基于双树复小波变换的非平稳时间序列去趋势波动分析方法

多重分形去趋势波动分析是研究非平稳时间序列非均匀性和奇异性的有效工具, 针对该方法中趋势项难以确定的问题, 提出一种基于双树复小波变换的方法, 实现了非平稳信号的多重分形自适应去趋势波动分析. 利用双树复小波变换提取信号的多尺度趋势和波动信息, 通过小波系数的希尔伯特变换确定每个时间尺度不重叠子区间的长度, 使多重分形分析具有信号自适应性及较高的计算效率. 以具有解析形式分形特征的倍增级联信号和分数布朗运动时间序列为例验证本文方法的有效性, 所得结果与解析解相吻合. 与传统的多项式去趋势多重分形方法相比, 本文方法根据信号自身特点自适应地确定信号的趋势和不重叠等长度子区间长度, 所得结果更加精确. 对倍增级联信号时间序列取不同的长度, 验证了算法的稳定性. 分别与基于极大重叠离散小波变换和离散小波变换多重分形方法进行比较, 表明本文方法具有更精确的结果和更快的运算速度.     

分段式线性拟合校正拉曼光谱基线漂移

基线漂移是目前光谱仪收集拉曼光谱时难以避免的现象,基线校正是光谱数据处理中一个不可或缺的重要步骤。针对传统的基于多项式拟合的基线校正方法存在的不足,本工作采用线性拟合的方法分段拟合背景基线,与计算机相结合,实现快速、准确、自动的基线校正;经聚苯乙烯小球、红细胞和酿酒酵母等多批次拉曼光谱数据处理的验证,表明该改进方法可以有效地对拉曼光谱进行基线校正,为进一步分析光谱数据提供更准确的信息,是一种可行的基线校正方法。     

基于分段硬化曲线的X射线CT射束硬化校正方法

研究了X射线CT射束硬化的形成机理,分析了射束硬化校正的常用方法,建立了以投影灰度为自变量的射束硬化校正模型,从而降低了射束硬化校正的计算难度。分析了采用多项式拟合射束硬化曲线的优缺点,提出一种基于多项式的分段硬化曲线表达新方法。该方法首先采用过原点的多项式曲线拟合硬化数据,然后通过所得多项式曲线的曲率变化,判断该曲线在拟合区间两端是否出现振荡,并对振荡部分的多项式曲线采用幂函数曲线进行替换,同时保证各段曲线在连接点处C1连续(曲线的C1连续定义为, 两条曲线交于一点且在交点处的一阶导数相等)。计算机CT仿真实验结果表明,该方法对理想CT图像和含噪CT图像的射束硬化校正,均表现出良好的稳定性,并可基本消除射束硬化造成的伪影。     

基于统计窗的恒星连续谱自动拟合方法

提出一种基于统计窗的恒星连续谱拟合方法。该方法将恒星光谱划分为若干个统计窗,在每个窗口内根据信噪比选取一定比例的流量点,然后对选出来的流量点进行低阶多项式迭代拟合,从而得到连续谱。实验表明,与其他方法相比,该方法得到的连续谱更接近于实际连续谱。该方法对SDSS中除M外的各种光谱型连续谱的拟合均具有很高的实用性和鲁棒性,对于郭守敬望远镜(LAMOST)先导巡天恒星光谱的连续谱拟合同样具有非常好的效果。     

A hybrid detrending method for fractional Gaussian noise

Determining trend and implementing detrending operations are important steps in data analysis. Yet there is neither precise definition of “trend” nor any logical algorithm for extracting it. In this paper, we propose a Hybrid Detrending Method (HDM) which is based on the Empirical Mode Decomposition (EMD) and the Detrended Fluctuation Analysis (DFA). Our method can remove the polynomial and sinusoidal trends from the fractional Gaussian noise (fGn) background. We illustrate the method by selected examples from artificial time series and climate data. In comparison with existing frequency domain based detrending methods, our method is a posteriori, the trend defined by our method is only derived from the data. Further, our method also preserves the scaling behavior of the original signals.     

