Spatially adaptive stationary wavelet thresholding for the denoising of DNA capillary electrophoresis signal

The spatially adaptive thresholding based on the stationary wavelet transform was applied to the noise removal in the signal of DNA separated and determined by capillary electrophoresis. The threshold is derived in a Bayesian framework, and previously used on the wavelet coefficients is the generalized Gaussian distribution. The threshold is simple and closed form, which is adaptive to each subband because it depends on data-driven estimates of the parameters. Using this strategy, the noise in the signal of the DNA-separated analysis by capillary electrophoresis could be removed adequately. Experimental results show that the proposed denoising method is effective, and the spatially adaptive thresholding yields a lower root-mean-square error than the universal thresholding. The text was submitted by the authors in English.     

Signal denoising and baseline correction by discrete wavelet transform for microchip capillary electrophoresis

Signal denoising and baseline correction using discrete wavelet transform (DWT) are described for microchip capillary electrophoresis (MCE). DWT was performed on an electropherogram describing a separation of nine tetramethylrohodamine-5-isothiocyanate labeled amino acids, following MCE with laser-induced fluorescence detection, using Daubechies 5 wavelet at a decomposition level of 6. The denoising efficiency was compared with, and proved to be superior to, other commonly used denoising techniques such as Fourier transform, Savitzky-Golay smoothing and moving average, in terms of noise removal and peak preservation by directly visual inspection. Novel strategies for baseline correction were proposed, with a special interest in baseline drift that frequently occurred in chromatographic and electrophoretic separations.     

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.     

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.     

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.     

Sub-optimal wavelet denoising of coaveraged spectra employing statistics from individual scans

This paper proposes a novel wavelet denoising method, which exploits the statistics of individual scans acquired in the course of a coaveraging process. The proposed method consists of shrinking the wavelet coefficients of the noisy signal by a factor that minimizes the expected square error with respect to the true signal. Since the true signal is not known, a sub-optimal estimate of the shrinking factor is calculated by using the sample statistics of the acquired scans. It is shown that such an estimate can be generated as the limit value of a recursive formulation. In a simulated example, the performance of the proposed method is seen to be equivalent to the best choice between hard and soft thresholding for different signal-to-noise ratios. Such a conclusion is also supported by an experimental investigation involving near-infrared (NIR) scans of a diesel sample. It is worth emphasizing that this experimental example concerns the removal of actual instrumental noise, in contrast to other case studies in the denoising literature, which usually present simulations with artificial noise. The simulated and experimental cases indicate that, in classic denoising based on wavelet coefficient thresholding, choosing between the hard and soft options is not straightforward and may lead to considerably different outcomes. By resorting to the proposed method, the analyst is not required to make such a critical decision in order to achieve appropriate results.     

Simultaneous multicomponent analysis of overlapping spectrophotometric signals using a wavelet-based latent variable regression

A wavelet-based latent variable regression (WLVR) method was developed to perform simultaneous quantitative analysis of overlapping spectrophotometric signals. The quality of the noise removal was improved by combining wavelet thresholding with principal component analysis (PCA). A method for selecting the optimum threshold was also developed. Eight error functions were calculated for deducing the number of factor. The latent variables were made by projecting the wavelet-processed signals onto orthogonal basis eigenvectors. Two-programs WMRA and WLVR, were designed to perform wavelet thresholding and simultaneous multicomponent determination. Experimental results showed the WLVR method to be successful even where there was severe overlap of spectra.     

小波滤噪用于示波计时电位信号处理的研究

根据信号（Ｓ）和噪声（Ｎ）在小波变换下表现出的截然不同的性质,提出了一种新的滤噪方法,研究了噪音在不同细节的性质、滤噪阈值的确定及平滑与滤噪的特点。对不同Ｓ／Ｎ的示波计时电位信号进行了实验结果表明;小波滤噪在大大提高Ｓ／Ｎ的同时,信号强度基本不损失,优于传统的滤噪方法。     

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.     

Suppressing the charged coupled device noise in univariate thin-layer videoscans: A comparison of several algorithms

The digital processing of chromatographic thin-layer plate images has increasing popularity among last years. When using a camera instead of flatbed scanner, the charged coupled device (CCD) noise is a well-known problem—especially when scanning dark plates with weakly fluorescing spots. Various techniques are proposed to denoise (smooth) univariate signals in chemometric processing, but the choice could be difficult. In the current paper the classical filters (Savitzky–Golay, adaptive degree polynomial filter, Fourier denoising, Butterworth and Chebyshev infinite impulse response filters) were compared with the wavelet shrinkage (31 mother wavelets, 3 thresholding techniques and 8 decomposition levels). The signal obtained from 256 averaged videoscans was treated as the reference signal (with noise naturally suppressed, which was found to be almost white one). The best choice for denoising was the Haar mother wavelet with soft denoising and any decomposition level larger than 1. Satisfying similarity to reference signal was also observed in the case of Butterworth filter, Savitzky–Golay smoothing, ADPF filter, Fourier denoising and soft-thresholded wavelet shrinkage with any mother wavelet and middle to high decomposition level. The Chebyshev filters, Whittaker smoother and wavelet shrinkage with hard thresholding were found to be less efficient. The results obtained can be used as general recommendations for univariate denoising of such signals.     

