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Multiwavelets have been revealed to be a successful generalization within the context of wavelet theory. Recently Lebrun and
Vetterli have introduced the concept of “balanced” multiwavelets, which present properties that are usually absent in the
case of classical multiwavelets and do not need the prefiltering step. In this work we present an algebraic construction of
biorthogonal multiwavelets by means of the well-known “lifting scheme”. The flexibility of this tool allows us to exploit
the degrees of freedom left after satisfying the perfect reconstruction condition in order to obtain finite k-balanced multifilters
with custom-designed properties which give rise to new balanced multiwavelet bases. All the problems we deal with are stated
in the framework of banded block recursive matrices, since simplified algebraic conditions can be derived from this recursive
approach.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
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Shiva Mittal Niraj K. Shukla Nadya A. S. Atlouba 《Numerical Functional Analysis & Optimization》2016,37(2):253-276
In this article, we study the theory of nonuniform minimally supported frequency multiwavelets and nonuniform multiscaling sets. A characterization of nonuniform multiwavelet sets is obtained which generalizes a result of Yu and Gabardo. After introducing a notion of generalized nonuniform scaling set, we obtain a characterization of nonuniform multiscaling sets associated with nonuniform multiresolution analysis having finite multiplicity. In addition, we provide a geometric construction to find families of symmetric nonuniform multiwavelet sets. 相似文献
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二元多重双正交小波包的性质 总被引:3,自引:0,他引:3
陈清江等:二元多重双正交小波包的性质 第1期 1引言 小波包川由于拥有优良的特性而受到人们的关注.它己被应用在信号处理{“】,图像 压缩【“】,编码理论【41等工程方面.我们知道,由护(功中的函数生成的正交小波基具有 较差的频率局部化性能,为了克服这一缺陷,Coifman,Me 相似文献
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仿酉对称矩阵的构造及对称正交多小波滤波带的参数化 总被引:4,自引:0,他引:4
仿酉矩阵在小波、多小波、框架的构造中发挥了重要的作用.本文给出仿酉对称矩阵(简记为p.s.m.)的显式构造算法,其中仿酉对称矩阵是元素为对称或反对称多项式的仿酉矩阵.基于已构造的p.s.m.和已知的正交对称多小波(简记为o.s.m.),给出o.s.m.的参数化.恰当地选择一些参数,可得到具有一些优良性质的o.s.m.,例如Armlet.最后作这一个算例,构造出一类对称的Chui-Lian Armlet滤波带. 相似文献
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双正交多重小波的一种构造方法 总被引:2,自引:0,他引:2
多重小波是近年来新兴的小波研究方向,它具有许多一维小波所不具备的优越性质.完全正交的多重小波在构造上有很大的难度,所以在许多应用中人们都可以用双正交多重小波作为分析的工具 相似文献
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A complete parameterization for the m‐channel FIR orthogonal multifilter banks is provided based on the lattice structure of the paraunitary systems. Two forms
of complete factorization of the m‐channel FIR orthogonal multifilter banks for symmetric/antisymmetric scaling functions and multiwavelets with the same symmetric
center
(1 + γ + γ/(m - 1)) for some nonnegative integer γ are obtained. For the case of multiplicity 2 and dilation factor m = 2, the result of the factorization shows that if the scaling function Φ and multiwavelet Ψ are symmetric/antisymmetric
about the same symmetric center γ +
for some nonnegative integer γ, then one of the components of Φ (respectively Ψ) is symmetric and the other is antisymmetric.
Two examples of the construction of symmetric/antisymmetric orthogonal multiwavelets of multiplicity 3 with dilation factor
2 and multiplicity 2 with dilation factor 3 are presented to demonstrate the use of these parameterizations of orthogonal
multifilter banks.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
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Abderrazek Karoui 《Central European Journal of Mathematics》2008,6(4):504-525
The construction of nonseparable and compactly supported orthonormal wavelet bases of L
2(R
n
); n ≥ 2, is still a challenging and an open research problem. In this paper, we provide a special method for the construction
of such wavelet bases. The wavelets constructed by this method are dyadic wavelets. Also, we show that our proposed method
can be adapted for an eventual construction of multidimensional orthogonal multiwavelet matrix masks, candidates for generating
multidimensional multiwavelet bases.
