Simultaneous quantitative analysis of overlapping spectrophotometric signals using wavelet multiresolution analysis and partial least squares

The mathematical bases and program algorithms of discrete wavelet transform (DWT), multiresolution and Mallat’s pyramid algorithm were described. The multiresolution analysis (MRA) based on Daubechies orthogonal wavelet basis was studied as a tool for removing noise and irrelevant information from spectrophotometric spectra. After wavelet MRA pre-treatment, eight error functions were calculated for deducing the number of factors. A partial least squares based on wavelet MRA (WPLS) method was developed to perform simultaneous spectrophotometric determination of Fe(II) and Fe(III) with overlapping peaks. Data reduction was performed using wavelet MRA and principal component analysis (PCA) algorithm. Two programs, SPWMRA and SPWPLS, were designed to perform wavelet MRA and simultaneous multicomponent determination. Experimental results showed the WPLS method to be successful even where there was severe overlap of spectra.     

Development of wavelet transform voltammetric analyzer

An on-line wavelet transform algorithm and development of voltammetric analyzer with the on-line wavelet transform (WT-voltammetric analyzer) are described. Because the on-line wavelet transform decomposes the sampled signal simultaneously with the progress of sampling, the WT-voltammetric analyzer gives all the components contained in the sampled voltammogram. Applications of the WT-voltammetric analyzer in linear sweep voltammetric analysis of mixtures of Pb(II) and Tl(I) and in square wave voltammetric analysis of mixture of Cd(II) and In(III) were investigated. Results showed that the overlapping peaks of Pb(II) and Tl(I) can be separated easily, and the peak position after the on-line wavelet transform does not change. The linearity of the calibration curves for Cd(II) and In(III) in the overlapping square wave voltammetric curves were kept after the on-line wavelet transform. Quantitative determination of Cd(II) and In(III) in mixture samples were investigated. The recoveries are between 92.5 and 107.1%.     

Wavelet frequency spectrum and its application in analyzing an oscillating chemical system

Based on the continuous wavelet transform (CWT), three types frequency spectra, wavelet frequency spectrum (WFS), point frequency spectrum (PFS) and time frequency spectrum (TFS), were developed. Two data sets were simulated and treated with the proposed spectra, the results indicated that WFS could extract the frequency information, which was like Fourier analysis but more accurate, PFS could obtain the frequency at any moment, TFS could show frequency change with time. These abilities of PFS and TFS were impossible for Fourier analysis. An oscillating chemical signal was processed with WFS and TFS. From the processed results, two points could be learned about the oscillating chemical reaction: one was the oscillating chemical reaction was a mixture one including two or more complex kinetics processes, the velocity of the switch from the reduced state (RS) to the oxidized state (OS) was faster than the reverse switch (from OS to RS); the other was increase of KBrO₃ could decrease the velocities of both switches, which led to the oscillating period became longer.     

Application of multi-dimensional wavelet transform to fluid mechanics

This paper first reviews the application research works of wavelet transform on the fluid mechanics. Then the theories of continuous wavelet transform and multi-dimensional orthogonal(discrete) wavelet transform, including wavelet multiresolution analysis, are introduced. At last the applications of wavelet transform on 2 D and 3 D turbulent wakes and turbulent boundary layer flows are described based on the hot-wire, 2 D particle image velocimetry(PIV) and 3 D tomographic PIV.     

小波变换用于示波信号中有用信息提取的研究

示波分析是近年来在我国发展起来的一个新的电化学分析研究领域［１～４］．它根据阴极射线示波器荧光屏上示波图及其变化进行分析测试,从原理上可以将其分为示波电位法和示波计时电位法;从测定方式上可以将其分为示波滴定和示波测定．关于示波电位法的一些理论问题（如...     

基于小波降噪与支持向量机的恒星光谱识别研究

提出了一种对恒星光谱识别的新方法。 根据恒星光谱数据的特性,我们以支持向量机为核心技术构建光谱识别器。 由于恒星光谱数据通常含有较高的噪声,如果直接进行分类,识别率往往较低。 因此作者首先采用小波分析的方法对原始光谱数据进行降噪预处理,提取光谱的特征,然后馈送到支持向量机完成对光谱数据的最终识别。 利用实际光谱数据(Jacoby, 1984)对所提出的技术进行检测,实验结果表明使用这种小波分析结合支持向量机的技术的识别效果要优于使用支持向量机结合主分量分析降维技术的识别方法。 另外,作者还比较了支持向量机与传统甄别分析的分类性能,对实际及合成光谱进行实验的结果显示了支持向量机的识别正确率不但优于常见的5种甄别分析方法的识别率,而且有较强的泛化能力。     

污染气体红外光谱特征的快速提取与识别

利用小波变换的多尺度分析对污染气体红外光谱数据进行处理,并使用神经网络对红外光谱数据进行分类识别。实验结果表明：小波变换与神经网络的有机结合,有利于污染气体红外光谱的快速特征提取和识别, 并具有较高的识别率,是一个有效的识别系统。     

基于不同类型小波变换的SAR与可见光图像融合研究

利用具有不同变换形式及不同小波基的小波变换对合成孔径雷达与可见光图像进行融合实验,研究了不同类型小波变换的特征,对融合实验结果进行了分析和比较,综合实验结果和计算复杂度两个方面考虑进行性能评价,为不同的应用场合下正确选择适合合成孔径雷达与可见光图像融合的小波变换类型提供了理论依据.     

小波域内的盲水印提取

在对水印嵌入位的假设检验基础上,提出了一种盲水印的逐位提取模型,并在小波域得到了实现.为平衡水印的不可见性和鲁棒性,根据图像小波域的特征,并利用上下文建模的方法为每个高频小波系数确定不同的水印幅度,从而使水印的嵌入强度依图像的特征而变化.由于水印提取的结果在很大程度上依赖于图像小波系数的统计分布模型,因此小波域中的系数建模采用了广义高斯分布,并使用极大似然法估计参量.实验表明,该方法具有良好的鲁棒性.     

再生核空间中的微分算子样条小波

0　引　　言r次多项式样条小波是从一个满足特殊的广义微分方程Dr+1φ(x)=δ(x)(D是广义微分子算子)的解φ(x)=xr+r!出发来构造的,文献[1]根据这一思想给出非多项式的H1(R)空间中微分算子样条小波分析的构造方法,本文基于这一思路来讨论W2(R)空间中的微分算子样条小波理论.在W2(R)空间中讨论非多项式形式的微分算子样条小波分析理论,这是多项式小波理论自然深入的发展.本文首先给出W2(R)空间中小波分析定义,然后给出小波函数在时、频域上的表达式,最后利用W2(R)空间中的若干特殊性质,给出小波的投影表达式.并证明了投影逼近函数uj(X)…