基于多重分形谱的高光谱数据特征提取

针对单一分形维数在高光谱数据处理中的不足,提出了一种基于多重分形谱的光谱信号奇异性特征提取方法,引入多重分形谱表征光谱曲线的奇异性特征.该方法根据分形测度将光谱曲线进行划分,用光谱概率测度计算配分函数,通过尺度指数的Legendre变换实现光谱曲线多重分形谱的提取,根据各类地物间的类别可分性准则Bhattacharyya距离选择有效特征,最后利用地物分类实验来验证该方法的有效性.实验结果表明,多重分形谱用于分类时分类精度达95.2%,当其维数为原数据波段数的10%时,总体分类精度仍可达82.2 %.多重分形谱表征了具有相同奇异性的波段子集的分形维数,准确的描述了光谱曲线的奇异性和分布特点,该方法能够有效地实现高光谱数据的特征提取.     

亚像素多重分形方法在图像处理中的应用

提出了一种用亚像素多重分形原理求取图像奇异性的新型算法,降低了单纯依靠整数像素位置灰度级梯度信息计算边缘测度所产生的误差。该算法结合CCD成像机理给出在亚像素位置的灰度级梯度分布规律,利用多重分形理论将实际图像分割成一系列具有不同奇异性指数的分形集合,对应着从边缘到纹理各层面的图像内容。模拟计算了投影小波中心点改变单位距离对边缘测度的影响程度,得出亚像素分割梯度的方法可以增加计算结果鲁棒性的结论。此方法用于标准图像的分割中,选用5×5亚像素数目提取的最奇异性集合与索贝尔(Sobel)算子(默认阈值为36.7920)提取的边缘的峰值信噪比为9.3981 dB。应用于复杂路面的裂纹提取中,其结果更符合人类的视觉观测。     

基于小波leaders的海杂波时变奇异谱分布分析

海杂波的奇异谱分析不仅能从理论上揭示海洋表面的动力学机理,同时也是对海探测雷达的关键技术之一.本文提出基于小波leaders的海杂波时变奇异谱分析方法,将时间信息引入海杂波的奇异谱分析之中,从而实现动态的解析描述海杂波随时间变化的奇异谱特性.在理论上,通过信号自身加窗,将时间信息引入传统的奇异谱(或称多重分形谱),实现了对海杂波时变奇异谱分布分析;在算法上,充分利用了小波leaders技术对于多种奇异性的提取能力(包括chirp奇异性和cusp奇异性),通过对时变奇异性指数和时变尺度函数的Legendre变换,实现对海杂波时变奇异谱分布的计算;在应用部分,采用经典的多重分形模型——随机小波序列(RWC)以及三级海态条件下连续波多普勒体制雷达海杂波进行仿真分析,实验结果表明:1)基于小波leaders的奇异谱分布能跟踪海杂波的时变尺度特性,有效展示其时变奇异性谱分布;2)算法具有较好的负矩特性和统计收敛性.该方法能为复杂非线性系统及随机多重分形信号分析提供参考.     

基于多重分形谱的光纤周界振动信号识别

为了有效识别光纤周界系统的振动信号,提出一种多重分形谱参数和改进概率神经网络相结合的光纤振动信号识别方法.该方法能够避免特征提取过程中需要选择经验阈值和模式识别过程中需要确定平滑因子的不足.首先,检验分析光纤振动信号多重分形的存在性和有效性.然后,计算和提取光纤振动信号的多重分形谱参数,构成能够准确描述信号非线性和复杂性特性的特征向量.最后,采用改进的概率神经网络算法进行自适应地学习和分类,实现对不同光纤振动信号的识别.采用现场实验采集的四种振动信号对该方法进行验证,结果表明,平均识别率达到96.25%,识别时间为1.63s.该方法在正确识别率方面优于传统的概率神经网络算法.     

多重分形降趋波动分析法和移动平均法的分形谱算法对比分析

多重分形降趋波动分析法(MFDFA)和多重分形降趋移动平均法(MFDMA)是用来估算一维随机分形信号多重分形谱的两种算法, 已被拓展应用于二维和高维分形信号的分析. 本文简要介绍了MFDFA和MFDMA算法及其在一维时间序列中的应用. 首次系统地从算法模型、计算统计精度、样本量的敏感性、无标度区选取的敏感性、矩选择的敏感性和计算量这六个方面对两种算法进行了对比分析, 以典型多重分形信号BMC信号为例, 分析两种算法的适用性和优劣性. 为实际应用中, 针对具体信号如何选用MFDFA或MFDMA算法, 以及两种算法的参数设置提供了有价值的参考.     

一种多尺度边缘测度融合加权HD算法

一般的边缘加权Hausdorff算法,由于单尺度边缘检测算子本身对噪音敏感,会造成真实和虚假边缘显著性差异小,从而加权后对噪音鲁棒性改善有限.为此,提出了一种基于多尺度边缘测度融合加权的Hausdorff景象匹配算法.对图像提取多尺度边缘测度后,引入证据推理理论,提出一种双向指数基本置信指派构造方法,并构造出多尺度边缘测度的基本置信指派函数,然后采用冲突再分配DSmT组合规则进行融合.为了进一步区别真实边缘与高频噪音,对加权Hausdorff公式进行了一些改进,给出了更为有效利用融和后边缘测度的加权Hausdorff公式.对可见光和SAR景象的匹配实验证明:本文算法所提取边缘在抑制噪音的同时保留了大量景象细节信息,并通过横向对比验证本文算法提高了噪音鲁棒性.     

