一种新的双正交小波的构造方法研究

在二进提升方案相关理论的基础上,结合双正交性、消失矩性和对称性条件,提出一种构造提升双正交小波的新方法.此方法从二进小波出发,考虑小波所具有的特性,通过选取适当的提升参数,具体构造了具有紧支撑、对称性、高阶消失矩和速降性的提升双正交小波.     

一种基于二进提升方案的医学图像增强

通过分析和研究二进提升方案,得到一种新的提升二进小波滤波器的构造方法.以新的B-样条二进小波作为初始二进小波滤波器,结合二维6 trous算法对原始医学图像进行多层分解,根据分解后系数特点,一方面对不同级数的高频系数利用单阈值和双阈值函数增强,对低频子带系数用线性拉升来扩大图像的整体对比度.另一方面结合消失矩条件,调整滤波器的提升参数,构造了具有线性相位、紧支撑、高阶消失矩及有限长的单位脉冲响应的提升二进小波,并将其与初始二进小波滤波器增强后图像进行比较.仿真结果表明提升后的滤波器对于对比度低、弱光照图像比初始滤波器的增强效果有了进一步提高,噪声放大问题有明显改善,更好地突出图像边缘特征、保留了图像更多细节信息.     

多小波与多进小波滤波器研究

本文给出了多小波与多进小波的滤波器构造过程,得到了它们的一些良好性质,并给了具体的实例,最后还对某些类型的多小波滤波器、多进小波滤波器之间存在的关系作了研究.     

二进小波变换的卷积定理

本文研究二进小波变换在信号处理中的应用.首先证明了两个满足容许性条件和规范性条件的二进小波的卷积和相关仍满足容许性和规范性条件,然后证明了二进小波变换的卷积定理和相关性定理,最后给出数值例子说明二进小波变换的卷积定理在加噪信号重构中的优越性.     

推广的二进小波与信号处理

本文给出二进小波的推广,并讨了在信号处理中的应用.     

多进小波展开的Gibbs函数的渐近性质

本文研究了一类多进小波展开的Gibbs函数的渐近性质,特别地,包括了多进Daubechies型小波．     

多进小波展开的Gibbs函数的渐近性质

具有道断面S°的正则半群可表示为有Saito's结构的半群W（I,S°,Λ,*,α,β）.我们利用由I,S°和Λ上的同余构成的所谓同余聚抽象地表示这类半群上的同余,进而给出了这类半群的同态象的构造法．     

双正交小波滤波器簇代数结构及构造

研究了一类向量多项式两种特殊分解结构,由此引进了与双正交小波滤波器簇相应的多相向量概念,分析了多相向量分解代数结构,得到了在低通滤波器给定条件下,满足任意阶可和规则的对偶低通滤波器构造方法.分析并证明了双正交滤波器簇对应多相向量至多具有的3种代数分解结构,根据其分解的形式得到了双正交小波基构造的新方法,该方法便于双正交小波构造计算机程序化.     

具有高消失矩的3-进正交对称小波的构造(英文)

本文给出一类具有高消失矩的对称3-进正交小波的构造.首先通过解非线性方程组构造出高消失矩的尺度函数.其次,基于矩阵扩充的方法,我们给出新的定理和算法.相应的关于原点对称/反对称的小波由我们提出的方法构造,并且,该方法便于计算机程序化实现.最后,我们通过3个实例来验证相关的结论,该类小波为应用提供了好的选择.     

基于消失矩的多带Cofilet型小波的构造

本文通过研究多带对称小波完全重构、线性相位以及消失矩性质,提出了多带Cofilet型小波的一种简单构造方法,数值试验表明了理论的正确性与算法的简单特性。     

Boundedness Is Redundant in a Theorem of Daubechies

We polish a theorem and its proof of Daubechies by removing the boundedness condition. The importance of the original theorem is that it links the vanishing of moments to the smoothness.     

