一种基于二进小波变换的自适应滤波方法

根据信号和噪声经小波变换后在不同尺度上有不同的特征，将相邻尺度二进小波变换值的相关量进行归一化处理并与小波变换值比较来判断信号与噪声，以噪声在各尺度的方差作为终止迭代的标准，提出了一种基于二进小波变换小波域选择噪声的自适应滤波方法。研究了模拟信号的去噪过程、半峰宽和信噪比对去噪结果的影响，并对模拟含噪信号和含噪毛细管电泳信号去噪前后的结果进行了比较。实验结果表明：由于该方法具有良好的自适应性和显著的滤波效果，必将得到广泛的应用。     

基于小波理论的化学谱图数据自适应滤波方法研究

运用小波理论,利用噪声与真实信号小波变换极大模性态之间的显著差异,提出了一类新的化学谱图数据自适应滤波算法,从根本上突破了现有算法均依据信噪频率特性进行滤波的传统模式.经大量色谱谱图数据处理试验证明,这种算法具有无需设置初始参数,消除人为误差因素对分析计算结果的影响,信噪分离性能好及峰位和峰高保持不变等一系列优点,其鲁棒性、自适应性和谱峰保真度完全符合仪器分析信号处理的要求.     

二进小波变换极大模法用于分析化学信号的滤噪

实验数据的滤噪在分析化学领域中具有重要的意义。小波变换技术具有很强的信号分离能力，容易把随机噪声从信号中分离出来，从而提高信号的信噪比。本文使用滤噪方法不同于传统离散小波变换方法，而是通过引入二进小波变换和李氏指数的概念，根据噪声与有用信号的极大模截然不同的特征，实现信号滤噪。实验数据的仿真结果研究也证明该方法的可行性。     

利用二进样条小波模极大方法消除毛细管电泳信号噪声的研究

根据毛细管电泳信号中噪声与真实信号的模极大值特性之间存在较大差异的特点，提出了一种利用二进样条小波模极大值法去噪的方法研究了信号的半峰宽、不同信噪比以及阈值的选取对去噪结果的影响，并对模拟含噪信号和含噪毛经电泳信号去噪前后的结果进行了比较，实验结果表明，该法能效地消除谱带较宽的毛细管电泳等信号中存在的噪声。     

小波系数区域相关阈值滤噪方法研究

报道了一种基于小波分析的新的滤噪方法小波系数区域相关阈值滤噪法的基本原理 ,并将其用于模拟信号与含噪色谱信号的滤噪研究。系统的描述了该方法的滤噪过程 ,讨论了相关运算区域大小、软硬阈值法、信号的频率、信噪比对滤噪结果的影响。对高效液相色谱信号的滤噪结果表明 ,该方法在保留信号的特征信息的同时能够有效地滤除信号中的噪音     

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。     

分析化学信号在多尺度空间的滤噪

从多分辨率分析出发，结合离散正交小波变换(DWT)的理论，通过对各尺度下未抽取前的小波系数进行非线性滤波处理，达到在保护信号边缘的同时，有效实现白噪声及脉冲噪声的滤除。实验数据仿真结果研究也证明了该方法的可行性。     

毛细管电泳激光诱导荧光检测信号的小波滤噪

采用小波滤噪方法对毛细管电泳激光诱导荧光检测信号进行了处理，研究了小波变换中小波基的选择及噪声阈值的选择对滤噪的影响。结果表明，采用DB4小波基能有效消除毛细管电泳激光诱导荧光检测信号中存在的噪声，使信噪比得到较大改善。     

利用小波变换检测电化学噪声信号波形

简述了应用小波变换检测点蚀电化学噪声信号的基本原理,对在3.5％ NaCl溶液中工业纯铝发生点蚀的电化学噪声信号检测分析表明：小波变换能够提取发生点蚀的电化学噪声信号和测量系统噪声在多惊讶分辨空间中的波形特征,根据表征该特征的小波系数模极大值在不同尺度下的传播特性,可实现对点蚀电化学噪声信号波形的检测。     

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。     

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.     

毛细管电脉在柱安培检测信号的小波滤噪研究

采用一种新的小波滤噪方法对毛细管电泳在柱安培检测信号进行了处理,研究了小波基的选择、噪音在不同细节中的特征以及噪音阈值的确定等,用此方法对酚类定量分析,结果信噪比、检测限和线性范围均有较大改善。     

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.     

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.     

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.     

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.     

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。