Multivariate calibration of near infrared spectra by orthogonal WAVElet correction using a genetic algorithm

Orthogonal WAVElet correction (OWAVEC) is a pre-processing method aimed at simultaneously accomplishing two essential needs in multivariate calibration, signal correction and data compression, by combining the application of an orthogonal signal correction algorithm to remove information unrelated to a certain response with the great potential that wavelet analysis has shown for signal processing. In the previous version of the OWAVEC method, once the wavelet coefficients matrix had been computed from NIR spectra and deflated from irrelevant information in the orthogonalization step, effective data compression was achieved by selecting those largest correlation/variance wavelet coefficients serving as the basis for the development of a reliable regression model. This paper presents an evolution of the OWAVEC method, maintaining the first two stages in its application procedure (wavelet signal decomposition and direct orthogonalization) intact but incorporating genetic algorithms as a wavelet coefficients selection method to perform data compression and to improve the quality of the regression models developed later. Several specific applications dealing with diverse NIR regression problems are analyzed to evaluate the actual performance of the new OWAVEC method. Results provided by OWAVEC are also compared with those obtained with original data and with other orthogonal signal correction methods.     

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。     

基于小波的恒电量瞬态响应信号的滤波处理

利用小波变换的阈值法对恒电量响应信号进行滤波处理, 同时与传统的时域和频域的滤波方法进行分析比较, 并且讨论了小波变换的分解层数对恒电量响应信号滤波效果的影响. 结果表明, 利用小波变换可以在时域和频域同时对恒电量响应信号取得良好的去噪效果. 这不仅能提高时域曲线拟合的精度, 还大大地提高了恒电量频谱解析的可靠性. 在实际应用中, 小波变换的分解层数取5～7层可以收到满意的效果.     

病态分析体系有偏估计的研究

运用广义岭估计和Ｌｉｕｋｅｊｉａｎ提出的有偏估计，对病态分析体系进行了数值模拟和实际光度测定，结果表明，广义岭估计显优于最小二乘估计，Ｌｉｕｋｅｊｉａｎ法有功效，可和为解析病态分析体系的化学计量学方法。     

Simultaneous kinetic determination of thiocyanate and sulfide using eigenvalue ranking and correlation ranking in principal component-wavelet neural network

In this work, two toxic compound, sulfide and thiocyanate were determined simultaneously using kinetic spectrophotometry. These anions have shown the catalytic effects on the reaction between iodine and azide. Since the system was nonlinear, a nonlinear model, principal component-wavelet neural network (PC-WNN) was used as the multivariate calibration method. The principal component analysis was used to decrease the dimension of the original matrix. In other words, the scores of the PCs, 5, instead of the original variables, 301, were used as the input for the model. Two methods were used to select the most relevant principal components: eigenvalue ranking and correlation ranking. In this work, eigenvalue and correlation ranking methods have shown better results for thiocyanate and sulfide, respectively, and it can be concluded that these methods are complementary. The WNN has several advantages relative to other types of neural network such as better convergence ability. The data set was divided to calibration, prediction and validation sets. Each set was selected so that the concentrations of the analytes were approximately covered the entire ranges of the analytes. Mean relative error for thiocyanate and sulfide in validation set were 8.5 and 10.6, respectively. Thiocyanate and sulfide can be determined in the range of 60–700 ng ml⁻¹ and 20–400 ng ml⁻¹, respectively. The proposed method was applied for the determination of sulfide and thiocyanate in real samples such as tap, waste and river waters with satisfactory results.     

小波变换用于高效液相色谱的基线校正

本文根据小波变换将信号分频的性质，用Ｄａｕｂｅｃｈｉｅｓ小波成功地解决了高效液相色谱中基线校正问题，用于定量分析乳酸－稀土络合物体系中的十六个稀土元素，所得结果与仪器给出了结果进行比较，准确度提高，重现性良好。     

A Background and noise elimination method for quantitative calibration of near infrared spectra

A new hybrid algorithm is proposed to eliminate the varying background and noise simultaneously for multivariate calibration of near infrared (NIR) spectral signals. The method is based on the use of multi-resolution, which is one of the main advantages provided by wavelet transform. The signals are firstly split into different frequency components, which keep the same data points of the original signals. In conjunction with a modified uninformative variable elimination (mUVE) criterion, the new method can be used to remove the low-frequency varying background and the high-frequency noise simultaneously. The method is successfully applied to simulated spectral data set and experimental NIR spectral data, resulting in more parsimonious multivariate models with higher precision. In addition, the proposed strategy can be applied to other spectral signals as well.     

Review of wavelet methods for the solution of reaction–diffusion problems in science and engineering

Wavelet method is a recently developed tool in applied mathematics. Investigation of various wavelet methods, for its capability of analyzing various dynamic phenomena through waves gained more and more attention in engineering research. Starting from ‘offering good solution to differential equations’ to capturing the nonlinearity in the data distribution, wavelets are used as appropriate tools at various places to provide good mathematical model for scientific phenomena, which are usually modeled through linear or nonlinear differential equations. Review shows that the wavelet method is efficient and powerful in solving wide class of linear and nonlinear reaction–diffusion equations. This review intends to provide the great utility of wavelets to science and engineering problems which owes its origin to 1919. Also, future scope and directions involved in developing wavelet algorithm for solving reaction–diffusion equations are addressed.     

Construction of Multivariate Tight Framelet Packets Associated with Dilation Matrix

In this paper, we present a method for constructing multivariate tight framelet packets associated with an arbitrary dilation matrix using unitary extension principles.We also prove how to construct various tight frames for L2(Rd) by replac-ing some mother framelets.