Pattern recognition for rapid T2 mapping with stimulated echo compensation

Indirect echoes (such as stimulated echoes) are a source of signal contamination in multi-echo spin-echo T₂ quantification and can lead to T₂ overestimation if a conventional exponential T₂ decay model is assumed. Recently, nonlinear least square fitting of a slice-resolved extended phase graph (SEPG) signal model has been shown to provide accurate T₂ estimates with indirect echo compensation. However, the iterative nonlinear least square fitting is computationally expensive and the T₂ map generation time is long. In this work, we present a pattern recognition T₂ mapping technique based on the SEPG model that can be performed with a single pre-computed dictionary for any arbitrary echo spacing. Almost identical T₂ and B₁ maps were obtained from in vivo data using the proposed technique compared to conventional iterative nonlinear least square fitting, while the computation time was reduced by more than 14-fold.     

核能谱单能峰快速高精度高斯函数拟合算法研究

在核能谱分析中,高斯函数最小二乘拟合法是计算单能峰净峰面积常用的方法,该方法精度较高,但噪声敏感性较强,导致拟合出的高斯函数在峰位附近的残差向量较大。针对该问题,对高斯函数最小二乘拟合法进行了详细推导,分析了峰位附近残差向量较大的原因,提出了一种基于高斯函数最小二乘拟合法的高斯函数加权最小二乘拟合法,即在高斯函数最小二乘拟合法的基础上,引入了权重因子。该权重因子与取对数后数据权重削弱趋势相反或与数据本身趋势相符,以减小噪声敏感性。由于在求解高斯函数参数的过程中涉及到求逆矩阵运算,计算量较大,耗时较长,为了提高实时性,将求逆矩阵的运算过程转换为了简单的方程组运算,并给出了高斯函数的幅值、中心及方差参数的快速求解公式。将这两种方法用于55Fe的特征X射线单能峰的实际拟合中,结果表明,高斯函数加权最小二乘拟合法效果均较好,这说明该方法降低了噪声敏感性,减小了高斯函数在峰位附近的残差向量,进一步提高了拟合精度。另外,使用快速求解公式,也减小了运算量,增强了实时性,为在便携式设备中的有效使用提供了可能。     

荧光衰减曲线的一种多指数拟合方法

在荧光衰减测量中，总要遇到荧光衰减解卷积，进行非线性参数拟合问题。目前已有的非线性求极小值方法，都对参数估计值非常敏感，而且计算程序运行时间较长。我们建立了一种基于经典的步长加速法实现非线性最小二乘拟合，进行荧光衰减解卷积的方法，按程序给出参数初值，即能解卷积。     

光学非球面元件非球面度计算方法

详细介绍光学非球面元件非球面度计算的牛顿迭代法、近似法、最小二乘法3种方法，并根据工程实践比较了3种方法的优缺点，得出了工程应用中的结论：近似法适用于一些相对孔径较小的非球面，否则误差会较大；牛顿迭代法的精度较高，但计算量大也最复杂，且不能直接得到最接近参考圆的圆心位置坐标；最小二乘法的计算方法简单，不涉及求导、积分、迭代，适合编写计算程序，且可直接得到最接近参考圆的圆心位置坐标。     

On the mono-exponential fitting of phosphorescence decays

Several methods for mono-exponential fitting of decay curves are presented and compared among each other in terms of precision, accuracy and computational time. Simulated noisy data sets are generated and evaluated in order to determine the main contributors to a loss in performance. The influence of the temporal discretization of the decay curve on the precision of the fitting methods is discussed. Correlations between the background offset and the decay time are analyzed. Variations of the signal-to-noise ratio are shown, allowing for evaluation of systematic errors and precision in the presence of noise. Finally, the algorithms are applied to experimental data, and the computational efforts for the different algorithms are compared. The results of this latter investigation confirm the conclusions drawn from the simulated data and the following conclusions are drawn: The frequently applied method of performing a linear regression to the logarithm of a background-corrected decay showed systematic errors in the presence of noise. Best results in terms of precision and accuracy were obtained by a nonlinear least-squares approximation and a method denoted as the linear regression of the sum. Additionally, this latter method required the lowest computational time and is finally recommended for determining decay times from experimental data.     

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。     

一种线性最小二乘法的声源目标精确定位方法

在分析了声音能量距离衰减模型的基础上,提出了一种声源发射能量未知下的声源目标位置精确定位计算方法。将声音能量定位模型转化为非约束线性最小二乘法估计问题,其定位结果直接用代数解表示。同时对非约束线性最小二乘法下的参数进一步优化,提出了约束线性最小二乘法以提高定位精度。对信标节点位置坐标存在高斯噪声下的定位计算方法进行了改进以减少定位误差。仿真验证了该定位计算方法的有效性,数值模拟了不同观测信号噪声和信标节点位置噪声对定位误差的影响。结果同时表明,约束线性最小二乘法比非约束线性最小二乘法的定位误差更小,更接近于定位误差的克拉美罗下界值。      

Simultaneous Multi-Wavelength Study of the Reduction Reaction of Chromic Acid with Oxalic Acid Using a Photodiode Array Spectrophotometer

The reduction reaction of chromic acid by oxalic acid was studied by using a single beam photodiode array (PDA) spectrophotometer. The principal component analysis (PCA) and the target factor analysis (TFA) techniques were applied to handle the spectral data obtained and to determine the absorptivities of the light absorpting species involved as well as the rate constants of the reduction process. The result of computation confirms that an intermediate with an absorption spectrum similar to that of chromium (V) in the spectral range of 476 to 596nm was generated. The kinetic parameters obtained agree with those derived from the standard nonlinear least square fitting treatment and those reported in the literature.     

