An intelligent background‐correction algorithm for highly fluorescent samples in Raman spectroscopy

Fluorescent background is a major problem in recoding the Raman spectra of many samples, which swamps or obscures the Raman signals. The background should be suppressed in order to perform further qualitative or quantitative analysis of the spectra. For this purpose, an intelligent background‐correction algorithm is developed, which simulates manual background‐correction procedure intelligently. It basically consists of three aspects: (1) accurate peak position detection in the Raman spectrum by continuous wavelet transform (CWT) with the Mexican Hat wavelet as the mother wavelet; (2) peak‐width estimation by signal‐to‐noise ratio (SNR) enhancing derivative calculation based on CWT but with the Haar wavelet as the mother wavelet; and (3) background fitting using penalized least squares with binary masks. This algorithm does not require any preprocessing step for transforming the spectrum into the wavelet space and can suppress the fluorescent background of Raman spectra intelligently and validly. The algorithm is implemented in R language and available as open source software ( http://code.google.com/p/baselinewavelet ). Copyright © 2009 John Wiley & Sons, Ltd.     

乙醇含量拉曼光谱检测中噪声与背景同时消除方法研究

乙醇含量拉曼光谱检测中,拉曼光谱信号中的各种噪声及光谱荧光造成的基线漂移和样品池背景等,影响了校正模型的预测精度。利用总体平均经验模态分解,将光谱信号分解成若干无模态混叠的内在模式分量,根据排列熵的信号随机性检测判据判断出代表背景信息和噪声信息的内在模式分量,将其置零即可同时消除拉曼光谱中的噪声与背景。将总体平均经验模态分解与排列熵相结合的预处理方法应用于乙醇含量的拉曼光谱检测中,并与小波变换和平均平滑滤波做了对比。实验结果表明：应用总体平均经验模态分解与排列熵相结合的方法能够有效的同时消除乙醇含量拉曼光谱检测中的噪声和背景信息,提高校正模型的预测精度,且使用简便,无需参数设置,对乙醇含量拉曼光谱检测具有实用价值。     

基于特征提取的低信噪比拉曼光谱去噪方法研究

为了提高拉曼光谱检测系统的时间分辨率,常常需要采用较短的采样积分时间,此时带有分子结构振动谱的有用拉曼信号可能完全淹没在噪声中,严重影响信号的进一步分析,因此有必要对测量所得的光谱信号进行噪声消除处理。传统的消噪方法是基于信号与噪声在频域或统计特性之间的差异,通过平滑滤波或取平均值的方法来消除噪声,一般适用于噪声强度不高的情况,对于信噪比较低的情况处理效果并不理想。针对传统去噪方法的不足,从信号重构的角度,利用基于小波变换的谱峰识别、半峰宽检测提取光谱特征参数,再利用最小二乘拟合的方法,能够有效地提取淹没于强噪声背景下的有用拉曼信号。在仿真中,运用该算法得到的光谱曲线光滑,峰位置准确,信噪比改善明显。在实验中,分别利用该方法处理头孢呋辛酯片和罗红霉素拉曼光谱数据,得到了清晰的谱峰位置、幅值及半峰宽信息,实现了对短积分时间、强噪声背景的拉曼信号的有效还原,提高了检测系统的时间分辨率。仿真和实验结果表明,该方法需要调整参数少,易于实现,在信噪比比较低的情况下依然能够得到良好的去噪效果,为进一步分析光谱数据提供准确可靠的信息。     

Background removal from polarized Raman spectra of tooth enamel using the wavelet transform

A wavelet transformation method is introduced to remove the large fluorescence background from polarized Raman spectra of stained tooth enamel. This method exploits the wavelet multiresolution decomposition where the experimental Raman spectrum is decomposed into signals with different frequency components, and where the lowest frequency background and highest frequency noise are removed. This method is optimized using a simulated collection of parallel‐polarized and cross‐polarized Raman spectra of the enamel and then applied to a set of experimental data. The results show that the wavelet transform technique can extract the pure spectra from background and noise, with the depolarization ratio used to discriminate between early dental caries and sound enamel preserved. Copyright © 2010 Crown in the right of Canada. Published by John Wiley & Sons, Ltd.     

