构建三元双正交小波的矩阵扩充方法

讨论三元双正交小波滤波器构造的矩阵扩充问题.运用多小波提升思想与矩阵多相分解方法,给出了由插值尺度函数构造三元双正交小波滤波器一般公式.刻画了三元双正交小波包的性质,得到了2个双正交公式.     

正交双向小波包

在引入正交双向小波的基础上,给出紧支撑正交双向小波包的定义及其构造方法.讨论了这类正交双向小波包的性质.正交双向小波包是正交小波包的推广.     

m尺度正交双向小波的构造

将2尺度双向加细函数和双向小波的研究以及相关性质推广到m尺度.同时,给出了双向加细函数和双向小波在对称与反对称时应满足的条件.最后研究了如何利用正交尺度函数和对应的正交小波.构造正交双向小波,并给出了具体算例.     

高维紧支撑不可分正交小波的构造

高维不可分小波在小波分解时能够反映一定的高频性质.在尺度函数的符号为罗朗多项式的条件下给出了紧支撑0211022100211111-小波的构造方法.该小波在尺度函数的符号满足给定条件时,具有相应消失矩     

基于三维小波变换的图像融合

比较了目前常用的各种二维图像融合算法 ,并就其中最理想的基于小波变换的图像融合算法利用可分离多分辨分析方法给出三维形式 ,为纺织领域各种适应特殊应用要求的三维图像融合算法的研究提供了一个好的框架。     

r重正交小波的构造

首先引入r重正交小波和多尺度分析的概念，然后讨论了r重多尺度分析中闭线性子空间和尺度函数的性质，最后在最一般的情况下，给出了r重正交小波的存在性证明。     

多尺度分析生成的多重正交小波的性质

首先讨论了多尺度分析中子空间V0的性质,在此基础上得到多尺度分析生成的多重正交小波的几个等价条件,使得H.O.K im的定理2.6成为其的一种特殊情形.     

基于小波包分析的纸浆浓度信号去噪方法

针对造纸过程的纸浆浓度检测信号,给出了一种基于小波包分析的去噪方法.讨论了小波包分析和去噪的原理、阈值和阈值函数的选取,比较了选择不同阈值以及不同阈值函数对纸浆浓度信号去噪的效果.理论分析和仿真都表明基于小波包分析的去噪方法的有效性.     

盘磨机故障的振动特征分析

当前盘磨机故障特征尚属一个不明确的问题。本文在讨论磨浆机组成结构的基础上,借助于振动方程和运行过程中的力学分析,给出了盘磨机不平衡情况下的故障振动特征。根据实际采样数据的小波包分解分析可以得出结论,即通过盘磨机振动的小波包分解,能够找出隐藏在振动信号中的故障特征分量。     

基于二维康托尔二元群的小波变换

根据经典的康托尔集构造了二维康托尔集,将一维康托尔二元群上的小波变换推广到二维康托尔二元群上.利用一维多分辨分析的张量积构造出二维可分离多分辨分析,提出相应的尺度函数和小波函数,并给出基于该小波的分解与重构算法.     

求解微分方程的二代小波配点法

采用Lagrange插值细分方法构造了紧支撑双正交小波的尺度函数.以此尺度函数为基函数,考虑区间内外基函数的不同,选择不同的配点,形成了区间上求解微分方程的小波配点法.由于二代小波自身的特性使该方法结构简单,计算复杂度小.对对流占优方程第一边值问题,当扩散系数很小时用本文方法也能得到较精确解,表明了该方法的有效性.     

