Recursive Wavelet Peak Detection of Analytical Signals

A novel algorithm, entitled recursive wavelet peak detection (RWPD), is proposed to detect both normal and overlapped peaks in analytical signals. Recursive peak detection is based on continuous wavelet transforms (CWTs), which can be used to obtain initial peak positions even for overlapped peaks. Genetic algorithm (GA) and Gaussian fitting are used to refine peak parameters (peak positions, widths, and heights). Finally, area of peaks can be calculated by numeric integration. Simulated and ultrahigh performance liquid chromatographic ion trap time-of-flight mass spectrometry (UPLC-IT-TOF-MS) data sets have been analyzed by RWPD, MassSpecWavelet, and peakfit package by Tom O’Haver. Results show that RWPD can obtain more accurate positions and smaller relative fitting errors than MassSpecWavelet and peakfit, especially in overlapped peaks. RWPD is a convenient tool for peak detection and deconvolution of overlapped peaks, and it has been developed in R programming language and is available at https://github.com/zmzhang/RWPD.

     

Pattern recognition in capillary electrophoresis data using dynamic programming in the wavelet domain

A novel approach for CE data analysis based on pattern recognition techniques in the wavelet domain is presented. Low-resolution, denoised electropherograms are obtained by applying several preprocessing algorithms including denoising, baseline correction, and detection of the region of interest in the wavelet domain. The resultant signals are mapped into character sequences using first derivative information and multilevel peak height quantization. Next, a local alignment algorithm is applied on the coded sequences for peak pattern recognition. We also propose 2-D and 3-D representations of the found patterns for fast visual evaluation of the variability of chemical substances concentration in the analyzed samples. The proposed approach is tested on the analysis of intracerebral microdialysate data obtained by CE and LIF detection, achieving a correct detection rate of about 85% with a processing time of less than 0.3 s per 25,000-point electropherogram. Using a local alignment algorithm on low-resolution denoised electropherograms might have a great impact on high-throughput CE since the proposed methodology will substitute automatic fast pattern recognition analysis for slow, human based time-consuming visual pattern recognition methods.     

基于多尺度小波变换的红外光谱谱峰识别算法

传统的谱峰检测方法一般分为3个步骤:谱线平滑、基线校正和谱峰识别.现有的基于小波变换的峰值检测方法能较好地将基线校正和谱峰识别两个步骤融为一步.在此基础之上,本研究将谱线平滑也很好地融入到小波变换的峰值检测算法中,使整个峰值检测算法成为一个整体.在峰值提取时,原始谱图直接处理,不再是处理加工过的谱图,减小了谱峰检测结果...     

在线小波变换用于伏安分析仪的研制

将在线小波变换应用于伏安信号的在线处理,研制了具有小波变换功能的伏安分析仪。该系统利用在线小波变换对采集到所数据进行实时处理,具有控制灵活,分辨率高,数据处理方便等特点。通过对低浓度Ｃｙ＾２＋和Ｆｅ＾３＋混合样品的阶梯斜坡扫描伏安珠滤噪及定性,定量分析,结果表明可获得满意的分析结果。     

Kinetic determination of lactate dehydrogenase in blood serum by multi-detection with a cyclic flow-injection system

The use of a cyclic flow-injection system for the determination of lactate dehydrogenase (LDH) is proposed. This configuration allows the repeated passage of the reacting plug through the detector resulting in multiple peak recordings. From the data obtained, which correspond to a typical kinetic curve, the required sensitivity can be selected by using procedures based on fixed-time measurements (peak maxima or minima) or reaction-rate measurements (signal increment between two successive maxima or minima). The methods were applied successfully to the determination of LDH in blood sera; the average recovery was 100.9%.     

End-point detection in potentiometric titration by continuous wavelet transform

The aim of this work was construction of the new wavelet function and verification that a continuous wavelet transform with a specially defined dedicated mother wavelet is a useful tool for precise detection of end-point in a potentiometric titration. The proposed algorithm does not require any initial information about the nature or the type of analyte and/or the shape of the titration curve. The signal imperfection, as well as random noise or spikes has no influence on the operation of the procedure.The optimization of the new algorithm was done using simulated curves and next experimental data were considered. In the case of well-shaped and noise-free titration data, the proposed method gives the same accuracy and precision as commonly used algorithms. But, in the case of noisy or badly shaped curves, the presented approach works good (relative error mainly below 2% and coefficients of variability below 5%) while traditional procedures fail. Therefore, the proposed algorithm may be useful in interpretation of the experimental data and also in automation of the typical titration analysis, specially in the case when random noise interfere with analytical signal.     

