Adaptive wavelet transform suppresses background and noise for quantitative analysis by Raman spectrometry

Discrete wavelet transform (DWT) provides a well-established means for spectral denoising and baseline elimination to enhance resolution and improve the performance of calibration and classification models. However, the limitation of a fixed filter bank can prevent the optimal application of conventional DWT for the multiresolution analysis of spectra of arbitrarily varying noise and background. This paper presents a novel methodology based on an improved, second-generation adaptive wavelet transform (AWT) algorithm. This AWT methodology uses a spectrally adapted lifting scheme to generate an infinite basis of wavelet filters from a single conventional wavelet, and then finds the optimal one. Such pretreatment combined with a multivariate calibration approach such as partial least squares can greatly enhance the utility of Raman spectroscopy for quantitative analysis. The present work demonstrates this methodology using two dispersive Raman spectral data sets, incorporating lactic acid and melamine in pure water and in milk solutions. The results indicate that AWT can separate spectral background and noise from signals of interest more efficiently than conventional DWT, thus improving the effectiveness of Raman spectroscopy for quantitative analysis and classification.     

Discrete wavelets transform for signal denoising in capillary electrophoresis with electrochemiluminescence detection

Discrete wavelets transform (DWT) was applied to noise on removal capillary electrophoresis-electrochemiluminescence (CE-ECL) electropherograms. Several typical wavelet transforms, including Haar, Daublets, Coiflets, and Symmlets, were evaluated. Four types of determining threshold methods, fixed form threshold, rigorous Stein's unbiased estimate of risk (rigorous SURE), heuristic SURE and minimax, combined with hard and soft thresholding methods were compared. The denoising study on synthetic signals showed that wave Symmlet 4 with a level decomposition of 5 and the thresholding method of heuristic SURE-hard provide the optimum denoising strategy. Using this strategy, the noise on CE-ECL electropherograms could be removed adequately. Compared with the Savitzky-Golay and Fourier transform denoising methods, DWT is an efficient method for noise removal with a better preservation of the shape of peaks.     

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.     

Analyzing functional similarity of protein sequences with discrete wavelet transform

This paper applies discrete wavelet transform (DWT) with various protein substitution models to find functional similarity of proteins with low identity. A new metric, 'S' function, based on the DWT is proposed to measure the pair-wise similarity. We also develop a segmentation technique, combined with DWT, to handle long protein sequences. The results are compared with those using the pair-wise alignment and PSI-BLAST.     

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.     

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...     

The Application of Complex Wavelet Transform to Spectral Signals Background Deduction

The accuracy of spectrograms may be affected by baseline excursion or drift when infrared spectrometers are used in the analyses of gases. Background deduction or baseline correction is one of the effective pretreatment methods that can improve measurement accuracy. This paper presents a novel methodology based on complex wavelet transform algorithm to perform background deduction. The complex wavelet transform methodology establishes a complex wavelet filter to decompose the spectral signals first, and set the decomposition coefficients in the high-frequency section to zero, and then reconstruct the background signals; finally, the background deduction can be realized by deducting the background signals. In this study, the complex wavelet established by Daubechies was selected to demonstrate background deduction aiming at simulative spectral signals with different backgrounds and the real spectral signal of SF6 decomposition gases. Compared with the results done by the real wavelet transform in the same conditions, the results indicate that complex wavelet transform methodology can perform background deduction more efficiently than real wavelet transform methodology, thus improving the effectiveness and precision of spectrogram measurements greatly, which is useful for SF6 gas decomposition compositions analysis

     

The Application of Complex Wavelet Transform to Spectral Signals Background Deduction

The accuracy of spectrograms may be affected by baseline excursion or drift when infrared spectrometers are used in the analyses of gases. Background deduction or baseline correction is one of the effective pretreatment methods that can improve measurement accuracy. This paper presents a novel methodology based on complex wavelet transform algorithm to perform background deduction. The complex wavelet transform methodology establishes a complex wavelet filter to decompose the spectral signals first, and set the decomposition coefficients in the high-frequency section to zero, and then reconstruct the background signals; finally, the background deduction can be realized by deducting the background signals. In this study, the complex wavelet established by Daubechies was selected to demonstrate background deduction aiming at simulative spectral signals with different backgrounds and the real spectral signal of SF6 decomposition gases. Compared with the results done by the real wavelet transform in the same conditions, the results indicate that complex wavelet transform methodology can perform background deduction more efficiently than real wavelet transform methodology, thus improving the effectiveness and precision of spectrogram measurements greatly, which is useful for SF6 gas decomposition compositions analysis     