Range‐independent background subtraction algorithm for recovery of Raman spectra of biological tissue

An important requirement for the use of Raman spectroscopy for tissue diagnostic applications is an appropriate algorithm that can faithfully retrieve weak tissue Raman signals from the measured raw Raman spectra. Although iterative modified polynomial‐fitting‐based automated algorithms are widely used, these are sensitive to the choice of the fitting range, thereby leading to significantly different Raman spectra for different start and stop wavenumber selection. We report here an algorithm for automated recovery of the weak Raman signal, which is range independent. Given a raw Raman spectrum and the choice of the start and the stop wavenumbers, the algorithm first truncates the spectrum to include the raw data within this wavenumber range, linearly extrapolates the truncated raw spectrum beyond the points of truncation on the two sides by using coefficients of linear least‐square fit, adds two Gaussian peaks of appropriate height and width on the extrapolated linear wings on either side and then iteratively smoothens the data with all these add‐ons such that the smaller of the ordinate values of the smoothed and the starting raw data serve as the input to each successive round of iterative smoothing until the added Gaussian peaks are fully recovered. The algorithm was compared with the modified polynomial‐based algorithms using mathematically simulated Raman spectrum as well as experimentally measured Raman spectra from various biological samples and was found to yield consistently range‐independent and artifact‐free Raman signal with zero baseline. Copyright © 2012 John Wiley & Sons, Ltd.     

Quantitative,comparable coherent anti‐Stokes Raman scattering (CARS) spectroscopy: correcting errors in phase retrieval

Coherent anti‐Stokes Raman scattering (CARS) microspectroscopy has demonstrated significant potential for biological and materials imaging. To date, however, the primary mechanism of disseminating CARS spectroscopic information is through pseudocolor imagery, which explicitly neglects a vast majority of the hyperspectral data. Furthermore, current paradigms in CARS spectral processing do not lend themselves to quantitative sample‐to‐sample comparability. The primary limitation stems from the need to accurately measure the so‐called nonresonant background (NRB) that is used to extract the chemically sensitive Raman information from the raw spectra. Measurement of the NRB on a pixel‐by‐pixel basis is a nontrivial task; thus, surrogate NRB from glass or water is typically utilized, resulting in error between the actual and estimated amplitude and phase. In this paper, we present a new methodology for extracting the Raman spectral features that significantly suppresses these errors through phase detrending and scaling. Classic methods of error correction, such as baseline detrending, are demonstrated to be inaccurate and to simply mask the underlying errors. The theoretical justification is presented by re‐developing the theory of phase retrieval via the Kramers–Kronig relation, and we demonstrate that these results are also applicable to maximum entropy method‐based phase retrieval. This new error‐correction approach is experimentally applied to glycerol spectra and tissue images, demonstrating marked consistency between spectra obtained using different NRB estimates and between spectra obtained on different instruments. Additionally, in order to facilitate implementation of these approaches, we have made many of the tools described herein available free for download. Published 2015. This article is a U.S. Government work and is in the public domain in the USA.     

基于自适应免疫算法重叠拉曼谱峰的解析

拉曼光谱测量速度快,可以实现原位实时测量,现已成为过程控制中物料检测的一种重要手段。但由于环境的复杂性以及拉曼光谱信号特点,目前在线检测时难免会出现一些重叠谱峰。基于免疫算法特点,将该方法用于芳烃重叠拉曼谱峰信号的解析中,提取混合物质中单个组分拉曼谱峰信息进行分析,结果表明该方法解析快速、定量准确,相对误差低于1%,是解析重叠拉曼光谱信号的有效方法。针对现场样品检测中出现的重叠谱峰伴随荧光背景信号,提出了结合独立成分分析的自适应免疫算法,有效地解析出荧光背景信号,为复杂样品的拉曼光谱检测分析提供了新的手段。     