Wavelet transforms in separation science for denoising and peak overlap detection

Wavelet transform is a versatile time‐frequency analysis technique, which allows localization of useful signals in time or space and separates them from noise. The detector output from any analytical instrument is mathematically equivalent to a digital image. Signals obtained in chemical separations that vary in time (e.g., high‐performance liquid chromatography) or space (e.g., planar chromatography) are amenable to wavelet analysis. This article gives an overview of wavelet analysis, and graphically explains all the relevant concepts. Continuous wavelet transform and discrete wavelet transform concepts are pictorially explained along with their chromatographic applications. An example is shown for qualitative peak overlap detection in a noisy chromatogram using continuous wavelet transform. The concept of signal decomposition, denoising, and then signal reconstruction is graphically discussed for discrete wavelet transform. All the digital filters in chromatographic instruments used today potentially broaden and distort narrow peaks. Finally, a low signal‐to‐noise ratio chromatogram is denoised using the procedure. Significant gains (>tenfold) in signal‐to‐noise ratio are shown with wavelet analysis. Peaks that were not initially visible were recovered with good accuracy. Since discrete wavelet transform denoising analysis applies to any detector used in separation science, researchers should strongly consider using wavelets for their research.     

Signal Processing in Normal Pulse Voltammetry by Means of Dedicated Mother Wavelet

In the work, a new signal processing algorithm is presented and applied for the transformation of the sigmoidal shaped curves, registered in normal pulse voltammetry (NPV), to the peak shaped curves. The method is based on the continuous wavelet transform (CWT) and specially constructed mother wavelet defined using the ideal wave‐shaped curve. Transformation of the signal, elimination of noises and separation of overlapping data can be achieved in one step by means of proposed procedure. The operation and effectiveness of the algorithm is presented using ideal, noised and overlapping simulated curves. The process of simultaneous determination of lead and indium as well as transformation of curves registered for elements' ions: lead, indium, thallium and cadmium is described. The obtained results show substantial improvement of the performance of NPV.     

基于小波理论的化学谱图数据自适应滤波方法研究

运用小波理论,利用噪声与真实信号小波变换极大模性态之间的显著差异,提出了一类新的化学谱图数据自适应滤波算法,从根本上突破了现有算法均依据信噪频率特性进行滤波的传统模式.经大量色谱谱图数据处理试验证明,这种算法具有无需设置初始参数,消除人为误差因素对分析计算结果的影响,信噪分离性能好及峰位和峰高保持不变等一系列优点,其鲁棒性、自适应性和谱峰保真度完全符合仪器分析信号处理的要求.     

Prediction of protein secondary structure based on continuous wavelet transform

In this paper, continuous wavelet transform (CWT) is used to extract the number and the relevant positions of the α-helices and short peptides connecting α-helices and β-strands (connecting peptides) from the amino acid sequences of proteins. The amino acid sequence is first mapped into hydrophobicity sequence, and then transformed into CWT value of sequence domain in appropriate scale via CWT. The number and the relevant positions of the α-helices and connecting peptides can be extracted easily and accurately according to the minima of wavelet coefficient in corresponding CWT plot of hydrophobic value sequences with appropriate scale. The analytical results demonstrate that α-helices and connecting peptides can be predicted conveniently and rapidly when this method is used in the processing of 100 non-homologous sequences. However, this method is not suitable for predicting the length of α-helices and connecting peptides.     

Dedicated mother wavelet in the determination of antimony in the presence of copper

In this paper, a new signal-processing procedure is applied to the optimization of voltammetric determination of antimony in the presence of copper and the parallel determination of these two elements. The proposed numerical algorithm for the separation of the overlapping peaks utilizes the continuous wavelet transform and the inverse continuous wavelet transform. As the base function, the specially defined dedicated mother wavelet is used. In its construction the ideal, simulated voltammetric peak is intensively exploited. This approach, corresponding to the wavelet theory, gives satisfactory signals separation, even in the cases when they constitute one peak. The possibility of Sb(III) determination is presented in the case of different distances between copper and antimony peaks and also in 10-, 20- and 50-fold excesses of Cu. The parallel determination of Cu(II) and Sb(III) is possible even in the case of a 10-fold excess of copper. The quality of the obtained results fulfills the requirements of validation.     

