Determination of chlorogenic acid in plant samples by using near-infrared spectrum with wavelet transform preprocessing.

By theoretical analysis, it is found that wavelet transform (WT) with a wavelet function can be regarded as a smoothing and a differentiation process, and that the order of differentiation is determined by the vanishing moment, which is an important property of a wavelet function. Therefore, a method based on the continuous wavelet transform (CWT) for removing the background in the near-infrared (NIR) spectrum is proposed, and it is used in the determination of the chlorogenic acid in plant samples as a preprocessing tool for partial least square (PLS) modeling. It is shown that the benefit of the proposed method lies not only in its performance to improve the quality of PLS model and the prediction precision, but also in its simplicity and practicability. It may become a convenient and efficient tool for preprocessing NIR spectral data sets in multivariate calibration.     

Elimination of interference information by a new hybrid algorithm for quantitative calibration of near infrared spectra

A new hybrid algorithm is proposed to eliminate the interference information for multivariate calibration of near-infrared (NIR) spectra that includes noise, background and systemic spectral variation irrelevant to concentration. The method consists of two parts: approximate derivative based on continuous wavelet transform (CWT) and orthogonal signal correction (OSC). After the approximate derivative calculated by CWT, OSC was performed. It was successfully applied to real complex NIR spectral data to eliminate the interference information. Correction for the interference of NIR spectra resulted in a substantial improvement in the predicted precision, and a more concise calibration model was obtained. The proposed procedure also compared favourably with several pretreatment methods, and the new method appears to provide a high-performance pretreatment tool for multivariate calibration of NIR spectra. In addition, the strategy proposed here can be applied to various other spectral data for quantitative purposes as well.     

An adaptive strategy for selecting representative calibration samples in the continuous wavelet domain for near-infrared spectral analysis

Sample selection is often used to improve the cost-effectiveness of near-infrared (NIR) spectral analysis. When raw NIR spectra are used, however, it is not easy to select appropriate samples, because of background interference and noise. In this paper, a novel adaptive strategy based on selection of representative NIR spectra in the continuous wavelet transform (CWT) domain is described. After pretreatment with the CWT, an extension of the Kennard–Stone (EKS) algorithm was used to adaptively select the most representative NIR spectra, which were then submitted to expensive chemical measurement and multivariate calibration. With the samples selected, a PLS model was finally built for prediction. It is of great interest to find that selection of representative samples in the CWT domain, rather than raw spectra, not only effectively eliminates background interference and noise but also further reduces the number of samples required for a good calibration, resulting in a high-quality regression model that is similar to the model obtained by use of all the samples. The results indicate that the proposed method can effectively enhance the cost-effectiveness of NIR spectral analysis. The strategy proposed here can also be applied to different analytical data for multivariate calibration.     

Variable selection by modified IPW (iterative predictor weighting)-PLS (partial least squares) in continuous wavelet regression models

Variable selection is often used to produce more robust and parsimonious regression models. But when they are applied directly to the raw near-infrared spectra, it is not easy to select appropriate variables because background and noise will often overshadow or overlap the absorption bands of analyte. In this work, a new hybrid algorithm based on the selection of the most informative variables in the continuous wavelet transform (CWT) domain is described. The strategy is a combination of CWT and a procedure of modified iterative predictor weighting-partial least square (mIPW-PLS). After elimination of the background and noise in NIR spectra by CWT, the mIPW-PLS approach is used to select the most informative CWT coefficients. With the selected CWT coefficients, a PLS model is built finally for prediction. It is indicated that the extraction of most important variables in the CWT domain can effectively avoid the interference of background and noise, and result in a high quality of regression model with a very small number of variables and fewer PLS components.     

A new hybrid strategy for constructing a robust calibration model for near-infrared spectral analysis

A new hybrid algorithm is proposed for construction of a high-quality calibration model for near-infrared (NIR) spectra that is robust against both spectral interference (including background and noise) and multiple outliers. The algorithm is a combination of continuous wavelet transform (CWT) and a modified iterative reweighted PLS (mIRPLS) procedure. In the proposed algorithm the spectral interference is filtered by CWT at the first stage then mIRPLS is proposed to detect the multiple outliers in the CWT domain. Compared with the original IRPLS method, mIRPLS does not need to adjust variable parameters to achieve optimum calibration results, which makes it very convenient to perform in practice. The final PLS model is constructed robustly because both the spectral interference and multiple outliers are eliminated. In order to validate the effectiveness and universality of the algorithm, it was applied to two different sets of NIR spectra. The results indicate that the proposed strategy can greatly enhance the robustness and predictive ability of NIR spectral analysis.     

