Parametric methods for frequency-selective MR spectroscopy-a review

Accurate quantitation of the spectral components in a pre-selected frequency band for magnetic resonance spectroscopy (MRS) signals is a frequently addressed problem in the MR community. One obvious application for such a frequency-selective technique is to lower the computational burden in situations when the measured data sequence contains too many samples to be processed using a standard full-spectrum method. Among the frequency-selective methods previously proposed in the literature, only a few possess the two features of primary concern: high robustness against interferences from out-of-band components and low computational complexity. In this survey paper we consider five spectral analysis methods which can be used for MRS signal parameter estimation in a selected frequency band. We re-derive the filter diagonalization method (FDM) in a new way that allows an easy comparison to the other methods presented. Then we introduce a frequency-selective version of the method of direction estimation (MODE) which has not been applied to MR-spectroscopy before. In addition, we present a filtering and decimation technique using a maximum phase bandpass FIR-filter and relate it to a similar ARMA-modeling approach known as SB-HOYWSVD (sub-band high-order Yule-Walker singular value decomposition). Finally, we study the numerical performances of these four methods and compare them to that of the recently introduced SELF-SVD (Singular Value Decomposition-based method usable in a SELected Frequency band) in several examples using simulated MR data, and discuss the benefits and disadvantages of each technique.     

基于迈克尔逊干涉仪的太赫兹光谱高速探测方法研究

太赫兹光谱技术作为获取物质在太赫兹频段信息的主要方法,已经被广泛应用于物质成分的测定,而其在成分分布成像方面则有着更广阔的应用前景,例如片剂药品的有效成分检测、行李安检的危险物品检测等。现有的太赫兹光谱探测方法时域光谱技术（THz-TDS）和频域光谱技术（THz-FDS）均不能很好地兼顾光谱分辨率与扫描时间;且获得物质光谱数据往往要花费数秒乃至数分钟时间（取决于光谱仪的结构）,这对多像素成像系统显得过于迟缓,更无法达到视频成像的速率需求,严重制约了太赫兹光谱成像的实际应用。目前的太赫兹波成像多为全频段波强度成像,只能反映样品的空间分布信息,并不能反映出样品的光谱即成分信息。因此,对太赫兹光谱探测速率的提升十分迫切,太赫兹光谱高速探测的实现不仅可以显著减少物质成谱的实验耗时,还为实现物质的太赫兹光谱成分分布成像提供了可能。提出了一种基于迈克尔逊干涉仪的太赫兹光谱高速探测方法,在设计了该方法装置结构的基础上,理论分析了其工作过程,同时进行了太赫兹光谱的计算。然后从数据采样、数据处理及参数选择这几个方面进行问题分析,计算得出该方法能够显著加快物质太赫兹光谱的扫描获取速率。最后,对该方法建模进行仿真研究,模拟实现其完整的探测过程。在仿真研究中,以太赫兹辐射源的频谱分布为例,将该方法的建模仿真结果与时域光谱技术（THz-TDS）测试结果进行了对比,结果表明时域光谱技术（THz-TDS）所测得的频谱曲线可以近似看作是该高速光谱探测法所得频谱曲线的包络线,两种不同方法所得频谱结果具有较强的一致性。总之,该方法能够进行样品的太赫兹光谱探测,且在保证分辨率相同的前提下,较时域光谱技术（THz-TDS）显著加快了成谱速率,为实用、高通量太赫兹光谱成像提供了一种可能。     

Spectral fitting of NMR spectra using an alternating optimization method with a priori knowledge.

As alternatives to the fast Fourier transform, advanced parametric methods based on the damped sinusoidal data model have been devised to better quantify the nuclear magnetic resonance (NMR) spectroscopy time-domain data. Previously, linear prediction (LP) fitting methods using Householder triangularization and singular value decomposition (SVD) techniques have been applied to the NMR spectroscopy data analysis. In this paper, we propose an alternating optimization method to quantify the time-domain NMR spectroscopy data. The proposed algorithm uses the a priori knowledge of the possible frequency intervals of the damped sinusoids to obtain more accurate parameter estimates when the NMR spectroscopy data are obtained under low signal-to-noise ratio conditions and the peaks are close together. None of the LP and SVD type of methods can use such approximate a priori knowledge. We have shown with measured NMR spectroscopy data that the proposed algorithm can be used to obtain accurate parameter estimates of frequencies, amplitudes, and damping ratios of the damped sinusoids and therefore the ultimate fit of the spectrum by using the a priori knowledge about the possible frequency intervals of the damped sinusoids.     

