小波变换在近红外光谱分析中的应用进展

小波变换(WT)具有很好的时频分离特征,信息处理能力强,已广泛用于分析化学领域;本文就小波变换在近红外光谱领域的应用进行简述。小波变换用于近红外预处理,提取有用信息,消除背景干扰,可以提高近红外的分析精度和模型稳健性;用于数据压缩可以减少数据库存储空间,提高建模速度;小波系数用于模型传递,具有传递速度快,稳健性强,所需标样少等特点;小波变换可以与神经网络、遗传算法等结合,在近红外分析领域呈现出良好的发展前景。     

结合小波分析法与导数光声光谱技术测量弱光谱信号的实验研究

结合导数光声光谱技术与小波分析方法,精确测量了光声光谱中的弱光谱信号.首先利用自己设计的仪器装置实现光声光谱的一阶导数,在此基础上,根据导数光声光谱的数据选择合理的分析小波,将光声光谱信号分解为不同频率信号的叠加,被分解的信号满足线性性质且原信号的峰值信息保持不变,由频率的差异可区分出光声信号和噪声信号,从而提取出光声光谱中的弱光谱信号.结合物理方法与软件方法的分析结果,准确地测量了氙灯的输出光声光谱中3个不明显的弱峰值,位置分别为699.7nm、753.4nm和776.5nm.该方法可以更准确地提取出光声光谱的峰值信息,有效地提高了光声光谱的测量精度,为光声光谱分析法在生物医学及化学分析中的应用提供了一种更精确的分析方法.     

基于小波变换和维纳滤波的半导体器件1/f噪声滤波

针对半导体器件中普遍存在的1/f噪声提出了一种结合了提升小波变换和维纳滤波器的处理方法.首先利用重新加权迭代最小二乘法拟合1/f噪声的功率谱曲线得到噪声参数的估计,从而选择恰当的小波.其次,对包含了1/f噪声的信号进行提升小波变换.考虑到小波变换对1/f噪声的白化作用,利用维纳滤波器对每一层小波系数进行处理.设计了最优全通滤波器以校正维纳滤波器的相频特性,使得小波系数经滤波后相位不变.最后利用提升小波逆变换获得被1/f噪声淹没的信号.利用实验检验了提出方法的有效性,实验数据采自用于微创外科手术机器人的力传感器.结果表明提出的方法能够有效抑制1/f噪声,并使传感器的分辨力提高了25%. 关键词： 半导体器件 f噪声')" href="#">1/f噪声 提升小波变换 维纳滤波     

An Adaptive Wavelet–Vaguelette Algorithm for the Solution of PDEs

The paper first describes a fast algorithm for the discrete orthonormal wavelet transform and its inverse without using the scaling function. This approach permits to compute the decomposition of a function into a lacunary wavelet basis, i.e., a basis constituted of a subset of all basis functions up to a certain scale, without modification. The construction is then extended to operator-adapted biorthogonal wavelets. This is relevant for the solution of certain nonlinear evolutionary PDEs where a priori information about the significant coefficients is available. We pursue the approach described in (J. Fröhlich and K. Schneider,Europ. J. Mech. B/Fluids13,439, 1994) which is based on the explicit computation of the scalewise contributions of the approximated function to the values at points of hierarchical grids. Here, we present an improved construction employing the cardinal function of the multiresolution. The new method is applied to the Helmholtz equation and illustrated by comparative numerical results. It is then extended for the solution of a nonlinear parabolic PDE with semi-implicit discretization in time and self-adaptive wavelet discretization in space. Results with full adaptivity of the spatial wavelet discretization are presented for a one-dimensional flame front as well as for a two-dimensional problem.     

Recent Analytical Applications of Molecular Spectroscopy in Bioorganometallic Chemistry—Part I: Metal Carbonyls

Abstract: This is the first part of a two-part review on the analytical applications of molecular spectroscopy in bioorganometallic chemistry since 2005. In this case, radiopharmaceutical studies are included and the review is focused particularly on biological molecules labeled with metal carbonyl fragments.     