Simultaneous wavelength selection and outlier detection in multivariate regression of near-infrared spectra.

Near-infrared (NIR) spectrometry will present a more promising tool for quantitative measurement if the robustness and predictive ability of the partial least square (PLS) model are improved. In order to achieve the purpose, we present a new algorithm for simultaneous wavelength selection and outlier detection; at the same time, the problems of background and noise in multivariate calibration are also solved. The strategy is a combination of continuous wavelet transform (CWT) and modified iterative predictors and objects weighting PLS (mIPOW-PLS). CWT is performed as a pretreatment tool for eliminating background and noise synchronously; then, mIPOW-PLS is proposed to remove both the useless wavelengths and the multiple outliers in CWT domain. After pretreatment with CWT-mIPOW-PLS, a PLS model is built finally for prediction. The results indicate that the combination of CWT and mIPOW-PLS produces robust and parsimonious regression models with very few wavelengths.     

Wavelet unfolded partial least squares for near-infrared spectral quantitative analysis of blood and tobacco powder samples

Continuous wavelet transform (CWT) has been shown to be a high-performance signal processing technique in multivariate calibration. However, the signal processed by CWT with a specific wavelet may account for only a part of the information. To effectively utilize more abundant information contained in analytical signals, a method, named as wavelet unfolded partial least squares (WUPLS), was proposed. In the approach, the measured dataset is firstly extended by CWT with different wavelets, and then partial least squares (PLS) is employed to develop the quantitative model between the extended dataset and the target values. In order to select the representative wavelets, principal component analysis (PCA) is used to investigate the distribution of the signals obtained by CWT with different wavelets. The performance of the method was tested with blood and tobacco powder samples. Compared with the results obtained by PLS methods, the WUPLS method combined with signal processing techniques is proven to be a promising tool for improving the near-infrared (NIR) spectral analysis of complex samples.     

Understanding the thermal stability of human serum proteins with the related near-infrared spectral variables selected by Monte Carlo-uninformative variable elimination

Understanding the thermal stability of the proteins in human serum is essential since human serum is the important source of pharmaceutical proteins. Near-infrared (NIR) spectroscopy was applied to the investigation of thermal changes in secondary structure and hydration of human serum proteins. However, as a multicomponent system, the overlap of the broad NIR bands makes the structural analysis very difficult directly using the spectra of serum samples. Therefore, continuous wavelet transform (CWT) was used to improve the resolution of NIR spectra, and Monte Carlo-uninformative variable elimination (MC-UVE) method was applied to the selection of the variables associated with the proteins for the structural analysis. The variables (5956, 5867, 5815, 5747, 4525, 4401, 4359 and 4328 cm^-1) related to protein secondary structures and those (7074, 6951, 6827 and 6700 cm^-1) connected with water species were selected. Then, the thermal stability was analyzed through the intensity variations of the selected variables with temperature from 30 ℃ to 80 ℃. It was found that the variation of the spectral variables related to both α-helix and β-sheetchanges apparently around 60 ℃, indicating the beginning of the thermal denaturation and the transition from α-helix to β-sheet. Moreover, an obvious change was found around 60 ℃ for the content of the water specie S₃, i.e., the water cluster containing three hydrogen bonds. The result demonstrates that MC-UVE can identify the protein-related NIR spectral variables, and the water species may be a marker for investigation of the structural change of proteins in biochemical systems.     