Nonparametric NMR spectroscopy

The parametric (or model-based) approach to NMR spectroscopy suffers from two general problems: it is sensitive to modeling errors and requires knowledge of the number of resonances present in the compound(s) under analysis. The nonparametric approach has neither of these drawbacks and it may also be computationally simpler than the parametric approach. However, if not applied properly, the nonparametric approach may yield significantly less accurate spectroscopic results than the parametric approach. In this paper we introduce a high-resolution nonparametric methodology for NMR spectroscopy based on the adaptive filter bank approach. The main salient feature of the new approach is that it provides 2D spectra versus both frequency and damping, as opposed to the classical 1D frequency spectra routinely used in NMR spectroscopy. To show the power of our new nonparametric approach we compare its performance with the ultimate performance of the parametric approach. We use both simulated and real NMR signals in our numerical performance study.     

基于扩散映射的太赫兹光谱识别

特征提取对于太赫兹光谱识别来说至关重要。传统方法是通过人工选取太赫兹光谱中差异性较大的吸收峰作为特征进行光谱识别,但当部分物质在太赫兹波段没有明显波峰、波谷等光谱图形特征时,这种方式便不再适用。为此,研究人员利用统计学习与机器学习方法对高维太赫兹光谱数据进行降维和特征提取。由于物质的太赫兹光谱数据各维度呈现非线性,尤其是当不同物质的太赫兹光谱曲线整体非常相似时,线性处理方法易产生较大误差。针对这一问题,提出了一种基于扩散映射(DM)的太赫兹光谱识别方法。扩散映射能在保持数据内在几何结构的同时对其进行非线性降维,提取的流形特征区分度较高,对数据还有聚类效果。首先用S-G滤波器对Alloxazine等10种物质的太赫兹光谱样本进行滤波,并用三次样条插值法对截取相同频段后的光谱样本进行统一分辨率处理;然后利用DM将高维太赫兹光谱数据映射到低维特征空间并提取太赫兹光谱的流形特征;最后用多分类支持向量机(M-SVM)对十种物质的太赫兹透射光谱进行分类。实验结果表明,相比于主成分分析(PCA)和等距映射(ISOMAP),使用DM提取的太赫兹光谱流形特征具有更高的区分度,而且DM可以直接得到太赫兹光谱数据本征维数的估计值,这为相似太赫兹光谱的快速精准识别提供了一条新的途径。     

Conceptual Design Study of a Novel Gyrotron for NMR/DNP Spectroscopy

In this paper we present some initial results from a conceptual design study focused on the development of a novel frequency tunable gyrotron for nuclear magnetic resonance (NMR) spectroscopy with signal enhancement based on the utilization of high field radiation and dynamic nuclear polarization (DNP) technique. The first variants of both the electron optical system and the resonant cavity which have been designed aiming continuous frequency tunability in a broad frequency band are presented and discussed. The selected method for frequency tunability is based on the excitation of higher order axial modes and smooth transition between them. It was selected after a critical examination of the known theoretical and practical results related to the frequency control in gyrotrons. It is believed that the current conceptual design is an appropriate basis for development of the next (optimized) design which will include also a detailed design of other components (mode converter, output window etc.) and magnetic circuit (superconducting magnet and supplementary solenoids) as well as for the overall mechanical design and fabrication of the prospective gyrotron.     