小波分析及其在光谱分析中的应用

近年来,一种被称为小波变换的数学理论和方法成为众多学科关注的焦点,在分析化学领域中,小波分析也逐渐应用于去噪与平滑,数据压缩等方面,本文介绍了小波分析理论并对其光谱分析中的应用进行了综述。     

Flicker noise in millimeter-wave backward wave oscillators

Conclusions Thus the proposed experimental — analytical technique has demonstrated its usefulness in investigation of the nonstationary noise in millimeter wave oscillators as well as allows one to get the oscillator output modelling spectrum comparable with the real one to distinguish the factors which take part in the oscillator signal spectrum forming. This technique can be successfully applied to the oscillator spectrum modelling atf<10H z off the carrier frequency domain.     

Singularity spectrum of fractal signals from wavelet analysis: Exact results

The multifractal formalism for singular measures is revisited using the wavelet transform. For Bernoulli invariant measures of some expanding Markov maps, the generalized fractal dimensions are proved to be transition points for the scaling exponents of some partition functions defined from the wavelet transform modulus maxima. The generalization of this formalism to fractal signals is established for the class of distribution functions of these singular invariant measures. It is demonstrated that the Hausdorff dimensionD(h) of the set of singularities of Hölder exponenth can be directly determined from the wavelet transform modulus maxima. The singularity spectrum so obtained is shown to be not disturbed by the presence, in the signal, of a superimposed polynomial behavior of ordern, provided one uses an analyzing wavelet that possesses at leastN>n vanishing moments. However, it is shown that aC behavior generally induces a phase transition in theD(h) singularity spectrum that somewhat masks the weakest singularities. This phase transition actually depends on the numberN of vanishing moments of the analyzing wavelet; its observation is emphasized as a reliable experimental test for the existence of nonsingular behavior in the considered signal. These theoretical results are illustrated with numerical examples. They are likely to be valid for a large class of fractal functions as suggested by recent applications to fractional Brownian motions and turbulent velocity signals.     

Dynamics of a quantum particle in a static modulated magnetic field B=(0,0,B/cosh ((x−x 0)/δ))

Quantum motion of a particle with its massm and its chargee>0 in thex–y plane under the influence of the static unidirectionally modulated magnetic fieldB=(0,0,B/cosh²((x–x ₀)/)) is studied in this paper. We solved the single-particle problem exactly. Expressions for eigenenergies and eigenfunctions are found. Several physical phenomena are described: the energy spectrum separates into two parts which we call a discrete part and a continuous part—the discrete part of the spectrum corresponds with those states states which describe localized behavior in the direction of the field modulation; these states are extended in the perpendicular direction; the effective mass of this quasi-one-dimensional motion is found to be negative and dependent on the discrete quantum numbern—the states corresponding to the continuous part of the energy spectrum are found to be of two types: the reflection states, which are extended only in that part of thex–y plane where the effective potential barrier is small, and the states describing overbarrier motion in the whole plane; there exists a minimum of the energy for the states from this part of the spectrum which corresponds with a nonzero momentum of the particle motion in they-direction and almost zero momentum for thex-direction motion; there exists twofold degeneracy for those states from the continuous part of the spectrum for which their energy is lower than a certain value.     

FTIR Spectrophotometric Methods Used for Antioxidant Activity Assay in Medicinal Plants

Abstract: Fourier transform infrared spectroscopy (FTIR) is a fast and nondestructive analytical method. Associated with chemometrics, it is a powerful tool for research and industry. The present review discusses the antioxidant activities assay of some plants (fruits, leaves, aerian part) with medicinal properties using an FTIR spectrophotometric method in comparison with other ultraviolet-visible (UV-Vis) spectrophotometric methods. A good correlation was found between the different methods used for measuring the antioxidant capacity of some of these herbs.     

