小波变换与分析化学信号处理

介绍了小波变换的基本理论并对小波变换的常用算法和应用进行了评述。由于小波变换的时2频局部化性质, 使其成为信号处理的强有力工具。在分析化学领域中, 小波变换在流动注射分析、伏安分析、高效液相色谱、红外光谱、质谱、核磁共振谱、可见-紫外光谱、光声光谱、扩展X-射线吸收精细结构(EXAFS) 谱等分析化学信号的平滑滤噪、数据压缩、重叠信号解析等方面都有成功的应用。     

电化学噪音数据小波分析法研究

电化学动力系统演化过程中 ,其状态参量 (如电极电位、电解池电流等 )的随机波动现象被称为“电化学噪音”(ECN) .小波变换是近年来数学与信号处理领域获得突破性进展的一种数据处理方法 .本文首次用连续小波变换的方法对混凝土中钢筋腐蚀产生的“电化学噪音”信号进行初步研究 ,通过将原始的时域信号变换至时_频相平面来观察其结构特征 ,并揭示出电化学腐蚀过程的混沌动力学行为 .     

小波变换用于近红外光谱数据压缩

近红外光潜数据量大,需要较大数据存储空间和较长的建模时间、本文以成品柴油性质分析为例．将小波变换用于近红外光谱数据压缩处理,详细考察了小波压缩参数,比较了压缩前后潜图差异以及性质分析偏差的变化。研究结果表明．采用Daubechies小波函数(N=2)为母函数．进行3次分解,直接采用其逼近系数(Ca3)作为谱图压缩数据,其重构光谱与原始光谱基本一致直接利用逼近系数进行性质分析,其分析精度与原始光谱数据基本相当,存储空间减少至原来的1／8,且能够明显缩短其建模时间和分析时间。     

共聚物红外光谱的小波变换

用傅里叶变换红外光谱研究了辐射合成的丙烯酰胺、丙烯酸钠均聚物水凝胶和几种丙烯酰胺／丙烯酸钠配比不同的共的水凝胶的组成变化，发现共聚物的特征吸收带重叠得比较严重，尤其当丙烯酸单元含量较代时，其特征吸收带大部分则不能分辨，将其红外光谱经波波变换后，这类共聚物的特征吸收带较好地得到分离，成功地提高了红外光谱图的分辨率，有助于更好地定性或定量表征共聚物的组成。     

小波Fourier自去卷积法

使用小波函数作为Fourier自去卷积的截止函数，提出了小波Fourier自去卷积法.通过研究不同小波去卷积函数的性质，建立了消除伪峰的阈值法以及正负极值比的小波负峰扣除法，从而使经典Fourier自去卷积技术中存在的滤噪效果差、过程复杂、易出现伪峰及负峰等缺陷得以较好地解决.　将其用于示波计时电位法中多组分测定的结果表明该方法具有处理效果好、过程简单等优点.     

小波变换及其在化学中的应用

介绍了傅里叶变换、加窗傅里叶变换和小波变换的基本概念，以及小波变换在化学中的应用。     

小波包去噪信号的分形特征

将分形理论与小波包滤波相结合，用盒维数的大小来评判信号曲线的滤波情况。随着小波包分解尺度的增大，滤波后信号曲线的盒维数逐渐减小，并最后趋于稳定值。因此可以根据盒维数-分解尺度曲线来选择最佳分解尺度。对仿真含噪信号进行了滤波实验，结果表明：即使在信噪比低至0．5时仍能得到较好的结果，并且该法用于毛细管电泳实验数据的处理结果同样令人满意。     

《分析化学中的小波分析技术》

小波变换的概念是由法国从事石油信号处理的工程师J．Morlet在1974年首先提出的并建立了反演公式。它解决了Fourier变换不能解决的许多困难问题，所以被誉为“数学显微镜”，具有分析发展史上里程碑式的意义。本书是分析科学现代方法丛书中的一册，是国内第一本介绍小波分析在分析化学中应用的图书。作者卢小泉教授自1994年始从事小波分析在分析化学中的应用研究，他在自己科研的基础上参阅了国内外大量的有关小波分析的文献后编著此书，书中内容具有很强的针对性和实用性。该书的出版能给分析化学工作者，特别是化学计量学工作者提供一些有价值的参考。     

小波变换在分析化学信号处理中的应用

介绍了小波变换的基本概念 ,将小波变换在分析化学信号处理中的应用概括为小波滤波、小波数据压缩和小波多尺度分析三个方面。     

Wavelet formulation of the polarizable continuum model

The first implementation of a wavelet discretization of the Integral Equation Formalism (IEF) for the Polarizable Continuum Model (PCM) is presented here. The method is based on the application of a general purpose wavelet solver on the cavity boundary to solve the integral equations of the IEF‐PCM problem. Wavelet methods provide attractive properties for the solution of the electrostatic problem at the cavity boundary: the system matrix is highly sparse and iterative solution schemes can be applied efficiently; the accuracy of the solver can be increased systematically and arbitrarily; for a given system, discretization error accuracy is achieved at a computational expense that scales linearly with the number of unknowns. The scaling of the computational time with the number of atoms N is formally quadratic but a N^1.5 scaling has been observed in practice. The current bottleneck is the evaluation of the potential integrals at the cavity boundary which scales linearly with the system size. To reduce this overhead, interpolation of the potential integrals on the cavity surface has been successfully used. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Wavelet transform-based Curve Fitting

Curve fitting methods are now widely applied both qualitative and quantitatively to separate overlapping peaks in composite profiles. Nevertheless, the achievement of a good representative fit requires the knowledge of five parameters:the number of component bands, their positions, shapes and widths, and the form of the baseline. Clearly, curve fitting is considerably facilitated if approximate values for some of the parameters are known at the outset. Up to present, there are many methods employed for improving the curve-fitted conditions^[1,2]. Wavelet transform is a high performance signal processing technique developed from the Fourier transform.     

