正交样条小波在图像压缩中的应用

给出了正交样条小波滤波器系数的计算方法和数据，将正交样条小波应用于图像压缩中，并与其他常用的小波如Daubechies小波和双正交小波进行了比较。结果表明，用正交样条小波进行图像压缩可以取得很好的效果。     

有限长标准正交小波基滤波器的构造

从紧支撑正交小波滤波器的正交性、规范性及正则性条件出发,获得了求解滤波器系数的非线性差分方程组,并采用最优化方法求解。由于该优化问题的目标函数是具有零残数的最小二乘,可以用Gauss-Newton法求解。为了克服Gauss-Newton法的局部收敛性,结合随机算法和Gauss-Newton法形成了一种更为可行的算法。它不仅计算出了Daubechies小波的滤波器系数,还可以得到其他对称性与局部性更好的小波。另外,该算法还可以用于双正交或多小波滤波器的构造,具有很好的可移植性。     

偶数长有理数对称紧支双正交小波滤波器设计

基于Daubechies紧支集小波构造方法所得到的小波滤波器多为非线性相位和无理数系数。非线性相位滤波器在图像处理过程中容易引起失真,而无理系数滤波器给小波变换的应用尤其是在算法的硬件实现方面带来不便。借助完全重构滤波器思想,进行了具有线性相位的双正交小波滤波器设计,同时通过添加消失矩特性条件,归纳推导出偶数长有理系数双正交对称紧支集小波滤波器的构造方法。以长度为8-4双正交小波设计为例,对设计方程中出现的自由变量的取值范围进行了讨论,得到了8-4有理系数双正交对称小波滤波器。     

基于小波神经网络的混沌时间序列分析与相空间重构

探讨了小波神经网络在混沌时间序列分析与相空间重构中的应用,通过混沌时间序列单步预测与多步预测的例子,比较了小波神经网络与MLP的逼近和收敛性能,对最近提出的一种多分辨率学习策略进行了改进,利用连续3次样条小和正交Daubechies小波代替Haar小波对时间序列做小波分解;用改进的学习算法训练网络并应用到混沌序列相空间重构中,实验结果表明,小波神经网络比MLP和ARMA模型具有更强大的逼近能力,因而十分适合应用于时间序列分析中;多分辨率学习算法可作为分析复杂混沌时间序列的一种重要工具。     

正交样条小波在信号奇异性检测中的应用

本文给出了正交样条小波在信号奇异性检测中的应用,并且与其它常用的小波如Daubechies小波和双正交小波作了比较。实验表明,用正交样条小波进行信号奇异性检测不仅计算量小,而且效果好。     

基于Haar小波的时间序列相似度量算法的实现

时间序列相似性搜索问题中,涉及到维数简约,对数据进行变换应用于时间序列数据的降维。在详细了解时间序列数据库相似搜索技术的基础上,本文选择Haar小波来处理时间序列,提供了系数子集的良好近似,用C＋＋语言实现基于Haar小波的时间序列相似度量算法。当需要线性数据时．Haar小波变换能够快速且容易的计算出在时间序列和简单编码的长度。     

Daubechies小波双尺度方程的简捷推导

本文从线性滤波器角度探讨了一种简单直观地推导Daubechies小波双尺度方程系数的方法,进一步揭示 了小波系数的构造方法,简化了小波理论的数学描述。     

复Daubechies小波域HMT模型Bayesian图像去噪

提出了基于复Daubechies小波域隐马尔可夫树(SDW-HMT)模型Bayesian图像去噪算法,由于SDW小波是紧支撑、对称、正交小波,且具有近似线性相位,将其与HMT模型结合,能够更加准确地刻画小波系数的统计特征,在Bayesian图像去噪中获得很好的效果,仿真实例显示了所提算法的有效性。     

基于小波变换的图像融合方法研究

介绍了图像融合的基本原理、结构模型及应用领域,简述图像小波分解与重构的Mallat算法。在Matlab7.0环境下,采用Daubechies小波(dB4)滤波器组对待融合图像进行了3级正交小波分解,低频系数采用边缘保持,高频系数采用基于区域能量最大的规则进行融合,并对融合图像进行质量评价。     

新Burt-Adelson双正交小波的优化设计

根据小波滤波器的精确重构条件,推导出Burt-Adelson双正交小波滤波器组的参数表达式。该表达式参数可任意取值,因此能够随意构造具有不同特征的Burt-Adelson小波。作为构造实例,构造出一个新的有理系数Burt-Adelson小波,它具有优化的编码增益。实验表明,其图像压缩性能略低于CDF-9/7小波,但优于JPEG2000标准推荐的7/5小波;而且其提升小波变换的计算效率比CDF-9/7小波高20%以上,也优于7/5小波。     

Beta wavelets. Synthesis and application to lossy image compression

Wavelets are known to have many connections to several other parts of mathematics, notably phase-space analysis of signal processing, reproducing kernel Hilbert spaces, coherent states in quantum mechanics, spline approximation theory, windowed Fourier transforms, filter banks and image analysis.In this paper, we study a new orthogonal mother wavelet and wavelet basis system based on Beta function as well as its derivatives. The most important conditions of mother wavelets to be satisfied are the admissibility, the regularity and the orthogonality. All these conditions were verified in the case of the proposed Beta wavelets family.Compared to most known wavelets as Haar, Daubechies, and Coifflet ones, the Beta wavelet family improves efficient results and performances presented in this paper for image compression context.     