基于小波变换的人血清血卟啉荧光光谱分析法

卟啉是生命活动的重要物质,原卟啉可做为肿瘤血液标志物.人血清中血卟啉含量很低,且受多种因素影响.基于小波变换的人血清血卟啉荧光光谱分析法可实现对其弱信号的分辨.用多功能光谱测量系统获取人血清血卟啉荧光光谱,对获取的荧光光谱通过数次小波变换进行分解,将噪声与光谱信号分离,滤波后的荧光光谱进行6次分解后得到了离散逼近信号(a1～a6)和离散细节信号(d1～d6).信号频率随着分解次数的增加逐步降低.当分解到第6次时,出现了血卟啉荧光特征峰,成功地观测到血卟啉的荧光发射峰,实现了弱信号分辨,得到了血清中所含血卟啉的准确成份和定量信息,从而进行定性和定量分析,为血清荧光光谱用于肿瘤的早期诊断提供了一种方法.     

The norms and variances of the Gabor, Morlet and general harmonic wavelet functions

This paper deals with certain properties of the continuous wavelet transform and wavelet functions. The norms and the spreads in time and frequency of the common Gabor and Morlet wavelet functions are presented. It is shown that the norm of the Morlet wavelet function does not satisfy the normalization condition and that the normalized Morlet wavelet function is identical to the Gabor wavelet function with the parameter σ=1.The general harmonic wavelet function is developed using frequency modulation of the Hanning and Hamming window functions. Several properties of the general harmonic wavelet function are also presented and compared to the Gabor wavelet function. The time and frequency spreads of the general harmonic wavelet function are only slightly higher than the time and frequency spreads of the Gabor wavelet function. However, the general harmonic wavelet function is simpler to use than the Gabor wavelet function. In addition, the general harmonic wavelet function can be constructed in such a way that the zero average condition is truly satisfied. The average value of the Gabor wavelet function can approach a value of zero but it cannot reach it.When calculating the continuous wavelet transform, errors occur at the start- and the end-time indexes. This is called the edge effect and is caused by the fact that the wavelet transform is calculated from a signal of finite length. In this paper, we propose a method that uses signal mirroring to reduce the errors caused by the edge effect. The success of the proposed method is demonstrated by using a simulated signal.     

Inversion formula and Parseval theorem for complex continuous wavelet transforms studied by entangled state representation

In a preceding letter (2007 Opt.Lett.32 554) we propose complex continuous wavelet transforms and found Laguerre-Gaussian mother wavelets family.In this work we present the inversion formula and Parseval theorem for complex continuous wavelet transform by virtue of the entangled state representation,which makes the complex continuous wavelet transform theory complete.A new orthogonal property of mother wavelet in parameter space is revealed.     

舰船噪声小波谱提取方法研究

人耳听测舰船噪声的特征,是声纳员非常重要的专业技能。本文根据小波变换与人耳蜗频率响应相近似的特点,以cmor1-0.5母小波为基础,构造了一系列基于小波变换的滤波器组。对于小波谱提取中涉及的带宽、分辨率等参数进行了分析,提出了小波谱提取过程中改善分辨率的办法。为检验该方法的可行性,对三种不同类型的舰船噪声进行了小波谱分析,与其FFT谱图进行了比较。为解决小波谱提取过程中高分辨率与计算量的矛盾,提出了对指定频带进行小波谱分析的方法,解决了计算量的问题。     

奇偶二项式光场态的小波变换

利用有序算符内积分方法,小波变换可以表示为被转换态矢|f〉在压缩平移算符U(μ,s)作用下向母小波态矢〈ψ|转换的矩阵元〈ψ|U(μ,s)|f〉. 在此基础上,计算了奇、偶二项式态的小波变换,得到小波变换谱. 结果表明,小波变换谱可以起到识别这些量子力学态的作用,具有直观易辨的优点. 关键词： 小波变换 奇偶二项式态 有序算符内积分     

Performance analysis of multi-spectral and panchromatic image fusion techniques based on two wavelet discrete approaches

