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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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1 引言 在小波的构造和应用中,对于2尺度单一小波已有相当成熟的理论,特别是在小波构造方面,若知道正交单一尺度函数,相应的单一小波是很容易构造出的。对于a尺度紧支撑多小波,如何从已知的a尺度紧支撑多重尺度函数构造出相应的多小波,到目前为止尚没有一般的构造方法。W.Lanton等用仿酉矩阵扩充的方法构造出相应的多小 相似文献
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基于紧支撑样条小波函数插值与定积分的思想,给出了由紧支撑样条小波插值函数构造数值积分公式的方法.并将该方法应用于二次、三次、四次和五次紧支撑样条小波函数,得到了相应的数值积分公式.最后,通过数值例子验证,发现该方法得到的数值积分公式是准确的,且具有较高精度. 相似文献
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[0,1]区间上的r重正交多小波基 总被引:6,自引:1,他引:6
本文利用L2(R)上的紧支撑正交的多尺度函数和多小波构造出有限区间[0,1]上的正交多尺度函数及相应的正交多小波.本文构造的逼近空间Vj[0,1]与相应的小波子空间Wj[0,1]具有维数相同的特点,从而给它的应用带来巨大方便.最后给出重数为2时的[0,1]区间上的正交多小波基构造算例. 相似文献
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本文研究了一元α尺度紧支撑、双正交多小波的构造.在区间[-1,1],给出了利用α尺度双正交尺度向量构造α尺度双正交多小波的推导过程得到了一种有效的小波构造算法,并给出了数值算例. 相似文献
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给出一类具有广义插值的正交多尺度函数的构造方法, 并给出对应多小波的显示构造公式. 证明了该文构造的多小波拥有与多尺度函数相同的广义基插值性.从而建立了多小波子空间上的采样定理. 最后基于该文提供的算法构造出若干具有广义基插值的正交多尺度函数和多小波. 相似文献
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CONSTRUCTION OF COMPACTLY SUPPORTED BIVARIATE ORTHOGONAL WAVELETS BY UNIVARIATE ORTHOGONAL WAVELETS 总被引:4,自引:0,他引:4
After some permutation of conjugate quadrature filter, new conjugate quadrature filters can be derived. In terms of this permutation, an approach is developed for constructing compactly supported bivariate orthogonal wavelets from univariate orthogonal wavelets. Non-separable orthogonal wavelets can be achieved. To demonstrate this method, an example is given. 相似文献
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In this paper, we construct a kind of bivariate real-valued orthogonal periodic box-spline wavelets. There are only 4 terms in the two-scale dilation equations. This implies that the corresponding decomposition and reconstruction algorithms involve only 4 terms respectively which are simple in practical computation. The relation between the periodic wavelets and Fourier series is also discussed. 相似文献
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Qiang Li Xuezhang Liang 《分析论及其应用》2005,21(3):266-279
In this paper, we construct a kind of bivariate real-valued orthogonal periodic wavelets. The corresponding decomposition and reconstruction algorithms involve only 8 terms respectively which are very simple in practical computation. Moreover, the relation between periodic wavelets and Fourier series is also discussed. 相似文献
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This paper describes a general construction of sets of vectors which are useful for the construction of multivariate interpolating wavelets. The specific example of bivariate interpolating wavelets on a triangle is presented to illustrate the general construction. 相似文献
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高维小波是处理多维信号的有力工具,张量积和栅格结构的小波有其自身的特点,但在实际应用中,我们仍需要构造小波滤波器来满足特定情形下的需要以提高滤波的效果,而构造正交滤波器,在多相域里就等价于构造仿酉阵,在本文中,我们通过对仿酉矩阵的研究,证明二元一次对称的仿酉阵一定能够块对角化,利用这种性质,给出了不可分离的二元正交小波滤波器组及线性相位小波滤波器的构造,并给出了相应的例子. 相似文献
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《分析论及其应用》2015,(3):221-235
The single 2 dilation orthogonal wavelet multipliers in one dimensional case and single A-dilation(where A is any expansive matrix with integer entries and|det A|=2) wavelet multipliers in high dimensional case were completely characterized by the Wutam Consortium(1998) and Z. Y. Li, et al.(2010). But there exist no more results on orthogonal multivariate wavelet matrix multipliers corresponding integer expansive dilation matrix with the absolute value of determinant not 2 in L~2(R~2). In this paper, we choose 2I2=(_0~2 _2~0)as the dilation matrix and consider the 2 I2-dilation orthogonal multivariate waveletΨ = {ψ_1, ψ_2, ψ_3},(which is called a dyadic bivariate wavelet) multipliers. We call the3 × 3 matrix-valued function A(s) = [ f_(i, j)(s)]_(3×3), where fi, jare measurable functions, a dyadic bivariate matrix Fourier wavelet multiplier if the inverse Fourier transform of A(s)( ψ_1(s), ψ_2(s), ψ_3(s)) ~T=( g_1(s), g_2(s), g_3(s))~ T is a dyadic bivariate wavelet whenever(ψ_1, ψ_2, ψ_3) is any dyadic bivariate wavelet. We give some conditions for dyadic matrix bivariate wavelet multipliers. The results extended that of Z. Y. Li and X. L.Shi(2011). As an application, we construct some useful dyadic bivariate wavelets by using dyadic Fourier matrix wavelet multipliers and use them to image denoising. 相似文献