小波变换用于近红外光谱性质分析

以汽油研究法辛烷值分析为例,研究了小波变换在近红外光谱分析中的应用。对近红外光谱的小波特性、小波变换参数以及变量提取方法进行了详细研究。研究结果表明：光谱噪音、有用信息和背景分别分布在小波高、中和低频区域;母小波函数对性质分析结果影响很大;小波变换可以同时扣除光谱背景、去除噪音和压缩变量,具有运算速度快、分析精度高以及无需去噪后处理等优点,在近红外光谱分析中具有很好的应用前景。     

Fusion of 2-D SIMS Images Using the Wavelet Transform

 Secondary ion mass spectroscopy (SIMS) is a powerful method for element distribution examination of conducting and semi-conducting surfaces at high spatial resolution and with a high sensitivity. Routine surface analysis produces about 8 to 15 images in a short time, each of which displays the intensity distribution of one mass, thus generating a multispectral SIMS image. Formation of occlusions, segregations, and the overall location of the elements relative to each other, are difficult to recognise when looking at n separate 2-D images. Image fusion is a process whereby images obtained from various sensors, or at different moments of time, or under different conditions, are combined together to provide a more complete picture of the object under investigation. The process of combining SIMS images may be viewed as an attempt to compensate for the inherent effect of SIMS to channel the information obtained from the sample into different images, corresponding to different element phases. The wavelet transform is a powerful method for fusion of images. This work covers the use of wavelet based fusion algorithms on multispectral SIMS images, evaluating the performance of different wavelet based fusion rules on different type of image systems and comparing the results to conventional fusion techniques. An aim of this study is to increase the information, i.e. the number of masses, which can be merged into one image in order to enhance the perception and interpretation of the SIMS surface images.     

一种基于二进小波变换的自适应滤波方法

根据信号和噪声经小波变换后在不同尺度上有不同的特征，将相邻尺度二进小波变换值的相关量进行归一化处理并与小波变换值比较来判断信号与噪声，以噪声在各尺度的方差作为终止迭代的标准，提出了一种基于二进小波变换小波域选择噪声的自适应滤波方法。研究了模拟信号的去噪过程、半峰宽和信噪比对去噪结果的影响，并对模拟含噪信号和含噪毛细管电泳信号去噪前后的结果进行了比较。实验结果表明：由于该方法具有良好的自适应性和显著的滤波效果，必将得到广泛的应用。     

基于小波和小波包变换的苯丙酮尿症傅里叶变换衰减全反射红外光谱筛查模型的研究

应用小波和小波包变换对傅里叶变换衰减全反射红外光谱(FTIR/ATR)进行去噪处理,以提高苯丙酮尿症(PKU)筛查模型的性能。首先优化小波和小波包变换的参数,然后分别对原始光谱(OS)、9点平滑光谱(9S)和一阶微分9点平滑光谱(1D9S)进行去噪处理,以均方根误差(RMSE)、平均相对误差(MRE)、预测准确率(Acc)等为指标,考察小波和小波包变换对模型性能的影响。结果与变换前相比,模型性能均有所提高,其中小波变换以1D9S+sym12处理结果为最优,而小波包变换以1D9S+sym1为最优;Acc全部提高为100%。     

基于提升格式的小波变换用于处理化学信号

将提升haar小波变换应用于对不同类型含高噪声化学信号的处理,提出1种用于高噪声化学信号中滤除噪声的快速新方法——提升小波滤噪法,并使之与重叠峰分辨技术联用;以优选的小波分解层数对低信噪比的分析化学信号进行基于提升格式的小波变换处理,取得满意的结果;方法简单、快捷、准确、易行．运算速度是传统小波变换的一半,对高噪声化学信号的处理结果信噪比提高几百倍,峰位置相对误差小于1．5％;应用于氨基酸体系毛细管电泳检测信号的处理,有效降低了实验噪声的影响,分辨提取了难以察觉的信号．结果峰形变窄,峰高增加．大大提高了峰的分辨率．验证和显示了方法的可行性和优越性。     

Analysis of Spontaneous Electrochemical Oscillations by the Wavelet Transformation Method

A new way of analyzing current oscillations that accompany anodic metal dissolution is presented. A wavelet transformation is used for separation and spectral analysis of singular courses—elementary components of electrochemical oscillation recordings. A method of obtaining oscillation energy distribution analogous to the spectral power density function is presented. It is shown that the chaotic component (Shil'nikov chaos) can be separated from the deterministic component of the described process.     

Wavelet transform-based analysis for electrochemical noise

Wavelet transforms are presented as a useful tool to analyse electrochemical noise data. Various concepts developed in the framework of wavelet transforms have been adapted to study electrochemical noise measurements. The most relevant feature of this method of analysis is its capability of decomposing electrochemical noise records into different sets of wavelet coefficients, which contain information about corrosion events occurring at a determined time-scale. Thus, this mathematical approach could become an alternative tool which solves the limitations of other more established procedures for the analysis of electrochemical noise data, such as statistical or Fourier transform-based methods.