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。     

连续小波变换-独立成分回归算法及其在多组分分析中的应用

采用连续小波变换（CWT）对光谱数据进行处理，用独立成分分析（ICA）进行特征提取，再用回归分析方法对被测组分进行测定，建立了连续小波变换一独立成分回归（CWT-ICR）方法。方法用于肉样品中水分、脂肪和蛋白质多组分的同时测定，所得结果与化学法测得结果相符。     

近红外漫反射光谱的小波变换滤波

利用小波变换对５２个烟草样品的近红外漫反射光谱进行滤波处理，并用ＰＬＳ法来计算烟草样品的总氮含量，结果表明小波变换滤波后，预测集的相对标准偏差由原来的９．２％降为７．４％，此结果也优于傅里叶变换和五点三次平滑。     

A consensus least squares support vector regression (LS-SVR) for analysis of near-infrared spectra of plant samples

Consensus modeling of combining the results of multiple independent models to produce a single prediction avoids the instability of single model. Based on the principle of consensus modeling, a consensus least squares support vector regression (LS-SVR) method for calibrating the near-infrared (NIR) spectra was proposed. In the proposed approach, NIR spectra of plant samples were firstly preprocessed using discrete wavelet transform (DWT) for filtering the spectral background and noise, then, consensus LS-SVR technique was used for building the calibration model. With an optimization of the parameters involved in the modeling, a satisfied model was achieved for predicting the content of reducing sugar in plant samples. The predicted results show that consensus LS-SVR model is more robust and reliable than the conventional partial least squares (PLS) and LS-SVR methods.     

Application of the wavelet method for the simultaneous quantitative determination of benazepril and hydrochlorothiazide in their mixtures

The discrete and continuous wavelet transforms were applied to the overlapping signal analysis of the ratio data signal for simultaneous quantitative determination of the title subject compounds in samples. The ratio spectra data of the binary mixtures containing benazepril (BE) and hydrochlorothiazide (HCT) were transferred as data vectors into the wavelet domain. Signal compression, followed by a 1-dimension continuous wavelet transform (CWT), was used to obtain coincident transformed signals for pure BE and HCT and their mixtures. The coincident transformed amplitudes corresponding to both maximum and minimum points allowed construction of calibration graphs for each compound in the binary mixture. The validity of CWT calibrations was tested by analyzing synthetic mixtures of the investigated compounds, and successful results were obtained. All calculations were performed within EXCEL, C++, and MATLAB6.5 softwares. The obtained results indicated that our approach was flexible and applicable for the binary mixture analysis.     

A method for near-infrared spectral calibration of complex plant samples with wavelet transform and elimination of uninformative variables

An algorithm is proposed for extracting relevant information from near-infrared (NIR) spectra for multivariate calibration of routine components in complex plant samples. The algorithm is a combination of wavelet transform (WT) data compression and a procedure for uninformative variable elimination (UVE). After compression of the NIR spectra by WT, the UVE approach is used to eliminate the irrelevant wavelet coefficients. Finally, a calibration model is built from the retained wavelet coefficients to enable prediction. Because irrelevant information can be removed from the spectra used for multivariate calibration, the model based on the extracted relevant features is better than those obtained with full-spectrum data. Both prediction precision and calculation speed are improved.     

Approximate derivative calculated by using continuous wavelet transform

A novel method of calculating approximate derivative of signals in analytical chemistry by using the continuous wavelet transform (CWT) is proposed. As compared with numerical differentiation, FT method and DWT method, fast calculation, and simple mathematical operation are remarkable advantages of CWT method. The signal-to-noise ratio (SNR) of approximate derivative of signals calculated by CWT method is easily enhanced only through appropriately adjusting the dilation, even in the case of very low SNR. Therefore, CWT method is a powerful tool for performing the approximate derivative calculation of signals in analytical chemistry. Additionally, the approximate second derivative evaluated via CWT method can be used to determine the peak potentials of the overlapping square wave voltammogram (SWV) of Cd(II) and In(III), and the results are very satisfactory.     

Application of wavelet transform to background correction in inductively coupled plasma atomic emission spectrometry

A background correction method based on wavelet transform was devised and applied to inductively coupled plasma atomic emission spectrometry (ICP-AES). The proposed approach separated background from analyte signal according to their different frequencies. Compared with the analyte signal, the background has a low frequency. By removal of the components attributed to the signal, the background over the spectral window of the analyte line can be fitted through wavelet reconstruction. The results showed that the wavelet transform technique could handle all kinds of background and low signal-to-background ratio spectra, and required no prior knowledge about the sample composition, no selection of suitable background correction points, and no mathematical assumption of the background distribution. This technique performed as well as the conventional three-point background correction method for linear backgrounds, and provided better results than the latter for curved backgrounds. The proposed procedure was illustrated, by processing real spectra, to be an effective and practical tool for background correction in ICP-AES.     