基于选择编码的超快速磁共振波谱方法

核磁共振(NMR)波谱技术是当今最有力的谱学工具之一,在化学、生物和医药等众多领域获得重要而广泛的应用．基于时空编码的快速采样方法自2002年Frydman小组提出后,大大增强了高维磁共振波谱的采样效率．在某一些应用体系中,存在若干个强度远超于其他谱峰的情况,很容易由于动态增益不足而检测不到某些较弱的谱峰,而往往这些较弱的谱峰包含着感兴趣的信息．且在实际的化学生物应用中,存在选择性感兴趣检测的情况,即只需要选择性地观察若干个具有标记作用的谱峰．由于时空编码技术借助于高速切换的双极性梯度来完成解码,因而无法选择性地检测若干个非连续的频点．为解决以上两个问题,该文提出一种选择编码的时空编码方法,即在序列中施加选择性脉冲,选择性破坏某些谱峰的编码过程,使之不能在解码期解码,从而简化谱图,实现选择性压制或者非连续频点的感兴趣检测．如果把选择性反转脉冲换为硬反转脉冲加选择性反转脉冲,则最终的谱图中只出现被选择性脉冲选中的谱峰．理论分析及相关的实验验证了这种方法的可行性和有效性.     

基于谱线频率特征的调谐二极管激光吸收光谱参数分析

调谐激光二极管吸收光谱(TDLAS)技术因其高分辨率、高灵敏度和快速测量等优点在工业生产、环境污染监测等方面受到广泛应用。波长调制光谱（wavelength modulation spectrum, WMS）的二次谐波信号经常用作气体浓度反演的检测信号。TDLAS检测性能与系统参数,如锁相放大器的时间常数、扫描幅度、扫描频率、调制幅度、调制频率等的选取紧密相关,实际测量中各参数的选择多以谱线形态特征为依据,参数之间的关联性未能得到较好体现。由于信号的采样与处理均在频域对谱线产生作用,各参数之间的作用相互关联。然而很少有研究参数对谱线频域的影响,针对此问题,在一定的理论基础上通过实验分别观察各调制参数对二次谐波信号的影响。通过保持其他参数不变,只改变一个参数的方法,得出各个参数对信号线型、频率特征及噪声引入的影响规律,继而分析并验证了多参数联合变化对谱线频带的决定作用。与基于时域特征的传统方法相比,基于谱线频率特征分析一方面具有与谱线信号采集检测处理机理相近的优点,另一方面可以直观得到各参数对主频带的影响和不同频率信号的衰减趋势。总结出基于频率特征的各参数的基本选取方法,以谱线频带和截止频率相互关系为判定标准,截止频率的大小由锁相放大器时间常数决定。通过设置合适的时间常数和扫描参数使信号频带与截止频率相近但不相交,使谱线频带内频率分量不产生衰减,频带外噪声得到最大抑制;再根据锁相放大器的性能和信号信噪比来确定调制参数,使谱线主频幅度最大;最后根据系统需求确定采样率。单周期采样点不变时,低扫描频率时检测精度相对提高但耗时较长;反之,扫描频率提高,速度变快但检测精度下降。通过联合影响规律调整关联参数,减小硬件限制对参数最优值选取造成的影响。可在考虑系统检测需求与硬件条件限制的前提下,通过参数选择得到最优二次谐波信号,为此技术的实际应用提供了参数优化的实验依据与参考方法。     

基于网络连接度指标的脑梗死患者脑电信号相同步分析

基于图论的脑功能网络分析是近年来的一个研究热点,而相同步分析已被证实为揭示多导联脑电信号之间功能连接的有效工具.针对当脑电采集系统中导联数目较少而不适用于采用图论分析的情况,提出使用基于导联间相同步分析的网络连接度指标研究脑功能网络的关联特性和整体特性.采用新的频带划分方法,将0.5—30 Hz带宽内的脑电信号划分到5个子带上,计算了不同数据长度下各子带分量的网络连接度指标,并对比分析了各子带分量的相对功率.结果表明:在对脑梗死患者的脑电图和正常人的脑电图进行分析时,需要合理的数据长度量化不同动力学系统之间的差异;在合理的数据长度下,在网络连接度指标的区分效果方面,19—24 Hz分量信号优于其他分量,而且仅在19—24 Hz频带上,脑梗死患者组的所有导联出现了与对照组的所有导联相同趋势的变化.研究表明19—24 Hz频带是脑梗死最佳的脑电图诊断频段,可将该频段下的网络连接度指标作为脑梗死辅助诊断的新指标.     