柑橘叶片叶绿素含量拉曼光谱定量分析方法研究

柑橘叶片叶绿素含量的准确检测对柑橘营养状况和生长态势具有极其重要的意义。研究了快速无损诊断柑橘叶片中叶绿素含量的方法,以期为拉曼光谱检测技术用于柑橘叶片叶绿素含量检测提供参考。采集不同冠层高度和不同地理分布的柑橘叶片120片,拭去叶片表面的灰尘,用去离子水对其清洗、晾干装入密封袋中并用标签分类标注。然后对柑橘叶片进行拉曼光谱采集,参数设置如下：分辨率为3 cm-1,积分时间为15 s;激光功率为50 mW。分别采用BaselineWavelet、迭代限制最小二乘（IRLS）和不对称最小二乘(ALS)三种算法对柑橘叶片的拉曼光谱背景进行扣除,使用偏最小二乘（PLS）方法建立定量模型;四种光谱预处理方法归一化(Normalization),Savitzky-Golay卷积平滑(SG smoothing, SG平滑)、多元散射校正(MSC)和Savitzky-Golay一阶导数(SG 1st Der)对扣除背景后的光谱进行进一步的优化处理。结果表明：采用原始光谱、BaselineWavelet、IRLS、ALS背景扣除处理后的光谱建立PLS模型,模型的相关系数r分别为0.858,0.828,0.885和0.862,交互验证均方根误差(RMSECV)分别为5.392,5.870,4.934和5.336,最佳因子数分别为8,3,8和8;IRLS背景扣除处理后的PLS模型的RMSECV最小,相关系数最高,建模效果最好。分别采用SG平滑、归一化、MSC和SG 1st Der预处理方法对IRLS背景扣除后光谱进行预处理并建立PLS模型,结果表明：IRLS光谱及其结合SG平滑、归一化、MSC和SG 1st Der四种预处理方法的PLS模型的R分别为0.885,0.897,0.852,0.863和0.888,RMSECV分别为4.934,4.715,5.595,5.182和4.962;最佳因子数分别为8,8,8,8和5;IRLS-SG平滑后PLS模型的RMSECV最小,模型效果最优。对IRLS-SG平滑预处理后的PLS模型展开验证,预测相关系数r为0.844,预测均方根误差(RMSEP)为5.29,预测精确度较高。采用拉曼光谱结合三种光谱背景扣除方法和四种预处理方法对柑橘叶片叶绿素含量进行定量分析表明：采用IRLS背景扣除结合SG平滑预处理后的PLS模型最优,建模集r为0.897,RMSECV为4.715;预测集r为0.844,RMSEP为5.29,预测精度较高。拉曼光谱结合背景扣除方法可以为柑橘叶片叶绿素含量的定量分析提供一种快速简便的分析方法。     

拉曼光谱的荧光背景扣除及其用于药物聚类分析

拉曼光谱分析中,由于有机分子或样品中污染物的荧光影响,常会使拉曼光谱产生高背景信号,以致其拉曼光谱吸收信号被淹没。利用自行开发的软件包baselineWavelet,本文对醋酸泼尼松片和格列本脲片的拉曼光谱进行了荧光背景扣除研究,采用主成分分析和随机森林算法对它们进行聚类分析,得到了较好的结果。通过这2种药物的拉曼光谱聚类分析结果,检验了该背景扣除算法的有效性和准确性,并讨论了荧光背景对拉曼光谱聚类分析的影响。结果说明,荧光背景对拉曼光谱聚类分析影响很大,在分析前必须预先扣除。     

基于自动线性拟合的快速拉曼基线校正算法

近年来拉曼光谱以其无创、灵敏度高等众多优点在化学表征、生物医药、材料等领域引起广泛关注,而基线漂移的存在为后续的定性定量分析带来严重困扰,因此设计高性能的基线校准算法以提高分析结果的有效性及准确性具有重要意义。针对传统算法在批量拉曼光谱数据基线校正方面的不足,基于自动线性拟合算法提出一种快速基线校正算法以校正具有相似背景的批量拉曼光谱数据并详细阐述了该算法的核心思想以及算法实现流程。该算法首先从批量拉曼光谱数据中自动选择一条拉曼光谱数据作为基准光谱,使用自动线性拟合算法对其进行基线校准得到其基线以及分段标记点,然后利用标记点快速计算出组内其他与基准光谱具有较高相关性的拉曼光谱数据的基线,对于组内与基准光谱相关性不满足阈值要求的拉曼光谱则使用自动线性拟合算法对其进行单独基线校正,这使得算法具有具有较强的鲁棒性,可以适应复杂的拉曼光谱基线校正情形。分别使用快速基线校正算法与单独基线校正算法对多组实际拉曼光谱数据进行基线校正以对比分析算法基线校正效果,结果表明该算法可以实现对批量拉曼光谱数据的快速校正,基线校正效果良好,并且相较于单独进行基线校正算法耗时减少了30%以上,算法无参,简单易行,无需额外人工干预,是一种切实可行的批量拉曼数据自动基线校正算法。     

