共查询到19条相似文献,搜索用时 140 毫秒
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本文考虑一般细分方程ψi(x)=Σ1≤j≤NΣk∈Zcij(k)ψj(2x-k),解的存在性,正则性和稳定性,及{ψi}1≤i≤N产生L^p多分辨率分析的条件。 相似文献
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设f(x)是一个Fourier系数为正的周期函数,我们构造了关f(x)的二维周期基数插值小波的尺度函数,并得到了一些对构造小波函数有重要意义的性质. 相似文献
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杨守志 《数学物理学报(A辑)》2005,25(6):811-820
基于a 尺度正交单尺度函数,分别给出重数为2和3的a 尺度正交多尺度函数的构造算法。并给出对应正交多小波的显式构造。最后给出伸缩因子为3的正交多小波的构造算例。 相似文献
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滤波长度为5的双正交多尺度分析的构造 总被引:4,自引:0,他引:4
In this paper,a general construction of biorthonormal multiresolution analyses with length 5 is studied.Both the existence of unique symmetric biorthonormal MRAs and the inexistence of antisymmetric ones are also proved.The regularity of the scale functions is analyzed and some examples are given at last. 相似文献
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本文证明:如果来自多尺度分析(伸缩因子为矩阵)的小波是标准正交的,那么相对应的尺度函数也是标准正交的,其中函数f_s(x)∈L~2(R~n)(s=1,2,…,r,r是正整数)的标准正交性是指f_s(x)的整平移所构成的函数族为L~2(R~n)的标准正交系。结果表明,如果我们想从多尺度分析出发构造正交小波,那么该多尺度分析必须有正交尺度函数。 相似文献
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本文在离散多尺度分析框架了讨论了关于给定数据的分解和回复过程的数值特征.它给出了数据分解和回复算法的一般设计原则,它能有效地解释在正交小波基和双正交小波基下的数据分解回复过程.据此设计原则,文中还给出了一种新的数据分解回复方法,它可以在线性分层基背景下得到解释. 相似文献
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In this paper, we study the properties of periodic multiresolution analysis, and present a complete characterization of the
scaling function sequence, which enables us to construct a new scaling function sequence from a given one. An application
of the main results is given at the end. 相似文献
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Veronika Furst Erich A. McAlister 《Numerical Functional Analysis & Optimization》2013,34(12):1511-1531
An equivalence relation between multiresolution analyses was first introduced in 1996; an analogous definition for generalized multiresolution analyses was given in 2010. This article describes the relationship between the two notions and shows that both types of equivalence classes are path connected in an operator-theoretic sense. The GMRA paths are restricted to canonical GMRAs, and it is shown that whenever two MRAs in L 2(?) are equivalent, the GMRA path construction between their corresponding canonical GMRAs yields the natural analog of the MRA path. Examples are provided of GMRA paths that are distinct from MRA paths. 相似文献
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多尺度分析生成元的刻画 总被引:1,自引:0,他引:1
本文将给出多尺度分析生成元的一种完全刻画.将证明:函数φ∈L~2(R)是二进多尺度分析生成元的充要条件是(1)存在{a_k}∈l~2,φ(x)=∑_(k∈Z)a_kφ(2x-k);(2)存在正数A相似文献
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A multiresolution analysis of a curve is normal if
each wavelet detail vector with respect to a certain subdivision
scheme lies in the local normal direction. In this paper we study
properties such as regularity, convergence, and stability of a
normal multiresolution analysis. In particular, we show that these
properties critically depend on the underlying subdivision scheme
and that, in general, the convergence of normal multiresolution
approximations equals the convergence of the underlying subdivision
scheme. 相似文献
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文中研究了对应于α-带尺度函数的小波紧框架,这个小波紧框架是由V1中的n个函数ψ1,ψ2,...,ψn构成. 首先给出了这n个函数构成小波紧框架的充分条件, 并借助尺度函数给出了构造小波紧框架的显式公式. 如果尺度函数的符号是有理函数,则可以构造出符号为有理函数的小波紧框架. 其次给出类似于正交小波的小波紧框架的分解与重构算法,并构造了小波紧框架的数值算例. 相似文献
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A multiresolution analysis is defined in a class of locally compact abelian groups G. It is shown that the spaces of integrable functions
and the complex Radon measures M(G) admit a simple characterization in terms of this multiresolution analysis. 相似文献
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The paper develops construction procedures for tight framelets and wavelets using matrix mask functions in the setting of a generalized multiresolution analysis (GMRA). We show the existence of a scaling vector of a GMRA such that its first component exhausts the spectrum of the core space near the origin. The corresponding low-pass matrix mask has an especially advantageous form enabling an effective reconstruction procedure of the original scaling vector. We also prove a generalization of the Unitary Extension Principle for an infinite number of generators. This results in the construction scheme for tight framelets using low-pass and high-pass matrix masks generalizing the classical MRA constructions. We prove that our scheme is flexible enough to reconstruct all possible orthonormal wavelets. As an illustration we exhibit a pathwise connected class of non-MSF non-MRA wavelets sharing the same wavelet dimension function. 相似文献