Data processing in metabolic fingerprinting by CE-UV: application to urine samples from autistic children

Metabolic fingerprinting of biofluids such as urine can be used to detect and analyse differences between individuals. However, before pattern recognition methods can be utilised for classification, preprocessing techniques for the denoising, baseline removal, normalisation and alignment of electropherograms must be applied. Here a MEKC method using diode array detection has been used for high-resolution separation of both charged and neutral metabolites. Novel and generic algorithms have been developed for use prior to multivariate data analysis. Alignment is achieved by combining the use of reference peaks with a method that uses information from multiple wavelengths to align electropherograms to a reference signal. This metabolic fingerprinting approach by MEKC has been applied for the first time to urine samples from autistic and control children in a nontargeted and unbiased search for markers for autism. Although no biomarkers for autism could be determined using MEKC data here, the general approach presented could also be applied to the processing of other data collected by CE with UV-Vis detection.     

Improving AFM images with harmonic interference by spectral analysis

Atomic force microscopy (AFM) is one of the most sensitive tools for nanoscale imaging. As such, it is very sensitive to external noise sources that can affect the quality of collected data. The intensity of the disturbance depends on the noise source and the mode of operation. In some cases, the internal noise from commercial AFM controllers can be significant and difficult to remove. Thus, a new method based on spectrum analysis of the scanned images is proposed to reduce harmonic disturbances. The proposal is a post-processing method and can be applied at any time after measurements. This article includes a few methods of harmonic cancellation (e.g., median filtering, wavelet denoising, Savitzky-Golay smoothing) and compares their effectiveness. The proposed method, based on Fourier transform of the scanned images, was more productive than the other methods mentioned before. The presented data were achieved for images of conductive layers taken in a contact AFM mode.     

Application of wavelet transforms and an approximate deconvolution method for the resolution of noisy overlapped peaks in DNA capillary electrophoresis

A new procedure for resolving noisy overlapped peaks in DNA separations by capillary electrophoresis (CE) is developed. The procedure combines both a wavelet-based denoising method that effectively denoises the signal and a novel approximate deconvolution technique that resolves the fragment peaks and improves the ability to separate highly overlapped peaks early in the electrophoresis process. Different kinds of overlapped peaks with and without noise simulated by computer as well as some DNA experimental electropherograms were submitted to the new procedure. A second order differential operator with variable coefficients is applied to the entire electrophoresis signal at any given time and approximate deconvolutions of the individual Gaussian peaks are performed. The operator incorporates the effect of the superposition and gives exact annihilation in the neighborhood of each peak. Overlapped peaks with a resolution higher than 0.46 can be resolved directly. Also, the method can determine the peak components of signals with a signal to noise ratio higher than 1.4     

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     

Noise filtering and deconvolution of XPS data by wavelets and Fourier transform

In experimental sciences, the recorded data are often modelled as the noisy convolution product of an instrumental response with the ‘true’ signal to find. Different models have been used for interpreting x‐ray photoelectron spectroscopy (XPS) spectra. This article suggests a method of estimate the ‘true’ XPS signal that relies upon the use of wavelets, which, because they exhibit simultaneous time and frequency localization, are well suited to signal analysis. First, a wavelet shrinkage algorithm is used to filter the noise. This is achieved by decomposing the noisy signal into an appropriate wavelet basis and then thresholding the wavelet coefficients that contain noise. This algorithm has a particular threshold related to frequency and time. Secondly, the broadening due to the instrumental response is eliminated through a deconvolution process similar to that developed in the previous paper in this series for the analysis of HREELS data. This step mainly rests on least‐squares and on the existing relation between the Fourier transform, the wavelet transform and the convolution product. Copyright © 2004 John Wiley & Sons, Ltd.     

Capillary electrophoresis with electrochemiluminescence detection: fundamental theory,apparatus, and applications

This review presents a comprehensive survey of recent progress on electrochemiluminescence (ECL) detection coupled with capillary electrophoresis (CE). The fundamental theories involved in CE-ECL, e.g., the mechanism involving both coreactant-based and inhibitor-based ECL, as well as the possible analytes to be detected by CE-ECL are summarized. Different schemes for the construction of CE-ECL apparatus, including methods for preparing the working electrode, approaches for addition of ECL reagents, ways to fabricate electrical decouplers, and factors affecting ECL efficiency are reviewed. Discussion of the literature related to the application of CE-ECL from January 2005 to September 2010 is sorted by the corresponding analyte matrixes, namely, the standard solution, urine, serum and plasma, and other matrixes. Finally, possible trends for CE-ECL in the near future are discussed.     

一种新的小波滤波方法在化学谱图信号滤噪中的应用

仪器分析测定中，噪声的存在往往影响分析的准确度和仪器的检出限。小波变换多分辨分析的特性使得它成为一种很好的滤噪方法。基于小波分解后信号与噪声的小波系数随尺度变化规律不同的特性，提出了一种新的滤波滤方法-空域相关法，即通过不同尺度上相关系数模值与小波系数模模值的比较，达到滤波滤的目的。本文提出的方法具有无需人为选定无需人为选定滤噪阈值和小波函数、方法简单、失真度小等优点，可以大在提高信号的信噪比。模拟数据和ICP-AES实验数据证明了该方法的有效性。     

小波潜变量回归和广义回归神经网络同时测定三组分混合物

本文采用小波潜变量回归（WLVR）方法，同时测定重叠的光谱信号。结合小波阈值法和主组分分析（PCA）改进除噪质量。八个误差判据用于推断因子数目。潜变量由小波处理过的信号投影到正交基矢量而获得。广义回归神经网络（GRNN）被应用于多组分同时测定。依据算法原理编制了三个程序（PWMRA、PWLVR和PGRNN）执行有关计算。三个方法（WLVR、LVR（潜变量回归）和GRNN）同时测定三组分混合物，获得满意的结果。     

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.