微流控电泳芯片中化学发光信号的分段门限小波降噪

采用分段门限小波降噪(STWD)方法对化学信号中的异方差噪声进行降噪处理.用STWD法和统一门限小波降噪法同时处理两种模拟信号(其中之一包含异方差噪声).结果显示,优化参数的STWD法能够更有效地提高降噪效果.采用STWD法对微流控芯片化学发光检测信号中的异方差噪声进行处理,取得了满意的降噪效果.     

Simultaneous quantitative analysis of overlapping spectrophotometric signals using wavelet multiresolution analysis and partial least squares

The mathematical bases and program algorithms of discrete wavelet transform (DWT), multiresolution and Mallat’s pyramid algorithm were described. The multiresolution analysis (MRA) based on Daubechies orthogonal wavelet basis was studied as a tool for removing noise and irrelevant information from spectrophotometric spectra. After wavelet MRA pre-treatment, eight error functions were calculated for deducing the number of factors. A partial least squares based on wavelet MRA (WPLS) method was developed to perform simultaneous spectrophotometric determination of Fe(II) and Fe(III) with overlapping peaks. Data reduction was performed using wavelet MRA and principal component analysis (PCA) algorithm. Two programs, SPWMRA and SPWPLS, were designed to perform wavelet MRA and simultaneous multicomponent determination. Experimental results showed the WPLS method to be successful even where there was severe overlap of spectra.     

Quantitative analysis of NO2 in the presence of CO using a single tungsten oxide semiconductor sensor and dynamic signal processing

We demonstrate that NO2 can be quantitatively analysed in the presence of CO using a single tungsten oxide based resistive gas sensor. The working temperature of the sensor was modulated between 190 and 380 degrees C and its dynamic response to different concentrations of CO, NO2, and CO + NO2 mixtures was monitored. Either the fast Fourier transform (FFT) or the discrete wavelet transform (DWT) was used to extract important features from the sensor response. These features were then input to different (statistical and neural) pattern recognition methods. The species considered can be discriminated with a success rate higher than 90% using a Fuzzy ARTMAP or a radial basis function neural network. The concentrations of the gases studied can be accurately predicted, by using the DWT coupled to partial least squares (PLS) models. The correlation coefficients of the predicted versus real concentrations were 0.923, 0.870 and 0.866 for CO, NO2, and NO2 in CO + NO2 mixtures, respectively.     

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.     

Identification of epilepsy from intracranial EEG signals by using different neural network models

In this work, a framework is provided for identifying intracranial electroencephalography (iEEG) seizures based on discrete wavelet transform (DWT) analysis of iEEG signals using forward propagation and feedback neural networks. The performance of 5 different data sets combination classifications is studied using the probabilistic neural network (PNN), learning vector quantization neural network (LVQ) and Elman neural network (ENN). Different feature combinations serve as the input vectors of the classifiers to obtain the best outcomes. It has been found that PNN has less running time and provides better classification accuracy (CA) than ENN and LVQ classifiers for all 5 classification problems. It is worth noticing that the CA for the C-D classification task, which shows the status of pre-ictal versus post-ictal, has been greatly improved, and reached 83.13%. Hence, the epilepsy iEEG signals pattern recognition based on DWT statistical features using the PNN classifier is more suitable for forming a reliable, automatic classification system in order to assist doctors in diagnosis.     

A partial least squares and wavelet-transform hybrid model to analyze carbon content in coal using laser-induced breakdown spectroscopy

A partial least squares (PLS) and wavelet transform hybrid model are proposed to analyze the carbon content of coal by using laser-induced breakdown spectroscopy (LIBS). The hybrid model is composed of two steps of wavelet analysis procedures, which include environmental denoising and background noise reduction, to pretreat the LIBS spectrum. The processed wavelet coefficients, which contain the discrete line information of the spectra, were taken as inputs for the PLS model for calibration and prediction of carbon element. A higher signal-to-noise ratio of carbon line was obtained after environmental denoising, and the best decomposition level was determined after background noise reduction. The hybrid model resulted in a significant improvement over the conventional PLS method under different ambient environments, which include air, argon, and helium. The average relative error of carbon decreased from 2.74 to 1.67% under an ambient helium environment, which indicated a significantly improved accuracy in the measurement of carbon in coal. The best results obtained under an ambient helium environment could be partly attributed to the smallest interference by noise after wavelet denoising. A similar improvement was observed in ambient air and argon environments, thereby proving the applicability of the hybrid model under different experimental conditions.     

