Principles and applications of wavelet transformation to chemometrics

This paper aims at serving two purposes: firstly, it gives a quick summary of aspects and properties of wavelets and wavelet transforms which are needed in order to understand how to (pre-)process data from spectrometry with wavelet methods. Secondly, it shows on a typical example (wheat NIR spectra) how wavelet transforms can be used in order to extract quantitative information. In contrast to other approaches in the literature, we use special types of wavelets which allow analysing finitely extended signals without introducing artifacts near the boundaries, and we introduce a new way of wavelet coefficient regression in order to build our chemometrical models.     

Determination of an acceptable level of spectral data compression by Discrete Wavelet Transforms

Today, due to the ever increasing amount of data generated by analytical instruments, good compression methods are desired to keep computation time acceptable. The lower the volume and noise content of data, the easier it becomes to investigate and interpret the modeling results. Discrete Wavelet Transform (DWT) is an effective data compression and noise suppression tool. Compression can be performed at different levels, in each, the size of signal part of the data reduces to half the size. This work includes an approach for determining an acceptable level of compression of data where the aim is to achieve minimal loss of information and no significant change in the structure of data, which could mean, e.g. no loss in predictive ability or the effective rank of the data-set. The method is based on estimation of the Singular Values (SVs) from a data matrix and the Singular Values at each level of compression followed by the application of Median Absolute Deviation (MAD) of the correlation between original SVs and compression SVs as a simple statistical test for the determination of the optimum level of compression. We illustrate the method using FT-Raman data from aqueous solutions of three sugars (glucose, trehalose and sucrose) and NMR data from mixtures of three alcohols. A sudden change in prediction error sum of square plots from Partial Least Squares (PLS) modeling confirms the results from MAD statistics.     

Solving chemical master equations by adaptive wavelet compression

Solving chemical master equations numerically on a large state space is known to be a difficult problem because the huge number of unknowns is far beyond the capacity of traditional methods. We present an adaptive method which compresses the problem very efficiently by representing the solution in a sparse wavelet basis that is updated in each step. The step-size is chosen adaptively according to estimates of the temporal and spatial approximation errors. Numerical examples demonstrate the reliability of the error estimation and show that the method can solve large problems with bimodal solution profiles.     

利用小波变换对1/f信号进行参数估计

1引言众所周知，l／f过程是一类其平均功率谱具有如下形式：的随机过程，式中，y称为1／f过程的谱参数，现实生活中众多的自然现象如：电器发出的噪声，道琼斯工业平均指数，大海的波涛声等等都是这类过程’“工‘X‘’‘［”．人们构造了各种模型来对1／f过程进行刻划，从最初的ARMA模型［‘倒后来Mandelbrot和VanNess提出的分数布朗运动模型（FBM）［’］．ARMA模型处理起来很复杂，FBM基本上较好地刻划了1／f过程，但对／的某些特殊值所对应的1／f过程却不尽人意．值得一提的是，乙W－Worned于1990年给出刻划1／f过程的小波基模…     

航空飞机计算机通信中滤波器的优化设计

航空飞机计算机通信系统进行通信的过程中,由于航空飞机上的电子设备相互之间的电磁干扰严重,导致信道中存在大量的干扰信号。提出基于小波变换算法的抗干扰滤波器设计方法。根据小波变换算法相关原理,综合航空飞机通信中特有的软阀值特点,利用自适应调整参数的方法得到高空通信中的最优小波系数阀值,使得高空噪声过滤阀值函数具有更强的适应性。利用新的阀值函数设计了新的滤波器,对行滤波模块和列滤波模块的设计进行了详细阐述。实验结果表明。利用设计的滤波器能够对航空飞机计算机通信过程中的干扰信号进行有效滤波,缩短了滤波时间,提高了高空通信系统的抗干扰能力。     

ITO导电薄膜透明图案对比度增强方法

铟锡氧化物(Indium Tin Oxide,ITO)导电层是触控显示技术的绝对定位元件,为保障定位的灵敏性和准确性,需对导电层表面缺陷进行质量检测.本文针对导电层透明区域机器视觉自动检测存在的问题,提出了图案对比度增强的方法.该方法首先利用ITO材料的光谱属性及其表面光学特性,设计出用于ITO导电层检测的近红外同轴光照明,将图像对比度从零提高到4.5%.在通过光学方法实现了对比度从无到有的转变后,充分利用数字图像预处理的优势,结合基于小波变换的非线性增强方法,最终成功将对比度提高至16%,为后续ITO导电层缺陷的分析和识别提供了良好保障.     