变焦距镜头高斯光学设计的新方法

突破了对像面漂移量的有理函数计算传统，考虑到组元运动曲线的间断性，给出了变焦距镜头高斯光学全新的最优化设计方法，供助于切比雪夫多项式，做到了任意组元联合直线运行的光学补偿，以及实现了简便的和有效的任意组元任意变焦方式的机械补偿。     

碲酸盐玻璃中稀土离子发光寿命的研究

掺稀土碲酸盐玻璃是宽带光纤放大器的一种非常重要的材料,具有传送区域宽、玻璃稳定性好等特点.讨论了在980 nm     

一种提高生物体拉曼光谱痕量测量精度的方法

微量物质拉曼光谱测量精度的提高是拉曼分析技术的难点之一,特别是高荧光背景下生物体中微量物质的测量。根据拉曼谱峰突发、离散特点,分别给出荧光背景和噪声拟合函数,通过监测总体拟合偏差A类不确定度函数实现拉曼谱峰定位和干扰信号滤波;进一步根据谱峰位置划分光谱区间,在单调区间内弱化非谱峰信号,实现谱峰信号增强。与其他光谱处理方法比较,可以准确拆分重叠特征峰,不会降低特征峰高度,提供更加灵敏的半谱峰面积指标。实验表明,该方法在处理皮肤拉曼光谱时,可以准确得到螺旋构象的酰胺I带、神经酰胺和CO的归属拉曼谱峰;另外经过该方法处理后数据建立水溶性糖(水稻叶片)含量测量模型,其精度优于小波分解、多项式拟合和非线性最小二乘法。     

氨气激光在线检测中浓度精确反演的研究

氨气是大气中含量最为丰富的碱性痕量气体,氨浓度检测是近年来环境和农业领域的一个重要研究方向。利用可调谐半导体激光吸收光谱(TDLAS)技术,结合波长高频扫描技术和多次反射池技术设计了氨气激光在线检测系统。通过激光中心波长锁定、背景基线拟合、吸收线型拟合、光强归一化和线性最小二乘拟合算法实现了氨浓度的精确反演。分析了系统性能,在24.32m光程下系统检测限为0.157mg/m3。使用该浓度反演方法实现了氨气的高灵敏、高精确在线检测。     

反演与拟合相结合处理核磁共振弛豫数据的方法

讨论非负最小二乘（NNLS）法和非线性拟合在分析处理核磁共振（NMR）弛豫数据中的应用.同时将二者结合，提出用NNLS的反演结果来设定非线性拟合初值的方法，并用计算机模拟和实验证明了该方法在分析处理NMR弛豫数据中的有效性. 关键词： 非负最小二乘法 非线性拟合 核磁共振 弛豫时间     

紫外傅里叶变换光谱仪干涉图数据处理

阐述了干涉图数据处理方法 ,采用紫外傅里叶变换光谱仪实验测量了汞灯光谱干涉图。使用四阶Blackman Harris窗函数作为切趾函数 ,采用最小二乘法拟和多项式对光源傅里叶变换光谱进行相位校正 ,获得了高精度的Hg紫外发射光谱     

Adaptive total linear least square method for quantification of mean transit time in brain perfusion MRI

Absolute quantification of cerebral blood flow (CBF), cerebral blood volume (CBV), and mean transit time (MTT) are of great relevance for clinical applications. One of the widely used methods for quantification of these parameters is gamma-variate fitting. Traditional nonlinear regression methods for gamma-variate fitting are inaccurate and computationally demanding. In this study, we developed an adaptive total least square method (ATSSL) to fit a gamma-variate function to the delayed concentration-time course. For each concentration-time curve, the beginning and ending time point of the curve are adaptively determined online. After the curves were fitted, a robust method for automatically determination of arterial input function (AIF) from whole and region of interest (ROI) was developed. Using the obtained AIF and fitted gamma-variate concentration-time curve, the MTT, CBV, and CBF were calculated by utilizing singular value decomposition algorithm. Computer simulations show that the suggested method is adaptive, reliable, and insensitive to noise. Comparison with the traditional nonlinear regression method indicated that the presented method is more accurate and faster to determine the CBV, CBF and MTT.     