基于小波神经网络的新型算法用于化学信号处理

基于紧支集正交小波神经网络的构造思想,用具有紧支集的Ｂ－样条函数的伸缩和平稳替代小波函数,提出了一种新型算法,并将其应用于化学信号的处理,实现了信号的压缩和滤噪,适应小波神经网络相比,学习速度得到了大幅度的提高。     

基于小波和轮廓提取的色谱基线算法研究

把基于小波和轮廓提取的基线算法引入了色谱基线提取领域;基于轮廓提取的算法为:通过构造一个滑动窗,沿着色谱数据滑动求窗内的最小值。把这些最小值插值平滑就获得了色谱基线。基于小波和轮廓提取的算法为:先用小波初步提取基线,然后把色谱数据减去小波提取的基线后再用轮廓提取算法获得基线,把小波提取的基线和轮廓提取的基线相加即为原数据的基线。对这两个算法进行了比较实验研究,结果表明:基于小波和轮廓提取的算法比轮廓提取的算法效果好,能更准确地提取色谱基线。     

基于迭代小波变换的光谱信号本底扣除方法研究

本底会对光谱分析结果产生很大的干扰作用,为获取特征峰的有效信息,必须首先去除本底。该文提出了一种基于小波变换的本底扣除算法,通过对光谱及后续光谱迭代进行小波变换,利用逼近系数估计本底,直到本底收敛。提出了判断多次估计的本底最大误差是否足够小的收敛准则。利用该算法去除本底后,即可进行特征峰信息的提取。分别利用仿真光谱和实验能量色散X射线荧光光谱对算法进行了验证,并与传统小波变换和多项式拟合法进行了对比。结果表明,该算法能够更准确扣除光谱本底,对其他光谱的本底扣除也具有借鉴意义。     

小波变换用于二次微分交流示波计时电位信号中有用信息的提取

小波分析是８０年代发展起来的一种新的数学分支。由于小波变换具有许多其它的信号处理手段所不具备的优良特性，如正交性，可变的时－频分辨率和可调节的局部支持等，使它成为信号处理的一种强有力的工具。     

Characterizing Long—range Correlation Properties in Nucleotide Sequences

Using continuous wavelet transform as the analytical tool,the fractal characteristic of nucleotide sequences was studied.The fractal dimension of the exon and intron sequences for different species was calculated.We use the Mexican hat wavelet function as the mother wavelet and Hurst exponent describe the long-range correlation.It is found that the Hurst exponent of intron sequence is larger than of exon sequence for the same gene.     

小波分析对奇异性检测用于滴定终点确定的研究

在分析化学领域中，利用数学判断法确定滴定终点，随着计算机的日益普及而备受关注。此文在介绍当前普遍采用的二进小波变换奇异性检测方法的基础上，提出基于多分辨率分析和连续小波变换两种奇异性检测方法，并应用于氢氧化钠对盐酸和磷酸滴定曲线判断终点的试验中，取得了良好的效果。     

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...     

Resolution enhancement of composite spectra using wavelet-based derivative spectrometry

An approach based on the using of the continuous wavelet transform (CWT) in derivative spectrometry (DS) is considered. Within the framework of the approach we develop a numerical differentiation algorithm with continuous wavelets for improving resolution of composite spectra. The wavelet-based derivative spectrometry (WDS) method results in best contrast in differential curves compared to the conventional derivative spectrometry method. A main advantage is that, as opposed to DS, WDS gives stable estimations of derivative in the wavelet domain without using the regularization. A wavelet shape and the information redundancy are of the greatest importance when the continuous wavelet transform is used. As an appropriate wavelet we offer to utilize the nth derivative of a component with a priori known shape. The energy distribution into scales allows one to determine a unique wavelet projection and in that way to avoid the information redundancy. A comparative study of WDS and DS with the statistical regularization method (SRM) is made; in particular, limits of applicability of these are given. Examples of the application of both DS and WDS for improving resolution of synthetic composite bands and real-world composite ones coming from molecular spectroscopy are given.