During the past few years, many fusion algorithms have been proposed to combine a high-resolution panchromatic image with a low-resolution multi-spectral image to generate a high-resolution multi-spectral image. Among them, the wavelet-based algorithm has gained its popularity due to its ability of multi-resolution decomposition. More specifically, the wavelet transform is first applied to images. The wavelet coefficients are then combined based on a certain rule to produce the fused image. In this paper, we evaluated the performances of both the wavelet transform discrete approaches and the coefficient combination methods when they are applied to fuse multi-spectral and panchromatic images. For the discrete approaches of the wavelet transform, Mallat and “à trous” algorithms are chosen. For the coefficient combination, the additive wavelet method, the additive wavelet intensity method and the additive wavelet principal component method are selected. To evaluate the spectral quality of the fused images, correlation coefficient and Q_avg index are used as a local and global measure, respectively. Meanwhile, average gradient and standard deviation are used to evaluate the spatial quality. Our experiments show that keeping the combination method the same, the “à trous” algorithm works better than the Mallat algorithm for the fusion purpose. In addition, if keeping the wavelet discrete algorithm the same, the combination methods mentioned above are found to have different advantages between the spatial resolution improvement and the spectral quality preservation.     

人血清血卟啉荧光光谱的双正交样条小波识别

人血清中血卟啉含量很低,其荧光光谱强度很弱,往往呈肩峰形态,难以识别其位置和荧光强度。双正交样条小波可实现对其弱信号的分辨。在血清背景荧光光谱上叠加血卟啉荧光信号,并改变其荧光强度,得到一系列强度改变的 血清血卟啉荧光光谱。用双正交样条小波bior5.5对获取的荧光光谱通过7次小波分解,将背景与卟啉荧光信号分离,得到了离散逼近信号(a₁～a₇)和离散细节信号(d₁～d₇)。结果 表明,信号频率随着分解次数的增加逐步降低。当分解到第7次时,出现了血卟啉荧光特征峰。信号峰的位置随着信号强度的下降蓝移约2.5 nm,而通过小波滤波器提取的信号峰的位置不变。随着信号的强度降低,信号峰的位置逐渐消失 ,因而其荧光强度与荧光峰的位置无法确定,而通过小波滤波器提取的信号则不受影响,且灵敏度高,从而实现了用双正交样条小波对人血清血卟啉荧光光谱的识别。由于小波变换是线性变换,离散细节信号保持信号原有的线性关系,可 以用来对血清中所含血卟啉的准确成份和定量信息,从而进行定性和定量分析,为血清荧光光谱用于肿瘤的早期诊断提供了一种方法。     

Vibrational Spectroscopy in Clinical Analysis

Abstract: Vibrational spectroscopy includes several different techniques, the most important of which are mid-infrared (IR), near-IR, and Raman spectroscopy. Raman and mid-IR spectroscopy are complementary techniques and usually both are required to completely measure the vibrational modes of a molecule. Vibrational spectrometry covers a series of well-established analytical methodologies suitable to be employed for both qualitative and quantitative purposes. In the first part of this review, we will focus on theoretical aspects related to vibrational techniques; in the second part, the most important papers, published during the period 2005–2014, related to clinical analysis performed with vibrational spectroscopy techniques will be critically discussed.     

Use of wavelet in specifying optics

Using power spectral density (PSD) function to specify large aperture optical components' quality of laser system is universal. But it cannot provide effective guidance to eliminate certain frequency segment error.In order to solve this problem, two-dimensional discrete wavelet transform (2D-DWT) is used to separate frequency segment error and detect the corresponding region of certain frequency segment error, which is used as feedback to a machining process. The experimental results show that the corresponding region of certain frequency segment can be found and machining can be guided effectively by using wavelet.     

烟气中SO_2紫外光谱的加性噪声去除及评价方法

用紫外差分吸收光谱法对烟气中主要污染物SO2测量中的噪声去除及信噪比评价的问题进行了研究.在获取被测气体吸收特征时,采用基于多分辨率的原始光谱预处理方法,在不同尺度下判断信号的能最幅度滤除加性噪声,并根据烟气光谱信号在时间序列上不会出现突变的特性,在含有吸收特征的尺度上提高有用信号强度.再使用吸收截面构造理想吸收信号改善光谱的信噪比评价.新的去噪方法分别在实验室和现场进行了验证.在实验室中,使用上述方法对SO2气体进行多次测量,平均偏差均小于1.5%,重复性不超过1%.在现场测量中,以一个气体浓度变化范围较大的山东电厂为例,在18组比对数据中,最大偏差为2.31%.实验结果说明,该方法可有效地提高加性噪声污染严重的光谱的信噪比.