基于自适应变异果蝇优化算法和广义回归神经网络的布里渊散射谱特征提取

针对布里渊光时域反射光纤传感系统散射谱的高精度特征提取的要求,提出了一种基于自适应变异果蝇优化算法和广义回归神经网络的布里渊散射谱特征提取算法。不仅利用了广义回归神经网络在逼近能力、学习速度、模型的泛化等方面具有的优势,而且采用搜索能力较强的自适应变异果蝇优化算法进一步增强了神经网络的学习能力,从而提高了布里渊散射谱的拟合度和频移提取的准确度。在布里渊散射谱中心频率为11.213 GHz,线宽为40～50,30～60和20～70 MHz的散射谱白噪声实验模型中,将新算法分别与基于有限元分析的Levenberg-Marquardt拟合法、粒子群优化和拉凡格式混合拟合法、最小二乘法进行预测比较,新算法获得的最大拟合频移误差为0.4 MHz,平均拟合度为0.991 2,均方根误差为0.024 1。仿真结果表明所提出的算法拟合度较好,绝对误差小。因此,将此算法用于基于布里渊光时域反射的分布式光纤传感系统,可有效提高布里渊散射谱的拟合度和频移提取的准确度。     

相对误差最小二乘法的TDLAS气体浓度标定曲线拟合

可调谐半导体激光光谱技术（TDLAS）是光谱检测技术的一个分支,具有高灵敏度、高分辨率、实时监测、便携性好、小型化等优点,在工业环保、医疗检测、气象监测等领域得到了广泛应用。TDLAS气体传感器的测量精度与标定曲线密切相关,标定时,常用最小二乘法对标定曲线进行多项式拟合,但最小二乘法是以绝对误差的最小平方和作为评价标准,无法对相对误差进行约束,在低浓度量程下TDLAS气体传感器的标定曲线相对误差偏大,限制了标定量程。推导了光强透射率对数与气体浓度关系式作为目标函数,提出了基于相对误差意义下的最小二乘法,迭代方法采用高斯-牛顿迭代法（Gauss-Newton iteration method）,实验以雅士林DHS-100恒温恒湿箱来产生大量程范围的水汽标定浓度,Vaisala HMT337在线湿度检测仪的测量值作为标定浓度,自主研发的TDLAS湿度传感器选择波数为7 306.752 1 cm-1的水汽吸收峰,气室的光路长为50 mm,对1%~50%VOL的水汽浓度进行了拟合标定,对比了最小二乘法与相对误差最小二乘法的标定拟合结果。实验结果表明：采用最小二乘法拟合时,在低浓度量程下会出现较大的相对误差,高浓度量程下相对误差逐渐减小,无法保证整个大量程下测量精度要求;采用相对误差最小二乘法拟合时,在整个大量程范围下的相对误差波动比较小,相对误差分布曲线比较平稳,最大相对误差和相对误差标准差都远小于最小二乘法的拟合结果;以Ratio-C关系式作为目标函数,采用相对误差最小二乘法进行拟合标定时,最大相对误差为0.049 4,相对误差标准差为0.023 7,远优于最小二乘法的拟合结果,符合TDLAS传感器测量精度要求,验证了相对误差最小二乘法的标定算法可靠性,提高了TDLAS气体传感器的测量精度。     

基于叶绿素荧光诱导动力学曲线的光合作用参数反演算法研究

快相叶绿素荧光诱导曲线中蕴含着丰富光合作用信息。该信息可以反映出植物的生存状态、病理以及受到胁迫时的生理变化趋势等多种信息。通过采集藻类荧光及诱导光信号, 拟合快相叶绿素荧光动力学曲线。基于最小二乘拟合方法,提出自适应最小误差逼近的方法对快相叶绿素荧光动力学曲线进行多元非线性回归拟合,实现F_o（固定荧光）、F_m（最大荧光产率）、σ_PSII（PSII的功能吸收截面）等细节参数的反演。实现了蛋白核小球藻光合作用参数反演,并实验了在Cu2+胁迫环境下,蛋白核小球藻的生理变化趋势。     

光点定位中的曲面拟合迭代算法

在光电检测系统中,需要对光点信号的位置实现亚像素定位。光纤从一端照明,由光纤另一端出射光点,由面阵CCD摄像机获取光点的灰度分布。基于最小二乘法,采用高斯曲面拟合算法拟合其分布,用高斯拟合函数的极值点作为光点的定位点。实验结果表明,采用多次迭代算法可以提高定位精度;拟合算法的稳定性(标准差)为0.7μm.高斯曲面拟合算法具有重复精度高、稳定性好的特点。     

Numeral eddy current sensor modelling based on genetic neural network

This paper presents a method used to the numeral eddy current sensor modelling based on the genetic neural network to settle its nonlinear problem. The principle and algorithms of genetic neural network are introduced. In this method, the nonlinear model parameters of the numeral eddy current sensor are optimized by genetic neural network （GNN） according to measurement data. So the method remains both the global searching ability of genetic algorithm and the good local searching ability of neural network. The nonlinear model has the advantages of strong robustness, on-line modelling and high precision. The maximum nonlinearity error can be reduced to 0.037% by using GNN. However, the maximum nonlinearity error is 0.075% using the least square method.