Image Detection of Rice Fissures Using Biorthogonal B-Spline Wavelets in Multi-resolution Spaces

An image analysis method was developed with higher detection accuracy for rice fissures compared with using the classical Canny and Sobel methods. The rice images are obtained using a common scanning machine with resolution of 600 dpi. The scanning images are enhanced by the gamma correction and smoothed using the anisotropic nonlinear diffusion PDEs. The diffusion process is stopped when the peak signal to noise ratio is lower than 30 dB or changes slowly. After that the wavelet coefficients of the smoothed images are calculated using continuous wavelet transform with the biorthogonal B-spline wavelets bior1.5 in multi-resolution spaces. The wavelet coefficients in y forward direction are used as the magnitudes. Finally, the magnitudes are standardized and used for the judgment of the fissures as the local maxima. Two different kinds of rice kernels are used for the test of the effectiveness of the proposed algorithm, including 30 long- and 20 medium-cracked grains with 1, 2, 3, or 4 fissures. The results demonstrate a satisfying performance of the fissure detecting systems, and even the faint lines of the fissures can also be detected.     

Comparison of various wavelet texture features to predict beef palatability

The wavelet transform can be used to characterise the surface texture of beef images in a more efficient manner than classical algorithms such as co-occurrence and run lengths. Features extracted from wavelet decompositions have been used to develop predictive models of important palatability attributes. A variety of common wavelet transforms were considered (biorthogonal, reverse biorthogonal, discrete Meyer, Daubechie, symmetric modified Daubechie and Coifman modified Daubechie) to search for the most useful texture features. A classic run length and co-occurrence algorithm was used for comparison. Using the same data analysis methods for each wavelet type, predictive models of beef acceptability, tenderness, juiciness, flavour and hardness were developed. Genetic algorithms succeeded in finding more accurate models than stepwise and manual elimination except for hardness. An accurate model of flavour (r² = 0.84) was computed. A good model of overall acceptability (r² = 0.79) was computed that fell just short of an important benchmark of accuracy. An encouraging model of juiciness (r² = 0.71) was computed showing that with additional palatability information juiciness might be accurately modelled. Tenderness proved difficult to model with only the classic model satisfying stability criteria and a poorer result (r² = 0.64) meaning substantial additional palatability information is required for accurate modelling. Hardness was particularly difficult to model. The biorthogonal wavelet produced the best model for three palatability measurements but the symmetric modified Daubechie wavelet produced the best model of overall acceptability and thus must be viewed as the most useful wavelet type.     

利用lifting方法设计双正交滤波器组

研究了用lifting方法设计三通道自适应提升双正交滤波器组.在设计中,用子带编码增益作为设计准则,从任意一个滤波器组(标准正交或双正交)开始,通过联合自适应提升方法来设计三通道双正交滤波器组.最后,给出例子说明子带码增益明显提高.     

Characterization and application of objective pilling classification to patterned fabrics

Abstract

Previously, the authors proposed a new, simple method of frequency domain analysis based on the two-dimensional discrete wavelet transform to objectively measure the pilling intensity in sample fabric images. The method was further characterized, and the results obtained indicate that standard deviation and variance are the most appropriate measures of the dispersion of wavelet details coefficients for analysis, that the relationship between wavelet analysis scale and fabric inter-yarn pitch was empirically confirmed, and, that fabrics with random patterns do not appear to impact on the effectiveness of the analysis method.     

Simultaneous determination of calcium,magnesium and zinc in different foodstuffs and pharmaceutical samples with continuous wavelet transforms

This work presents novel and very simple spectrophotometric methods by ratio spectra–continuous wavelet transformation for the simultaneous determination of ternary mixtures of calcium, magnesium and zinc without prior separation steps. The methods are based on the complexation reaction of these elements with bromopyrogallo red (BPR) at pH 9.4. The results showed that calcium, magnesium and zinc could be determined simultaneously in the range of 0.1–3.5 mg L⁻¹, 0.2–3.2 mg L⁻¹ and 0.5–3.8 mg L⁻¹, respectively. Mexican hat and Morlet from the family of continuous wavelet transforms were selected and applied under the optimal conditions for multi-component determinations. In this study for improving the sensitivity the normalized spectra of divisors were used instead of standard spectrum of divisor. The method was tested by analyzing various synthetic ternary mixtures of Ca²⁺, Mg²⁺ and Zn²⁺. Under the working conditions, the proposed methods were successfully applied to simultaneous determination of elements in cows’ milk, powder milk, pharmaceutical product and tea samples.