Wavelet transform applications in analytical chemistry

The wavelet transform has been established with the Fourier transform as a data-processing method in analytical chemistry. The main fields of application in analytical chemistry are related to denoising, compression, variable reduction, and signal suppression. Analytical applications were selected showing prospects and limitations of the wavelet transform. An important aspect consists in showing the advantage of wavelet transform over Fourier transform with respect to dual localization of a signal in both the original and the transformed domain enabling principal new application fields in comparison with Fourier transform.     

Near-infrared spectroscopy and chemometric modelling for rapid diagnosis of kidney disease

Rapid diagnosis is important for efficient treatment in clinical medicine. This study aimed at development of a method for rapid and reliable diagnosis using near-infrared (NIR) spectra of human serum samples with the help of chemometric modelling. The NIR spectra of sera from 48 healthy individuals and 16 patients with suspected kidney disease were analyzed. Discrete wavelet transform (DWT) and variable selection were adopted to extract the useful information from the spectra. Principal component analysis (PCA), linear discriminant analysis (LDA) and partial least squares discriminant analysis (PLSDA) were used for discrimination of the samples. Classification of the two-class sera was obtained using LDA and PLSDA with the help of DWT and variable selection. DWT-LDA produced 93.8% and 83.3% of the recognition rates for the validation samples of the two classes, and 100% recognition rates were obtained using DWT-PLSDA. The results demonstrated that the tiny differences between the spectra of the sera were effectively explored using DWT and variable selection, and the differences can be used for discrimination of the sera from healthy and possible patients. NIR spectroscopy and chemometrics may be a potential technique for fast diagnosis of kidney disease.     

离散小波变换-支持向量回归方法同时测定苯酚、苯胺和苯甲酸

在波长范围200～400nm测定苯酚、苯胺和苯甲酸混合液的吸收光谱,用离散小波变换（DWT）对光谱数据进行处理,再用支持向量回归SVR方法进行建模,建立了离散小波变换一支持向量回归方法（DWT—SVR）。方法用于模拟样品和污染水样中苯酚、苯胺和苯甲酸的同时测定,结果满意。     

Sequence Hiberarchy Evolution Measurement Method and its Application

A novel method based on discrete wavelet transform （DWT） and cross-covariance for revealing the evolution of species at different spatial resolutions is presented. The trypsin proteins of different species are chosen as an example to describe the evolution relationship according to the evolution vectors by using this method. The results indicated that this method is a promising approach to reveal species evolution at different spatial resolutions.     

Adaptive approach for variable noise suppression on laser-induced breakdown spectroscopy responses using stationary wavelet transform

Spectral signals are often corrupted by noise during their acquisition and transmission. Signal processing refers to a variety of operations that can be carried out on measurements in order to enhance the quality of information. In this sense, signal denoising is used to reduce noise distortions while keeping alterations of the important signal features to a minimum. The minimization of noise is a highly critical task since, in many cases, there is no prior knowledge of the signal or of the noise. In the context of denoising, wavelet transformation has become a valuable tool. The present paper proposes a noise reduction technique for suppressing noise in laser-induced breakdown spectroscopy (LIBS) signals using wavelet transform. An extension of the Donoho's scheme, which uses a redundant form of wavelet transformation and an adaptive threshold estimation method, is suggested. Capabilities and results achieved on denoising processes of artificial signals and actual spectroscopic data, both corrupted by noise with changing intensities, are presented. In order to better consolidate the gains so far achieved by the proposed strategy, a comparison with alternative approaches, as well as with traditional techniques, is also made.     

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· 3 H₂O and PrCl₃· 6 H₂O were obtained using the proposed CWT method; the results are satisfactory. Received: 21 December 1999 / Revised: 28 February 2000 / Accepted: 7 March 2000