SPA-PLS的高含水原油近红外光谱含水率分析

准确及时的检测原油含水率对注水策略调整、原油开采能力评估、油井开发寿命预测等均具有重要意义。然而,当前我国大多数油田均已进入高含水的开发中晚期,含水率测量难度大且准确率不高。在此背景下,开展了高含水情况下利用近红外光谱进行原油含水率测量的研究。 首先介绍了目前原油含水率检测的常用方法,分析了它们的优劣。理论上,由于水的近红外光吸收带与原油中C-H键的吸收带有明显区别,根据Lambert-Beer吸收定律和吸光度线性叠加定律可知,不同含水率高含水原油近红外光谱会存在较强响应差异。为此,对高含水原油进行近红外光谱检测,建立原油含水率与近红外光谱响应间的非线性映射模型,可实现高含水原油含水率的精确测量。为了验证该方法的有效性,搭建了近红外光谱数据采集实验装置：采用白炽灯作为光源,经过光路调节成平行光后垂直射入样品池,用近红外光谱仪（海洋光学NIR512）采集光谱用于分析。其中,接收光谱仪带宽为900～1 700 nm,平均分成512个波段。光谱数据利用光谱仪配套软件储存在电脑中。样本采用相同厚度不同比例的油水混合物,样本含水率范围为70%～99%,共采集数据60组,每组重复3次取平均值。得到原始数据后,先进行原始数据预处理,以减少数据采集时来自高频随机噪音及温度不稳定、样本不均匀、基线漂移、光散射等不利因素的影响。分别选用了S-G滤波、一阶导数和S-G滤波+一阶导数作为数据预处理的方法,利用连续投影算法(SPA)对光谱数据进行降维,并利用偏最小二乘法（PLS）和多元线性回归（MLR）进行建模,模型精度通过计算均方根误差值（RMSE）和相关系数（r）来验证。对比发现,使用S-G滤波+一阶导数建立的模型RMSE值最小（RMSE=0.007 0,r=0.998 3）。使用SPA降维后的模型要优于全波段PLS模型（RMSE=0.083 3,r=0.920 6）与MLR模型（RMSE=0.099 9,r=0.967 1）。利用SPA提取出的31个特征波长建立的模型仅占全波段的6.05%,并获得了较好的精度。证明了利用光谱检测高含水原油含水率可行性,并且得到了满意的精度,为高含水原油的含水率检测提供了新的方法, 为进一步利用近红外光进行高含水原油的快速检测与在线监测提供参考。     

小波变换提高动态光谱法血液成分无创检测的精度

光谱采集过程中的各种时变噪声影响了动态光谱法血液成分无创检测定量校正模型的精度。该文采用小波变换法,在脉搏频段内对指端投射光谱的时域吸光度波形聚焦,提高了动态光谱数据的信噪比和血液成分含量定量校正模型的精度。对同一个体连续采集10次光谱数据,引入小波变换去噪后动态光谱数据的平均相关系数r自0.979 6提升至0.990 3。对110名志愿者进行血常规体检和指端透射光谱采集,建立动态光谱数据与血糖浓度生化分析值之间的神经网络模型,在引入小波变换去噪后,预测集相关系数自0.6774提升至0.846 8,平均相对误差自15.8%下降至5.3%。实验表明,引入小波变换可以有效地去除动态光谱数据中的噪声,提高定量校正模型的精度,推动了动态光谱法无创血液成分检测的发展。     

一种基于组分补偿的二维核磁共振测井数据高精度处理方法

二维核磁共振技术能够对储层中各类含氢流体进行无损、快速、定量的测量和表征，但受限于采集方式和参数，核磁共振设备在对页岩油等致密储层中的有机质、沥青等超快弛豫组分进行检测时，经常出现由于信号采集不完整所导致的二维谱中流体组分缺失或不准的问题.本文提出了基于超快弛豫组分补偿技术的T₂-T₁二维谱高精度反演方法，该方法将一维核磁共振前端信号补偿技术进行推广，通过在二维核磁数据反演前对回波数据进行组分补偿，能够有效解决二维核磁共振测井前端信号漏失的问题.实验及测井数据的应用表明，该方法在页岩油等富含快弛豫组分信号的储层中，可以得到更加精准和完整的储层信息.     

