: Dual multiwavelet frames with high balancing order and compact fast frame transform
cites work: Weighted irregular Gabor tight frames and dual systems using windows in the Schwartz class
cites work: Characterizations of tight frame wavelets with special dilation matrices
cites work: The characterizations of \(A\)-Parseval frame wavelet
cites work: Fractional calculus and Shannon wavelet
cites work: Shannon wavelets theory
cites work: Q3418030
cites work: Two-Scale Difference Equations II. Local Regularity, Infinite Products of Matrices and Fractals
description: scientific article; zbMATH DE number 6173453