小波基对多分形小波模型的影响

以多分形小波模型（MWM）为基础,选取了Haar, Daubechies, Coiflets, Symlets四种小波基,分别研究不同小波对此模型的影响。通过对真实流量、模型合成流量进行多种实验的分析、比较,得出结论：在多分形小波模型中采用Haar小波合成的流量,能够更准确的反映原始流量的统计特性。     

时变非线性分布参数控制系统的小波辨识算法

基于正交函数逼近理论,在Haar小波正交规范基的基础上,总结并推导出了其积分运算矩阵、微分运算矩阵、乘积运算矩阵及其运算性质,并应用于一类时变非线性分布参数系统的辨识.借助于正交小波函数逼近方法对分布参数系统进行辨识,经正交小波逼近变换转化为代数矩阵方程,因此该方法可以不考虑初始条件和边界条件,较其他辨识方法要简单得多.该算法简单、计算量小、简化了分布参数系统辨识的求解过程,应用在分布参数系统辨识中不失为一种有效的分析方法.     

简单双正交C9／7小波的提升构造

针对CDF9/7等小波的缺陷,灵活运用双正交对称滤波器的规一化和消失矩性质以及9/7小波的提升结构,构造了一组包含两个自由变量的9/7提升小波族。该小波族通过选取合适的自由变量值,得到了提升系数和滤波器系数都非常简洁,而且构造了部分系数分母为2的幂次方的C9/7系列小波,并结合滤波器理论,讨论了它们的正交性和消失矩;最后将C9/7小波与CDF9/7小波进行了对比分析,结果表明,C9/7小波在计算性能方面明显优于CDF9/7小波,而在客观质量评价和主观质量评价方面则与CDF9/7小波不相上下。     

WAVELET-BASED STEGANOGRAPHY

Wavelets, which are used to separate data into different components, have many applications. Steganography, one such application, is a form of secret communication where the existence of a message is concealed. Methods for applying univariate and bivariate wavelets to steganography include embedding messages into the insignificant wavelet coefficients of decomposed signals and images. Recomposing then creates stego-objects that appear unaltered from the original cover-objects. First demonstrated is a technique for hiding messages in strings of data with linear trends using the univariate Daubechies D ₄ wavelets. Then, after developing the bivariate Haar wavelets and filters, a unique process of decomposing and recomposing an image in greyscale in order to implement steganography will be illustrated.     

GPU-based 3D wavelet reconstruction with tileboarding

In this paper, we present a GPU-based algorithm for reconstructing 3D wavelets using fragment programs. To minimize the data transfer and fragment processing overhead, we propose a novel scheme that uses tileboards as a primary layout to organize 3D wavelet coefficients. By accessing the tileboards with correct texture coordinates, Haar and Daubechies wavelets can be evaluated by the GPU in real time. The tileboard also serves as input to the rendering programs. We demonstrate how the tileboards allow us to efficiently cull unnecessary data, and we extend our work to render large volumes with multiple resolution levels.     

滤波长度为4的双正交多尺度分析的构造

该文研究了滤波长度为4的双正交多尺度分析的一般构造，依据Lawton条件，通过解决一个线性代数问题，求出了其实滤波系数所在的范围，给出了一些构造的例子，并通过计算和分析这些小波用于图像压缩的熵和信噪比数据，研究了它们用于图像压缩的性能。     

Parallel Computation of Wavelet Transforms Using the Lifting Scheme

The lifting scheme [14] is a method for construction of biorthogonal wavelets and fast computation of the corresponding wavelet transforms. This paper describes a message–passing parallel implementation in which high efficiency is achieved by a modified data–swapping approach allowing communications to overlap computations. The method illustrated by application to Haar and Daubechies (D4) wavelets. Timing and speed–up results for the Cray T3E and the Fujitsu AP3000 are presented.     

Identification of linear time varying systems by Haar wavelet

This study addresses the identification of linear time varying systems. The identification is based on the expansion of all time functions in the state equations by Haar wavelets. The unknown time function can thus be identified in terms of Haar wavelets. A Haar wavelet is a set of complete, orthogonal basis and is easy to use computations. Several good properties of Haar wavelets are utilized in the algorithm. Both numerical and experimental results verify the analysis.