基于最小二乘法多项式拟合三角测量模型研究

激光三角法具有非接触测量、测量范围大、相对测量精度高、结构简单、环境适应性强等多种优点, 得到了广泛应用。但是三角测量的理论公式具有非线性特征, 而且光学结构参数(a、b、θ)等在现实工程中具有不可测性。研究了三角测量中数学模型的建立方法, 选用多项式展开方法建立数学模型。通过应用最小二乘法拟合多项式的方法求解模型系数, 提出了根据最大相对拟合残差要求、结合相关系数用于控制拟合多项式阶数的评价方法, 并通过实际光学系统验证了该方法的可行性, 达到了0.01%的相对误差。最小二乘法拟合多项式的方法对于激光三角位移传感器的标定和系统误差消除具有实际的指导意义。     

Relationship between Continuum of Hurst Exponents of Noise-like Time Series and the Cantor Set

In this paper, we have modified the Detrended Fluctuation Analysis (DFA) using the ternary Cantor set. We propose a modification of the DFA algorithm, Cantor DFA (CDFA), which uses the Cantor set theory of base 3 as a scale for segment sizes in the DFA algorithm. An investigation of the phenomena generated from the proof using real-world time series based on the theory of the Cantor set is also conducted. This new approach helps reduce the overestimation problem of the Hurst exponent of DFA by comparing it with its inverse relationship with α of the Truncated Lévy Flight (TLF). CDFA is also able to correctly predict the memory behavior of time series.     

Frequency-selective quantification of biomedical magnetic resonance spectroscopy data

In this paper the possibility of obtaining accurate estimates of parameters of selected peaks in the presence of unknown or uninteresting spectral features in biomedical magnetic resonance spectroscopy (MRS) signals is investigated. This problem is denoted by frequency-selective parameter estimation. A new time-domain technique based on maximum-phase finite impulse response (FIR) filters is presented. The proposed method is compared to a number of existing approaches: the application of a weighting function in the time domain, frequency domain fitting using a polynomial baseline, and the time-domain HSVD filter method. The ease of use and low computational complexity of the FIR filter method make it an attractive approach for frequency-selective parameter estimation. The methods are validated using simulations of relevant (13)C and (31)P MRS examples.     

显微视觉自动聚焦研究

提出一种评估空域聚焦函数的方法。从计算时间与聚焦曲线变化率两个方面,提出四个参量作为评估依据．可从多个函数中筛选出最佳聚焦测度。针对研制的微对准装配自动聚焦系统的评估结果表明：灰度熵函数是适合于该系统的最佳聚焦测度。为克服聚焦搜索运动中的机械传动回差,提出不同于传统聚焦策略的“定位法”。该方法的核心是建立聚焦函数值与离焦量之间的函数关系,提出采用多项式拟合、高斯函数拟合以及样条插值拟合的方法可以构建这种函数关系;并给出了计算结果。最后综合灰度熵函数与定位法策略进行自动聚焦实验．得到自动聚焦精度为3．4μm;完成一次自动聚焦平均时间为3．3s。实验结果证明所述方法可以实现准确、实时地自动聚焦。     

不同滤波方法在去趋势波动分析中去噪的应用比较

研究了连续噪声和尖峰噪声对去趋势波动分析的影响,发现噪声的存在使得双对数曲线在尺度较小时发生了"转折"现象.针对这一问题,文中采用三种不同滤波方法对理想时间序列进行了实验,结果表明,多级Vondrak滤波得到的高频序列与真实噪声序列无论是在强度还是在演变趋势上都展现出惊人的一致性,低频滤波序列的去趋势波动分析结果与真实信号十分接近,多级Vondrak滤波基本上能够消除由于噪声所引起的"转折"现象,而且这一研究结果对于滤波周期阈值的依赖性并不太大.多点滑动加权平均滤波虽然能够在一定程度上减轻噪声对于去趋势波动的影响,但不能从根本上消除由于噪声所引起的"转折"现象.快速傅里叶滤波在选择合适的滤波周期阈值时,能够基本消除噪声对去趋势波动分析的影响,但是由于其滤波结果对于滤波周期阈值的依赖较大,在实际应用中滤波周期阈值的选取比较困难.因此,多级Vondrak滤波是消除噪声对去趋势波动分析结果影响的一种有效的途径. 关键词： 多级Vondrak滤波 去趋势波动分析 多点滑动加权平均滤波 快速傅里叶滤波     

Comparison of detrending methods for fluctuation analysis

We examine several recently suggested methods for the detection of long-range correlations in data series based on similar ideas as the well-established Detrended Fluctuation Analysis (DFA). In particular, we present a detailed comparison between the regular DFA and two recently suggested methods: the Centered Moving Average (CMA) Method and a Modified Detrended Fluctuation Analysis (MDFA). We find that CMA performs the same as DFA in long data with weak trends and is slightly superior to DFA in short data with weak trends. When comparing standard DFA to MDFA we observe that DFA performs slightly better in almost all examples we studied. We also discuss how several types of trends affect different types of DFA. For weak trends in the data, the new methods are comparable with DFA in these respects. However, if the functional form of the trend in data is not a-priori known, DFA remains the method of choice. Only a comparison of DFA results, using different detrending polynomials, yields full recognition of the trends. A comparison with independent methods is recommended for proving long-range correlations.     