相似文献
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对称反对称紧支撑正交多小波的构造 总被引:1,自引:0,他引:1
对于给定的对称反对称紧支撑正交r重尺度函数,给出一种构造对称反对称紧支撑正交多小波的方法.通过此方法构造的多小波与尺度函数有相同的对称性与反对称性,并且给出算例. 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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For the construction of multiwavelets, there are no unified, explicit formulas as that in the scalar case available so far. In this paper, by studying the relationship between length 3 and length 4 filter sequences of orthogonal multiwavelets based on the result of Chui for the construction of length 3 orthogonal multiwavelets, a set of explicit formulas is given for the construction of length 4 high-pass filter sequence. Examples demonstrate that our proposed approach not only provides explicit formulas for the construction of length 4 high-pass filter sequence with multiplicity r, but also yields a set of new low-pass and high-pass filter sequences with length 3 and multiplicity 2r. 相似文献
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Patrick J. Van Fleet 《Journal of Computational Analysis and Applications》2003,5(1):161-178
In many applications of image processing, the given data are integer-valued. It is therefore desirable to construct transformations that map data of this type to an integer (or rational) ring. Calderbank, Daubechies, Sweldens, and Yeo [1] devised two methods for modifying orthogonal and biorthogonal wavelets so that they map integers to integers. The first method involves appropriately scaling the transform so that data that has been transformed and truncated can be recovered via the inverse wavelet transform. In developing this method, the authors of [1] created a useful factorization of the 4-tap Daubechies orthogonal wavelet transform [2]. We have observed that this factorization can be extended to 4-tap multiwavelets of arbitrary size. In this paper we will discuss this generalization and illustrate the factorization on two multiwavelets. In particular, the well-known Donovan, Geronimo, Hardin, and Massopust (DGHM) [3] multiwavelet transform can be scaled so that it maps integers to integers. Since this transform is (anti)symmetric in addition to orthogonal, regular, and compactly supported, the ability to modify it so that it maps integers to integers should be useful in image processing applications. 相似文献
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We use a multiwavelet basis with the Discontinuous Galerkin (DG) method to produce a multi-scale DG method. We apply this Multiwavelet DG method to convection and convection-diffusion problems in multiple dimensions. Merging the DG method with multiwavelets allows the adaptivity in the DG method to be resolved through manipulation of multiwavelet coefficients rather than grid manipulation. Additionally, the Multiwavelet DG method is tested on non-linear equations in one dimension and on the cubed sphere. 相似文献
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S. A. Yousefi 《Numerical Methods for Partial Differential Equations》2010,26(3):535-543
Recently, it is found that telegraph equation is more suitable than ordinary diffusion equation in modeling reaction diffusion for such branches of sciences. In this article a numerical method for solving the one‐dimensional hyperbolic telegraph equation is presented. The method is based upon Legendre multiwavelet approximations. The properties of Legendre multiwavelet are first presented. These properties together with Galerkin method are then utilized to reduce the telegraph equation to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009 相似文献
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Jian-Kang Zhang Timothy N. Davidson Zhi-Quan Luo K. Max Wong 《Applied and Computational Harmonic Analysis》2001,11(3):892
In this paper we characterize all totally interpolating biorthogonal finite impulse response (FIR) multifilter banks of multiplicity two, and provide a design framework for corresponding compactly supported multiwavelet systems with high approximation order. In these systems, each component of the analysis and synthesis portions possesses the interpolating property. The design framework is based on scalar filter banks, and examples with approximation order two and three are provided. We show that our multiwavelet systems preserve almost all of the desirable properties of the generalized interpolating scalar wavelet systems, including the dyadic-rational nature of the filter coefficients, equality of the flatness degree of the low-pass filters and the approximation order of the corresponding functions, and equality between the uniform samples of a signal and its projection coefficients for a given scale. This last property allows us to avoid the cumbersome prefiltering associated with standard multiwavelet systems. We also show that there are no symmetric totally interpolating biorthogonal multifilter banks of multiplicity two. Finally, we point out that our design framework incorporates a simple relationship between the multiscaling functions and multiwavelets that substantially simplifies the implementation of the system. 相似文献
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本文给出了多小波框架的sub-QMF条件,提出了多小波框架低通滤波器的参数化设计,由正交分解和矩阵的酉扩张得到其相应的高通滤波器表示的整套多小波框架设计的参数化方法,同时针对多描述编码的需求,构造了两个长折叠对称带参数的多小波紧框架. 相似文献