Singular spectrum analysis for an automated solvent artifact removal and baseline correction of 1D NMR spectra

NMR spectroscopy in biology and medicine is generally performed in aqueous solutions, thus in (1)H NMR spectroscopy, the dominant signal often stems from the partly suppressed solvent and can be many orders of magnitude larger than the resonances of interest. Strong solvent signals lead to a disappearance of weak resonances of interest close to the solvent artifact and to base plane variations all over the spectrum. The AUREMOL-SSA/ALS approach for automated solvent artifact removal and baseline correction has been originally developed for multi-dimensional NMR spectroscopy. Here, we describe the necessary adaptations for an automated application to one-dimensional NMR spectra. Its core algorithm is still based on singular spectrum analysis (SSA) applied on time domain signals (FIDs) and it is still combined with an automated baseline correction (ALS) in the frequency domain. However, both steps (SSA and ALS) have been modified in order to achieve optimal results when dealing with one-dimensional spectra. The performance of the method has been tested on one-dimensional synthetic and experimental spectra including the back-calculated spectrum of HPr protein and an experimental spectrum of a human urine sample. The latter has been recorded with the typically used NOESY-type 1D pulse sequence including water pre-saturation. Furthermore, the fully automated AUREMOL-SSA/ALS procedure includes the managing of oversampled, digitally filtered and zero-filled data and the correction of the frequency domain phase shift caused by the group delay time shift from the digital finite response filtering.     

The equilibrium unfolding of MerP characterized by multivariate analysis of 2D NMR data

A general problem when analysing NMR spectra that reflect variations in the environment of target molecules is that different resonances are affected to various extents. Often a few resonances that display the largest frequency changes are selected as probes to reflect the examined variation, especially in the case, where the NMR spectra contain numerous resonances. Such a selection is dependent on more or less intuitive judgements and relying on the observed spectral variation being primarily caused by changes in the NMR sample. Second, recording changes observed for a few (albeit significant) resonances is inevitably accompanied by not using all available information in the analysis. Likewise, the commonly used chemical shift mapping (CSM) [Biochemistry 39 (2000) 26, Biochemistry 39 (2000) 12595] constitutes a loss of information since the total variation in the data is not retained in the projection into this single variable. Here, we describe a method for subjecting 2D NMR time-domain data to multivariate analysis and illustrate it with an analysis of multiple NMR experiments recorded at various folding conditions for the protein MerP. The calculated principal components provide an unbiased model of variations in the NMR spectra and they can consequently be processed as NMR data, and all the changes as reflected in the principal components are thereby made available for visual inspection in one single NMR spectrum. This approach is much less laborious than consideration of large numbers of individual spectra, and it greatly increases the interpretative power of the analysis.     

RRT: the regularized resolvent transform for high-resolution spectral estimation

A new numerical expression, called the regularized resolvent transform (RRT), is presented. RRT is a direct transformation of the truncated time-domain data into a frequency-domain spectrum and is suitable for high-resolution spectral estimation of multidimensional time signals. One of its forms, under the condition that the signal consists only of a finite sum of damped sinusoids, turns out to be equivalent to the exact infinite time discrete Fourier transformation. RRT naturally emerges from the filter diagonalization method, although no diagonalization is required. In RRT the spectrum at each frequency s is expressed in terms of the resolvent R(s)(-1) of a small data matrix R(s), that is constructed from the time signal. Generally, R is singular, which requires certain regularization. In particular, the Tikhonov regularization, R(-1) approximately [R(dagger)R + q(2)](-1)R(dagger) with regularization parameter q, appears to be computationally both efficient and very stable. Numerical implementation of RRT is very inexpensive because even for extremely large data sets the matrices involved are small. RRT is demonstrated using model 1D and experimental 2D NMR signals. Copyright 2000 Academic Press.     