Improved methods for fluorescence background subtraction from Raman spectra

Raman spectroscopy has attracted interest as a non‐invasive optical technique to study the composition and structure of a wide range of materials at the microscopic level. The intrinsic fluorescence background can be orders of magnitude stronger than the Raman scattering, and so, background removal is one of the foremost challenges for quantitative analysis of Raman spectra in many samples. A range of methods anchored in instrumental and computational programming approaches have been proposed for removing fluorescence background signals. An enhanced adaptive weighting scheme for automated fluorescence removal is reported, applicable to both polynomial fitting and penalized least squares approaches. Analysis of the background fitting results for ensembles of simulated spectra suggests that the method is robust and reliable and can significantly improve the background fit over the range of signal, shot noise and background parameters tested, while reducing the subjective nature of the process. The method was also illustrated by application to experimental data generated from aqueous solutions of bulk protein fibrinogen mixed with dextran. Copyright © 2013 John Wiley & Sons, Ltd.     

基于匹配追踪的拉曼光谱信号重构算法

拉曼光谱技术是一种高灵敏度、无损伤、振动分子光谱技术,在医药、生物、分析化学等诸多领域有着重要的作用。然而,由于拉曼散射强度低,实际测得的拉曼信号容易被噪声所污染。特别是在较短的曝光时间,收集到的拉曼光谱的信噪比很低。因此,提出了一种基于匹配追踪算法的信号重构方法,用于提取低信噪比的拉曼信号。该方法首先通过阈值循环迭代的方法在平均谱上找出特征峰的位置、估计峰的区间。根据峰的位置区间等信息,用高斯密度函数生成字典。在噪声谱上,根据特征峰位置和区间,将其区分为有信号区间和无信号区间,在有信号区间上利用匹配追踪算法重构被噪声所掩盖的拉曼信号。该算法不仅能够很好的逼近掩盖在噪声中的拉曼信号,且在重构信号的过程中也会对基线进行扣除,无须作基线校正处理。在仿真和实验中对该算法与常规算法进行了比较,结果证明,该算法在低信噪比条件下能够较好的恢复拉曼信号。该算法不同于传统光谱去噪算法,能同时对拉曼光谱进行了基线扣除以及噪声的处理,且能取得较为理想的结果,不需要使用不同的算法对基线和噪声分别处理。其次,在算法上我们创造性地将匹配追踪算法用于拉曼光谱信号的稀疏逼近求解。     

拉曼光谱的局域动态移动平均全自动基线校准算法

基线校准是极其重要的光谱预处理步骤,能够显著提高后续光谱分析算法的准确性。目前基线校准算法大多数都是手动或半自动的,手动基线校准算法完全依赖于用户的经验,个人主观因素会严重影响基线校准的准确性,半自动基线校准需要针对不同的拉曼光谱设置不同的优化参数,使用不便。提出了一种局域动态移动平均(LDMA)全自动基线校准算法,并且详细阐明了该算法的基本思想和具体算法步骤。该算法采用了改进移动平均算法(MMA)实现拉曼光谱峰的逐渐剥离,通过自动识别原始拉曼光谱的基线子区间来将整个拉曼光谱区间自动分割为多个拉曼峰子区间,从而实现了在每个拉曼峰子区间中动态改变MMA窗口半宽度和控制平滑迭代次数,最大程度地避免了基线校准过度和基线欠校准现象。无论对于凸形基线、指数形基线、反曲线形基线模拟拉曼光谱,还是真实物质的拉曼光谱,LDMA全自动基线校准算法都取得了很好的基线校准效果。     