基于B样条的拉曼光谱基线校正方法

基线漂移是光谱检测仪器普遍存在的现象,会对光谱信号的特征提取带来十分不利的影响,而基线校正是解决该问题的重要手段,也是拉曼光谱信号预处理的重要组成部分。基线校正的原理一般是通过拟合基线的方法来去除光谱信号中的基线漂移。传统的基线校正方法是利用多项式拟合的方法对拉曼光谱信号的基线进行拟合的,但是该方法容易出现过拟合和欠拟合现象,且拟合阶数难以确定。针对传统方法的缺点进行了改进,利用B样条方法对拉曼光谱信号的基线进行拟合,发挥B样条低阶光滑的优点,能够有效地克服多项式方法的缺陷。在实验中,利用该方法对孔雀石绿、罗丹明B的拉曼光谱信号进行了基线校正,观察并比较该方法和传统方法的校正结果。实验结果表明,该方法能够有效地消除拉曼光谱信号的基线漂移,在基线漂移较小和较大的位置,可以采用相同的拟合阶数,不会出现欠拟合和过拟合的现象,获得了良好的基线校正效果,为进一步分析光谱数据提供准确可靠的信息。     

A wavelet space based approach for Doppler ultrasound blood signals separation

In medical Doppler ultrasound systems, a high-pass filter which is usually employed to filter wall clutter components, will remove the information of the low velocity blood flow. To extract intact Doppler ultrasound blood signals, a novel approach is proposed based on the spatially selective noise filtration. The wall signals are firstly estimated by the spatially selective noise filtration from wavelet spatial correlation property. Then the wall clutters are exactly obtained by a wavelet threshold de-noising technique which eliminates the residual blood flow signals. Finally the intact blood flow signals are achieved by subtracting the wall signals from the mixed signals. This approach is applied to both computer simulated and in vivo carotid Doppler ultrasound signals. The experiment results show that the wavelet space based approach can exactly extract the blood flow signals, and achieve about 45% lower results in the mean absolute error than that of the high-pass filtering. This approach is expected to be an effective method to remove the wall clutters in Doppler ultrasound systems.     

基于B样条的TERS形貌成像背景扣除方法

在针尖增强拉曼光谱(TERS)形貌成像过程中，由于针尖与扫描台无法绝对平行、样品电子密度骤变处针尖快速升降以及扫描控制系统响应时间特性差等综合原因的影响，往往使形貌图中带有倾斜或边界面卷曲的成像背景。成像背景对样品形貌的识别和分析带来十分不利的影响，而背景扣除就是解决该问题的重要手段，也是形貌成像预处理的重要组成部分。背景扣除的原理一般是通过拟合背景的方法来扣除成像中的背景。传统的背景扣除方法是利用多项式拟合的方法对成像进行逐行的基线校正，但是该方法在处理形貌成像时常常会由于过拟合而造成样品形貌的失真，同时容易在图片上留下明显的线条纹理。针对传统方法的缺点，本文提出采用B样条曲面拟合方法，直接对样品形貌图进行曲面背景拟合，发挥B样条低阶光滑的优点，能够有效克服传统方法的缺陷。在实验中，同时利用传统方法和该方法对金单晶和合成金片的形貌图进行背景扣除，实验结果表明，两种方法都能够扣除样品形貌图中的成像背景，但与传统方法相比，所提出的方法不会造成样品形貌的失真，且不会留下线条纹理，获得了更加良好的背景扣除效果，为进一步分析样品形貌特征提供了更准确可靠的信息，是一种更加有效的TERS形貌成像背景扣除算法。     

DCCA cross-correlation coefficient: Quantifying level of cross-correlation

In this paper, a new coefficient is proposed with the objective of quantifying the level of cross-correlation between nonstationary time series. This cross-correlation coefficient is defined in terms of the DFA method and the DCCA method. The implementation of this cross-correlation coefficient will be illustrated with selected time series.     