一种基于新型间歇混沌振子的舰船线谱检测方法

为了实现低信噪比下未知频率的舰船辐射线谱的检测,对常规型间歇混沌振子列检测方法进行了改进,提出了一种基于适应步长型间歇混沌振子的信号检测方法.该方法可以只用一个Duffing振子,通过设定一组能够覆盖待测信号所在频段的求解步长序列,实现对未知频率、具有任意初相位的微弱周期信号的搜索检测.为进一步提高系统的弱信号检测性能,分析了Holmes型Duffing方程在不同频率内置策动力下对弱信号灵敏度的差异.综合理论分析和仿真研究结果给出了Duffing振子在内置策动力角频率为0.4 rad/s时对弱信号检测性能最佳,并据此对所采用的Duffing振子进行了优化;仿真结果表明,改进后的Duffing振子的弱信号检测性能提高了12 dB.最后将此方法应用于一组含有舰船辐射线谱的实船数据,结果表明此方法可以实现低信噪比下的未知频率微弱线谱检测.     

基于多波段漫反射光谱古陶瓷窑口无损鉴定

古陶瓷是历史的遗存, 具有不可再生性，因而理想的古陶瓷分析技术应该是无损的。为客观、有效地对古陶瓷窑口进行无损鉴定，提出了一种基于紫外、可见光和近红外的多波段漫反射光谱无损鉴定方法。针对传统单一波段古陶瓷窑口鉴定对目标特征描述不足的问题，即在可见光波段区域，漫反射光谱数据可反映古陶瓷的颜色特征，但在同一窑口烧制的陶瓷也会有不同的颜色属性，仅仅根据可见光波段的漫反射反射率来鉴定窑口来源是不合理的，在紫外与近红外波段，古陶瓷内部分子与此波段光发生作用后的漫反射光谱数据，可反映古陶瓷携带的丰富样品结构和物质属性信息，结合紫外与近红外光谱漫反射光谱数据可有效提高特征的表达，因此提出利用紫外、可见光和近红外的多波段特征提取方法。在实验过程中，基于多波段线性特征融合窑口平均鉴定准确率为92.9%，相比于单波段的窑口鉴定平均准确率91.1%提高了1.8%，实验结果验证了所提多波段方法相对单波段方法的有效性；在特征提取过程中，常用小波变换对光谱信号进行处理，但由于古陶瓷漫反射光谱波信号在紫外、可见光与近红外波段形波动大，频率变化大，因此，在小波基的选取上存在很大困难，提出利用自适应时频分析特征提取方法，其特点是可自适应分配不同频率子波本征模态函数，通过选择合适的本征模态函数来提取古陶瓷不同波段的光谱特征，但在分解过程中存在过分解现象，即虚假的本征模态函数，将所有样本与分解的本征模态函数的平均相关系数和平均方差贡献率作为选择本征模态函数的标准，实验结果表明，随着分解阶次的递增平均相关系数和平均方差贡献率递减，当分解阶次为4时，相关系数和方差贡献率都为0.30，但当分解阶次为5时，相关系数和方差贡献率仅为0.15和0.18，因此选择4阶分解，用于不同波段的特征提取；所提取的特征给与分类器进行分类时，不同波段的特征对分类的准确率贡献不同，因此在此基础上，计算不同光谱特征的散布矩阵，利用类内与类间散布矩阵的迹，计算特征融合时不同波段特征的权重，自适应分配权重并进行非线性特征融合，权重越大，表明该类特征对鉴别的贡献越大，非线性特征融合时，平均鉴定准确率为94.5%，相比于线性特征融合鉴定平均准确率92.9%提高了1.6%；其中分类器采用k最近邻分类器对来自不同窑口的古陶瓷进行无损分类识别。通过客观定量地将该方法与同类方法进行对比，朱旭峰等利用非线性特征融合方法，窑口平均鉴定准确率为86.97%，该方法比其高7.53%。刘峰等采用基于协方差阵进行特征级融合多波段方法，窑口平均鉴定准确率为89.63%，该方法比其高4.87%。实验结果表明所提方法有效、可行，可作为古陶瓷窑口鉴定的有效辅助鉴定方法。     