Tight Multiwavelet Frames with Different Matrix Dilations and Matrix Translations

The characterization of tight multiwavelet frames with different matrix dilations and matrix translations for L ²(R ^d ) is established. The result contains and further extends the generalizations that have appeared in the literature. Two sufficient conditions for affine frames are also presented.     

Jump point detection for real estate investment success

In the literature, studies on real estate market were mainly concentrating on the relation between property price and some key factors. The trend of the real estate market is a major concern. It is believed that changes in trend are signified by some jump points in the property price series. Identifying such jump points reveals important findings that enable policy-makers to look forward. However, not all jump points are observable from the plot of the series. This paper looks into the trend and introduces a new approach to the framework for real estate investment success.The main purpose of this paper is to detect jump points in the time series of some housing price indices and stock price index in Hong Kong by applying the wavelet analysis. The detected jump points reflect to some significant political issues and economic collapse. Moreover, the relations among properties of different classes and between stocks and properties are examined. It can be shown from the empirical result that a lead-lag effect happened between the prices of large-size property and those of small/medium-size property. However, there is no apparent relation or consistent lead in terms of change point measure between property price and stock price. This may be due to the fact that globalization effect has more impact on the stock price than the property price.     

Combining orthogonal signal correction and wavelet packet transform with partial least squares to analyze overlapping spectra of three kinds of metal ions

A novel method named OSC-WPT-PLS approach based on partial least squares (PLS) regression with orthogonal signal correction (OSC) and wavelet packet transform (WPT) as pre-processed tools was proposed for the simultaneous spectrophotometric determination of Al(III), Mn(II) and Co(II). This method combines the ideas of OSC and WPT with PLS regression for enhancing the ability of extracting characteristic information and the quality of regression. OSC is used to remove information in the response matrix D by subtracting the structured noise that is orthogonal to the concentration matrix C. Wavelet packet transform was applied to perform data compression, to extract relevant information, and to eliminate noise and collinearity. PLS was applied for multivariate calibration and noise reduction by eliminating the less important latent variables. In this case, using trials, the kind of wavelet function, the decomposition level, the number of OSC components and the number of PLS factors for the OSC-WPT-PLS method were selected as Daubechies 4, 3, 2 and 3, respectively. A program (POSCWPTPLS) was designed to perform the simultaneous spectrophotometric determination of Al(III), Mn(II) and Co(II). The relative standard errors of prediction (RSEP) obtained for total elements using OSC-WPT-PLS, WPT-PLS and PLS were compared. Experimental results demonstrated that the OSC-WPT-PLS method had the best performance among the three methods and was successful even when there was severe overlap of spectra.     

Extraction of multiple pure component H and C NMR spectra from two mixtures: Novel solution obtained by sparse component analysis-based blind decomposition

Sparse component analysis (SCA) is demonstrated for blind extraction of three pure component spectra from only two measured mixed spectra in ¹³C and ¹H nuclear magnetic resonance (NMR) spectroscopy. This appears to be the first time to report such results and that is the first novelty of the paper. Presented concept is general and directly applicable to experimental scenarios that possibly would require use of more than two mixtures. However, it is important to emphasize that number of required mixtures is always less than number of components present in these mixtures. The second novelty is formulation of blind NMR spectra decomposition exploiting sparseness of the pure components in the wavelet basis defined by either Morlet or Mexican hat wavelet. This enabled accurate estimation of the concentration matrix and number of pure components by means of data clustering algorithm and pure components spectra by means of linear programming with constraints from both ¹H and ¹³C NMR experimental data. The third novelty is capability of proposed method to estimate number of pure components in demanding underdetermined blind source separation (uBSS) scenario. This is in contrast to majority of the BSS algorithms that assume this information to be known in advance. Presented results are important for the NMR spectroscopy-associated data analysis in pharmaceutical industry, medicine diagnostics and natural products research.