Correlation between detrended fluctuation analysis and the Lempel–Ziv complexity in nonlinear time series analysis

We focus on the study of the correlation between the detrended fluctuation analysis (DFA) and the Lempel-Ziv complexity (LZC) in nonlinear time series analysis in this paper. Typical dynamical systems including logistic map and Duffing model are investigated. Moreover, the influences of the Gaussian random noise on both DFA and LZC are analyzed. The results show a high correlation between DFA and LZC, which can quantify the non-stationarity and the nonlinearity of the time series, respectively. With the enhancement of the random component, the exponent α and the normalized complexity index C show increasing trends. In addition, C is found to be more sensitive to the fluctuation in the nonlinear time series than α. Finally, the correlation between DFA and LZC is applied to the feature extraction of vibration signals for a reciprocating compressor gas valve, and an effective fault diagnosis result is obtained.     

基于重投影的多项式拟合校正射束硬化

在X射线工业CT(ICT)中,射束硬化会导致重建的图像出现伪影,甚至产生变形。为了消除这种影响,提出了一种基于重投影的多项式拟合校正射束硬化的方法。该方法对原始CT图像进行阈值分割二值化,将物体目标区域的像素值设为1;重投影此二值图像以获取X射线贯穿物体的长度集合;利用多项式拟合此长度集合与多色投影间的关系来建立射束硬化校正模型,用该模型对多色投影进行校正。与传统的多项式拟合校正方法相比,该方法不需要楔状模体(用于测量不同厚度下的衰减值,以此来建立射束硬化校正模型)。研究表明,该方法能有效地抑制射束硬化的影响。     

基于径向基函数神经网络的传感布里渊散射谱特征提取

基于布里渊效应的分布式光纤传感器以其可在沿光纤中同时获得被测量场时间和空间上的连续分布信息,成为当前国际的研究热点。根据光纤中布里渊散射谱的传输特点和高精度特征提取的要求,提出了利用莱文伯-马夸特(L-M)算法调节权值的径向基函数神经网络(RBFN)对布里渊散射谱进行特征提取。通过与反向传播(BP)神经网络、五次多项式曲线拟合法和三次样条插值法进行预测比较,在中心频率为11.213GHz,权重比为4∶1的仿真散射谱模型中,本方法相对误差最小,仅0.0015179%,温度相对误差仅为0.152℃,且拟合度较好。在不同脉宽和不同温度下的同一检测系统中,前者的综合评价指标优于其他三种拟合方法。数值分析和实验研究均表明径向基函数神经网络适用于对布里渊散射谱进行拟合,有效提高了预测精度。     

Scaling characteristics of ocean wave height time series

Fluctuations in the significant wave height can be quantified by using scaling statistics. In this paper, the scaling properties of the significant wave height were explored by using a large data set of hourly series from 25 monitoring stations located off the west coast of the US. Detrended fluctuation analysis (DFA) was used to investigate the scaling properties of the series. DFA is a robust technique that can be used to detect long-range correlations in nonstationary time series. The significant wave height data was analyzed by using scales from hourly to monthly. It was found that a common scaling behavior can be observed for all stations. A breakpoint in the scaling region around 4-5 days was apparent. Spectral analysis confirms this result. This breakpoint divided the scaling region into two distinct parts. The first part was for finer scales (up to 4 days) which exhibited Brown noise characteristics, while the second one showed 1/f noise behavior at coarser scales (5 days to 1 month). The first order and the second order DFA (DFA1 and DFA2) were used to check the effect of seasonality. It was found that there were no differences between DFA1 and DFA2 results, indicating that there is no effect of trends in the wave height time series. The resulting scaling coefficients range from 0.696 to 0.890 indicating that the wave height exhibits long-term persistence. There were no coherent spatial variations in the scaling coefficients.     

自基准哈特曼波前测量装置的研制

采用自基准哈特曼径向斜率测量原理,设计了旋转加摩擦线性移动扫描机构,对被测波前进行连续极坐标扫描采样;用CCD相机采集光斑图像,经波面径向斜率计算和泽尼克径向斜率多项式最小二乘拟合,求出被测波面的泽尼克系数和波前畸变值。与干涉仪测量结果进行了比较,所以研制的波前测量装置可满足大口径光学系统的像质测量。