基于LASSO方法的傅里叶变换红外光谱快速定性识别方法

采用红外光谱技术对未知气体组分进行监测,需要对气体组分进行定性识别分析。基于多元线性回归模型的LASSO变量选择技术广泛应用于数据分析领域。将LASSO方法引入到红外光谱分析领域,提出一种LASSO变量选择技术结合循环线性最小二乘(LCLS)分析的定性识别方法,并开展了相关的实验对其进行验证。实验采集CO,C₂H₄,NH₃,C₃H₈,C₄H₁₀和C₆H₁₄六种单组分傅里叶变换红外(FTIR)光谱吸光度谱以及一组C₂H₄和NH₃混合组分的吸光度谱,结合实验室自建光谱数据库,先采用LASSO方法对采集的光谱进行初步定性分析,然后使用LCLS方法剔除干扰组分。实验结果表明,LASSO结合LCLS的方法能有效识别出光谱中的目标组分,即使是在干扰严重的光谱波段也可以剔除掉大部分的干扰组分。     

Application of wavelet transform on improving detecting precision of the non-invasive blood components measurement based on dynamic spectrum method

Time-varying noises in spectra collection process have influence on the prediction accuracy of quantitative calibration in the non-invasive blood components measurement which is based on dynamic spectrum (DS) method. By wavelet transform, we focused on the absorbance wave of fingertip transmission spectrum in pulse frequency band. Then we increased the signal to noise ratio of DS data, and improved the detecting precision of quantitative calibration. After carrying out spectrum data continuous acquisition of the same subject for 10 times, we used wavelet transform de-noising to increase the average correlation coefficient of DS data from 0.979 6 to 0.990 3. BP neural network was used to establish the calibration model of subjects' blood components concentration values against dynamic spectrum data of 110 volunteers. After wavelet transform de-noising, the correlation coefficient of prediction set increased from 0.677 4 to 0.846 8, and the average relative error was decreased from 15.8% to 5.3%. Experimental results showed that the introduction of wavelet transform can effectively remove the noise in DS data, improve the detecting precision, and accelerate the development of non-invasive blood components measurement based on DS method.     