Simultaneous spectrophotometric determination of metformin hydrochloride and glibenclamide in binary mixtures using combined discrete and continuous wavelet transforms

In this work, a combined discrete and continuous wavelet transform analysis was developed for simultaneous spectrophotometric determinations of metformin hydrochloride and glibenclamide, two antidiabetic drugs, in binary mixtures without any chemical pretreatment. Absorption spectra were subjected to the 4-level db4 discrete wavelet transform (DWT) for signal de-noising. Selected continuous wavelet transform (CWT) families (rbio3.1 with scaling factor, a = 80, and gaus2, a = 60) were applied on these de-noised signals. Finally, a zero-crossing technique was used for the construction of calibration curves for both drugs. The proposed method was validated by analyzing synthetic mixtures of the investigated drugs with various concentrations. The amount of metformin hydrochloride and glibenclamide were determined by using CWT amplitudes in zero-crossing points. The mean recovery values of metformin hydrochloride and glibenclamide were found between 98.6-102.0 and 97.9-102.4% for rbio3 and 98.3-101.2 and 97.1-101.4% for gaus2 families, respectively. The obtained results showed that the developed method is a simple, rapid and precise procedure for the simultaneous determination of metformin hydrochloride and glibenclamide in binary mixtures.     

A novel method to calculate the approximate derivative photoacoustic spectrum using continuous wavelet transform

A novel method based on continuous wavelet transform (CWT) using Haar wavelet function for approximate derivative calculation of analytical signals is proposed and successfully used in processing the photoacoustic signal. An approximate nth derivative of an analytical signal can be obtained by applying n times of the wavelet transform to the signal. The results obtained from four other different methods--the conventional numerical differentiation, the Fourier transform method, the Savitzky-Golay method, and the discrete wavelet transform (DWT) method--were compared with the proposed CWT method; it was demonstrated that all the results are almost the same for signals without noise, but the proposed CWT method is superior to the former four methods for noisy signals. The approximate first and second derivative of the photoacoustic spectrum of Pr(Gly)3Cl3.3H2O and PrCl3.6H2O were obtained using the proposed CWT method; the results are satisfactory.     

应用连续小波变换预测蛋白质的二级结构

将代码为lgca蛋白质的氨基酸序列映射为疏水值序列，在合适的尺度下，通过 连续小波变换法分别对其α螺旋,α螺旋和β折叠之间的连接多肽(即部分规则和无 规则二级结构)进行预测，准确率分别为76．5％和85．7％．从PDBsum数据库中随 机抽取100个蛋白质作为测试对象，其中全α螺旋、全β折叠、α／β以及α+β蛋 白质各25个．在100个蛋白质中共有1618个连接多肽和747个α螺旋.本法预测到的 连接多肽共有1536个，其中1308个与实际结构一致，平均预测准确率为85.2％；预 测到的α螺旋有770个，其中581个与实际结构一致，平均预测准确率为75．5％． 结果表明：该法可较好地预测蛋白质的α螺旋、连接多肽，具有极大的发展前景．     

Radial basis function network calibration model for near-infrared spectra in wavelet domain using a genetic algorithm

Near-infrared (NIR) spectrometry is now widely used in various fields and great attention is paid to the application of it to addressing complex problems, which brings about the need for the calibration of systems that fail to exhibit satisfactional linear relationship between input-output data. In this work we present a novel method to build a multivariate calibration model for NIR spectra, i.e. genetic algorithm-radial basis function network in wavelet domain (WT-GA-RBFN), which combines the advantages of wavelet transform and genetic algorithm. The variable selection is accomplished in two stages in wavelet domain: at the first stage, the variables are pre-selected (compressed) by variance and at the second stage the variables are further reduced by a special designed GA. The proposed method is illustrated through presenting its application to three NIR data sets in different fields and the comparison to PLS model.