基于双尺度相关运算的拉曼谱峰识别方法

拉曼谱峰识别是拉曼定性分析中的关键技术之一, 针对现有拉曼谱峰识别方法中存在的缺陷和不足提出了一种双尺度相关拉曼光谱谱峰识别方法,即采用两个尺度下的相关系数与局部信噪比相结合来实现拉曼谱峰识别。利用MATLAB对所提算法与传统的连续小波变换法进行了对比分析,并通过实测拉曼光谱进行验证。分析结果：双尺度相关法识别一幅拉曼谱的平均时间为0.51 s,连续小波变换法为0.71 s;当谱峰信噪比≥6时(现代拉曼光谱仪器均可达到较高的信噪比),双尺度相关法的谱峰识别准确率高于99%,连续小波变换法的谱峰识别准确率小于84%,且双尺度相关法谱峰位置识别误差的均值与标准差均要小于连续小波变换法。通过仿真对比分析和实验验证表明：双尺度相关法具有无需人工干预,无需做去噪及去背景等预处理操作,识别速度快,识别准确率高等特点,是一种切实可行的拉曼谱峰识别方法。     

Heterodyne interferometric polarization coherent anti‐Stokes Raman scattering (HIP‐CARS) spectroscopy

We demonstrate a new technique that combines polarization sensitivity of the coherent anti‐Stokes Raman scattering (CARS) response with heterodyne amplification for background‐free detection of CARS signals. In this heterodyne interferometric polarization CARS (HIP‐CARS), the major drawbacks of polarization and heterodyne CARS are rectified. Using a home‐built picosecond optical parametric oscillator, we are able to address vibrational stretches between 600 and 1650 cm⁻¹ and record continuous high‐resolution Raman equivalent HIP‐CARS spectra. Copyright © 2010 John Wiley & Sons, Ltd.     

A background elimination method based on linear programming for Raman spectra

In this paper, we consider a new background elimination method for Raman spectra. As a background is usually slowly varying with respect to wavelength, it could be approximated by a slowly varying curve. However, the usual curve‐fitting method cannot be applied because there is a constraint that the estimated background must be beneath a measured spectrum. To meet the requirement, we adopt a polynomial as an approximating function and show that background estimation could be converted to a linear programming problem which is a special case of constrained optimization. In addition, we present an order selection algorithm for automatic baseline elimination. According to the experimental results, it is shown that the proposed method could be successfully applied to experimental Raman spectra as well as synthetic spectra. Copyright © 2011 John Wiley & Sons, Ltd.     

自适应的EEMD残余相关基线校正算法

基线校正是光谱分析的重要环节,现有算法通常需要设定关键参数,不具备自适应性。根据总体平均经验模态分解(ensemble empirical mode decomposition,EEMD)残余量特点,提出用残余量拟合光谱基线。通过残余量与信号相关性、残余量自相关和互相关性(称为残余相关准则)判断残余量是否是基线组成部分,以此为基础提出一种自适应的EEMD残余相关基线校正算法。对叠加曲线背景和线性背景的模拟光谱数据进行实验,结果显示在已知基线数学假设情况下,EEMD残余相关法逊于多项式拟合,同非线性拟合相差不多,优于小波分解。在没有光谱背景知识情况下,对真实拉曼光谱数据进行试验。经过上述方法预处理过的玉米叶片光谱采用3层BP神经网络建立与叶绿素之间预测模型,经过残余相关基线校正的模型具有最大校正相关系数和预测相关系数,最小交叉验证标准差和相对分析误差。各种基线校正方法中,残余相关基线校正对特征峰峰位、峰强和峰宽影响最小。实验表明,该算法可用于拉曼谱图基线校正,无需分析样品成分的先验知识,无需选择合适的拟合函数、拟合数据点、拟合阶次以及基函数和分解层数,也无需基线信号分布的数学假设,自适应性很强。     

Estimation of signal backgrounds on multivariate loadings improves model generation in face of complex variation in backgrounds and constituents