White noise nonlinear system analysis in nuclear magnetic resonance spectroscopy

Nonlinear noise excitation in nuclear magnetic resonance is a form of nonlinear spectroscopy which exploits the nonlinear susceptibilities in a very direct way. The nonlinear susceptibilities are defined by perturbation theory in the frequency domain. In nonlinear system analysis, on the other hand, the system response is described by a Volterra series in the time domain. The kernels of the Volterra functionals carry the information about the system and are to be determined by experiment.The series expansion of a molecular, atomic or nuclear system response is derived in quantum mechanics by time dependent perturbation theory, leading to a Volterra series with time ordered, triangular kernels. The kernels are multi-dimensional products of decaying exponentials, which describe coherence decays of particular density matrix elements. The Fourier transforms of the triangular Volterra kernels are the susceptibilies, which are formally identical in NMR spectroscopy and nonlinear optical spectroscopy. The nonlinear susceptibilities are multi-dimensional spectra, which in NMR spectroscopy reveal the spin communication pathways. These are established by various forms of single quantum coherence connectivities, such as indirect coupling, chemical exchange, cross-relaxation, dipolar and quadrupolar coupling.If the functionals of the Volterra series are orthogonalized with respect to Gaussian white noise excitation, the Wiener series results. The Wiener kernels can be derived by multi-dimensional cross-correlation of the system response with different powers of the Gaussian white noise excitation.Cross-correlation of the transverse magnetization response to noise excitation in NMR leads to multi-dimensional time functions, the Fourier transforms of which closely resemble the nonlinear susceptibilities. The cross-correlation spectra differ from the susceptibilities in the governing Liouvillean and the dynamic density matrix, which are affected by saturation for continuous excitation. Cross-correlation spectra and susceptibilities converge for vanishing excitation power. Therefore the cross-correlation spectra are referred to as stochastic susceptibilities.In stochastic NMR spectroscopy only odd order susceptibilities exist for transverse magnetization. The first nonlinear order is the third, and the nonlinear spectral information is derived from the third order susceptibility. Higher order susceptibilities are not feasible to derive from experimental data. An important share of the nonlinear information is found on the six subdiagonal 2D cross-sections through the third order susceptibility. These cross-sections arise in three pairs, which carry distinct information, separated according to longitudinal magnetization and population effects, zero quantum coherences, and double quantum coherences.In practice a nonlinear 3D spectrum is computed from experimental data by an algorithm in the frequency domain, which yields access to selected regions in the 3D spectrum. This spectrum is the symmetrized stochastic third order susceptibility. All its sub-diagonal 2D cross-sections are equivalent. They are the average of the six different sub-diagonal 2D cross-sections through the asymmetric third order susceptibility.The stochastic excitation technique in NMR is characterized by several unique attributes. (1) There is no minimum time for a data acquisition cycle, so that, at the expense of signal-to-noise ratio, strong samples can be investigated faster with stochastic NMR than with pulsed FT NMR. (2) Stochastic excitation tests the sample extensively, and measures a maximum amount of information in a single experiment. This feature is of particular interest for investigation of short-lived samples and of samples with little a priori information. (3) An experiment with stochastic excitation is simple to perform, but the data processing is more complex than in FT spectroscopy. (4) The nonlinear information about spin communication pathways is derived for individual frequency regions only, which are identified in the stochastic ID spectrum. This information is located primarily on the sub-diagonal 2D cross-sections through the third order susceptibility. (5) Stochastic NMR spectra derived from random noise excitation are contaminated by systematic noise. In the sub-diagonal 2D cross-sections the noise is reduced by filtering and symmetrization during data processing. (6) Sub-diagonal 2D cross-sections are sensitive to experimental phase distortions in one direction only. They are readily adjusted in phase with the same parameters as the ID spectrum. (7) Stochastic multi-dimensional spectra can be computed at variable resolution from one and the same set of raw data.So far stochastic NMR spectroscopy is not applied routinely in analytical spectroscopy. More practical experience is needed to evaluate its merits in comparison with Fourier transform NMR.Stochastic excitation is distinguished from continuous wave and sparsely pulsed excitation by low input power in connection with large bandwidth. This important property cannot be exploited in high resolution NMR in liquids, because excitation power is not a restricting factor in this case. The situation is different in NMR imaging, where large field gradients require large bandwidths and the excitation power becomes a point of concern. For this reason stochastic RF excitation is being investigated in NMR imaging.The multi-dimensional cross-correlation functions obtained from random noise excitation generally are contaminated by systematic noise. The occurrence of systematic noise can be avoided if pseudo-random excitation is used in combination with a transformation of the system response to obtain the kernels. This technique is used successfully in Hadamard spectroscopy, where the linear Volterra kernel is the Hadamard transform of the linear response functional. Nonlinear transformations^(220,221) for retrieval of nonlinear kernels have not yet been realized in NMR spectroscopy.The cross-correlation technique underlying the data evaluation in stochastic nonlinear system analysis is equivalent to interferometry in optical spectroscopy. The Michelson interferometer is the most prominent optical correlator. The time resolution of the kernels derived by cross-correlation is determined by the inverse bandwidth of the excitation. With the Michelson interferometer a time resolution of 10⁻¹⁴ s is achieved in IR spectroscopy. Since the IR correlogramm is Fourier transformed for spectral analysis, the time resolution cannot be exploited otherwise. For analysis of fast time dependent processes a two-dimensional interferometer should be constructed, which performs a 2D cross-correlation of the system response to two in general different noise inputs. One input pumps the time dependent process, the other is used to investigate the time dependence spectroscopically. This technique is introduced by the name of ‘two-dimensional interferometry’. It uses low excitation power, but provides high time resolution at large response energy. Related work is pursued in nonlinear optical spectroscopy with incoherent excitation. In this area the use of broad band lasers is investigated for generation of echoes and for correlation based measurements of relaxation times.