一种构造CDF型双正交小波的方法

利用提升格式，构造了CDF型的双正交小波，并探讨了提升算子S的选择规律，最后给出构造实例，结果表明：这种构造方法比传统的构造方法简单、易行，而且选择不同的提升算子S，可以得到不同性质的双正交小波，充分显示出这种构造方法的实用性和广泛性。     

Continuous two-scale equations and dyadic wavelets

The objective of this paper is to investigate the solvability of a continuous two-scale (or refinement) equation and to characterize the solutions of the equation. In addition, the notion of continuous multiresolution analysis (or approximation), CMRA, generated by such a solution is introduced. Here, the notion of continuity follows from a standard engineering terminology, meaning that continuous-time instead of discretetime considerations are studied. This solution, also called a scalling function of the CMRA, gives rise to some dyadic wavelet, a notion introduced by Mallat and Zhong, for multilevel signal decompositions. This research was supported by NSF Grant DMS-92-06928, ARO Contract DAAL 03-90-G0091, and Texas Coordinating Board of Higher Education Grant ATP 999903-054.     

Finite-element wavelets on manifolds

We construct locally supported, continuous wavelets on manifolds that are given as the closure of a disjoint union of generalsmooth parametric images of an n-simplex. The wavelets are provento generate Riesz bases for Sobolev spaces H^s () when s (–1,3/2), if not limited by the global smoothness of . These resultsgeneralize the findings from Dahmen & Stevenson (1999) SIAMJ. Numer. Anal., 37, 319–352, where it was assumed thateach parametrization has a constant Jacobian determinant. Thewavelets can be arranged to satisfy the cancellation propertyof, in principle, any order, except for wavelets with supportsthat extend to different patches, which generally satisfy thecancellation property of only order 1.     

具有特殊伸缩矩阵的三元不可分正交小波的构造

多元小波分析是分析和处理多维数字信号的有力工具.不可分多元小波被广泛地应用在模式识别、纹理分析和边缘检测等领域.给出了构造具有伸缩矩阵(101-1-110-10)的紧支撑三元不可分正交小波的算法,利用该算法得到的小波函数继承了来源于尺度函数和符号函数的对称性和消失矩性质,从而为这类小波在信号处理方面的应用提供了便利.最后给出了数值算例.     

联系Butterworth滤波器的双正交小波

联系Butterworth滤波器的双正交小波称为Butterworth小波,它们具有很好的性质:包括对称性,插值性及消失矩．本文定义了离散空间L~2(Z)中的双正交小波并给出一个易于验证的充分条件．利用这一条件,重新得到Butterworth小波;进一步,构造了一类双正交小波．它们不仅具有Butterworth小波的前述所有性质,而且具有最短可能的支集．     

A construction of multiscale bases for Petrov–Galerkin methods for integral equations

In this paper, a construction of multiscale bases for Petrov–Galerkin methods for Fredholm integral equations of the second kind is proposed. The properties of multiscale bases are presented including additional order of vanishing moments, compact supports and stability. Communicated by A. Zhou Dedicated to Professor Charles A. Micchelli on the occasion of his sixtieth birthday with friendship and esteem Mathematics subject classifications (2000) 41A10, 65R20, 65D15. Min Huang: Supported in part by Professor Yuesheng Xu's support under the program of “One Hundred Distinguished Young Scientists” of the Chinese Academy of Sciences and by the Graduate Innovation Foundation of the Chinese Academy of Sciences.     

Boundedness of dyadic derivative and Cesáro mean operator on some B-valued martingale spaces

In this article, it is proved that the maximal operator of one-dimensional dyadic derivative of dyadic integral I* and Cesàro mean operator σ* are bounded from the B-valued martingale Hardy spaces pΣα, Dα, pLα, p H#α, pKr to Lα (0 < α < ∞), respectively. The facts show that it depends on the geometrical properties of the Banach space.     

Riesz products on the ring of dyadic integers

A class of Riesz products on the ring of dyadic integers is introduced. Using almost everywhere convergence of certain series, Hausdorff dimension of these Riesz products is determined. Other properties, such as mutually absolute continuity, quasi-invariance and quasi-Bernoulli property, are also discussed.