The present study is designed to understand further implications of using multivariate loadings for the correction of background signal, which has previously been shown to be highly reproducible even for very low quality signals. Singular value decomposition (SVD)‐based background correction was compared with the traditional per‐signal paradigm for a biomedical dataset to generate qualitative and quantitative models. The qualitative effect on a principal component analysis model and the quantitative effect on a partial least square regression model were assessed for these background correction methods. The chosen quantitative parameter was the concentration of a pathologically relevant protein modification, pentosidine. Of the approaches tested, the SVD‐based paradigm provided the regression model with the highest correlations, highest accuracy (lowest standard error of prediction) and repeatability (lowest sampling error). Contrasted against the traditional approaches, it was determined that the improved accuracy and repeatability of the SVD‐based approach arises from its ability to simultaneously handle very complex background shapes alongside the complex variation in biochemical species that resulted in Raman signals with incompatible baseline regions. A better understanding of the interaction of SVD‐based baseline correction, and data will give the reader more insight into the potential applicability of the procedure for other datasets. Copyright © 2012 John Wiley & Sons, Ltd.     

Passive signal enhancement in spatially offset Raman spectroscopy

We demonstrate experimentally, for the first time, the feasibility of enhancing signals in Spatially Offset Raman Spectroscopy (SORS) using a dielectric bandpass filter, building on our earlier experimental work on the enhancement of transmission Raman signals. The method is shown to lead to the enhancement of both the surface and subsurface Raman layer signal improving the signal‐to‐noise ratio of Raman spectra from the deep areas of samples, thus enhancing the technique's sensitivity and penetration depth. The filter is placed over the laser illumination zone, on the sample surface acting as a ‘unidirectional’ mirror transmitting the collimated laser beam on one side and reflecting photons escaping from the sample back into it. This enhances the degree of coupling of laser radiation into the medium and associated generated Raman signal. The feasibility study was performed on a two‐layer sample with the second layer located at the limit of the penetration depth of the method for this sample. The sample consisted of a 2.2‐mm over‐layer of a thinned paracetamol tablet followed by a 2‐mm layer of trans‐stilbene powder. The Raman signal was collected from a spatially offset region through a hole fabricated within the filter. The experiments demonstrate the presence of an enhancement of the Raman signal from both the layers by a factor of 4.4–4.5 and the improved signal‐to‐noise ratio of sublayer signal by a factor of 2.2, in agreement with photon shot noise dominated signal. Copyright © 2008 John Wiley & Sons, Ltd.     

A comparison of noise models in a hybrid reference spectrum and principal components analysis algorithm for Raman spectroscopy

Raman spectroscopy exploits the Raman scattering effect to analyze chemical compounds with the use of laser light. Raman spectra are most commonly analyzed using the ordinary least squares (LS) method. However, LS is known to be sensitive to variability in the spectra of the analyte and background materials. In a previous paper, we addressed this problem by proposing a novel algorithm that models expected variations in the analyte as well as background signals. The method was called the hybrid LS and principal component analysis (HLP) algorithm and used an unweighted Gaussian distribution to model the noise in the measured spectra. In this paper, we show that the noise in fact follows a Poisson distribution and improve the noise model of our hybrid algorithm accordingly. We also approximate the Poisson noise model by a weighted Gaussian noise model, which enables the use of a more efficient solver algorithm. To reflect the generalization of the noise model, we from hereon call the method the hybrid reference spectrum and principal components analysis (HRP) algorithm. We compare the performance of LS and HRP with the unweighted Gaussian (HRP‐G), Poisson (HRP‐P), and weighted Gaussian (HRP‐WG) noise models. Our experiments use both simulated data and experimental data acquired from a serial dilution of Raman‐enhanced gold‐silica nanoparticles placed on an excised pig colon. When the only signal variability was zero‐mean random noise (as examined using simulated data), HRP‐P consistently outperformed HRP‐G and HRP‐WG, with the latter coming in as a close second. Note that in this scenario, LS and HRP‐G were equivalent. In the presence of random noise as well as variations in the mean component spectra, the three HRP algorithms significantly outperformed LS, but performed similarly among themselves. This indicates that, in the presence of significant variations in the mean component spectra, modeling such variations is more important than optimizing the noise model. It also suggests that for real data, HRP‐WG provides a desirable trade‐off between noise model accuracy and computational speed. Copyright © 2013 John Wiley & Sons, Ltd.