液体可视图象序列中杂质小目标的检测方法（英）

在分析红外图象和可视图象差异的基础上,研究了一种适用于可视图象序列的运动小目标检测算法.受目标影响的象素点具有较弱的时间相关性,即相对普通象素点有较大的时间方差,根据此特征,用管道更新的方法产生新方差图象序列,再用管道更新的方法累积,增加信噪比,然后用基于统计均值的自适应门限方法分割出目标,最后将原图象的梯度倒数作为象素点强度的加权,有效地抑制灰度突变边界的传感器噪音,保存目标点.     

基于多个无标度区的多重分形分析方法

用计算机模拟生成了多重分形结构,通过对比分析结构的解析多重分形谱和配分函数法计算得到的多重分形谱,总结出多重分形谱可以描述结构在某一无标度区内生长规律的特性,发现结构的各个无标度区都具有研究价值,针对传统方法不能充分利用数据的缺陷,提出了基于多个无标度区的多重分形谱计算方法.     

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.     

基于小波的雷暴强放电前地面电场的多重分形分析

根据远离平衡的复杂系统演化的雪崩性和自相似倍增串级性，强调了多重分形工具的重要；利用青藏高原中部地区雷暴放电的地面电场仪资料，基于多重分形谱的小波估计方法，对强放电前雷电活动的多重分形特征进行了分析，发现多重分形谱可用推广的多重分形二项倍增串级模式描述，强放电前放电过程具有强烈的奇异性和明显的多重分形性，谱宽度Δα＞1.6，最小标度指数α_min＜-0.3；随着放电的活跃，Δα表现出明显的增加，而强的放电则发生在随后Δα的高值区或下降区，并对相关的原因进行了讨论. 关键词： 多重分形 雪崩 倍增串级 小波 闪电放电     

Using dithering for implementing geometric moment function estimation in a correlation retina

Correlation retinas measure the correlation product of an image projected on a sensor by optical means and a function f(x, y) stored in the retina. This optical correlation is well suited for the measurement of geometric moments, and this is why one can find in the literature several correlation retina circuits dedicated to it. Unfortunately, these architectures are not programmable and are dedicated to specific applications. Moment functions are of great interest in pattern recognition. This application needs to compute, for example, geometric moments whose order can depend on the application. Thus, the implementation of this function in a correlation retina requires a flexible architecture where the function f(x, y) can be modified to allow the measurement of the product of the image under analysis and f(x, y). The most robust solution is to memorize f(x, y) in memory devices distributed in the array of pixels constituting the retina. But, for technological problems, it is necessary to limit the number of bits used to store f(x, y) in the sensor. In this article, we propose to use dithering algorithms to code f(x, y) on only one bit. We present herein the architecture of the retina circuit on which we are currently working and show that it is possible to obtain approximate geometric moment values with it. The text was submitted by the authors in English.     

Relationships of exponents in multifractal detrended fluctuation analysis and conventional multifractal analysis

Multifractal detrended fluctuation analysis (MF-DFA) is a relatively new method of multifractal analysis. It is extended from detrended fluctuation analysis (DFA), which was developed for detecting the long-range correlation and the fractal properties in stationary and non-stationary time series. Although MF-DFA has become a widely used method, some relationships among the exponents established in the original paper seem to be incorrect under the general situation. In this paper, we theoretically and experimentally demonstrate the invalidity of the expression τ(q)=qh(q)-1 stipulating the relationship between the multifractal exponent τ(q) and the generalized Hurst exponent h(q). As a replacement, a general relationship is established on the basis of the universal multifractal formalism for the stationary series as τ(q)=qh(q)-qH'-1, where H' is the nonconservation parameter in the universal multifractal formalism. The singular spectra, α and f(α), are also derived according to this new relationship.     

Multifractal properties of the Indian financial market

We investigate the multifractal properties of the logarithmic returns of the Indian financial indices (BSE & NSE) by applying the multifractal detrended fluctuation analysis. The results are compared with that of the US S&P 500 index. Numerically we find that qth-order generalized Hurst exponents h(q) and τ(q) change with the moments q. The nonlinear dependence of these scaling exponents and the singularity spectrum f(α) show that the returns possess multifractality. By comparing the MF-DFA results of the original series to those for the shuffled series, we find that the multifractality is due to the contributions of long-range correlations as well as the broad probability density function. The financial markets studied here are compared with the Binomial Multifractal Model (BMFM) and have a smaller multifractal strength than the BMFM.     

Invariants and chaotic maps

A one-dimensional mapf(x) is called an invariant of a two-dimensional mapg(x, y) ifg(x, f(x))=f(f(x)). The logistic map is an invariant of a class of two-dimensional maps. We construct a class of two-dimensional maps which admit the logistic maps as their invariant. Moreover, we calculate their Lyapunov exponents. We show that the two-dimensional map can show hyperchaotic behavior.     

A multifractal study of wave functions in 1-D quasicrystals

Using multifractal analysis we study extended, self-similar and non-self-similar type of wave functions in the Fibonacci model. Extended states arising due to commutation of transfer matrices for certain blocks of atoms in quasiperiodic systems are shown to have the same signature as the Bloch states in terms of the singularity spectrum withf(α)=α=1. Numerically, however, the extended states show a typical multifractal behaviour for finite chain lengths. Finite size scaling corrections yield results consistent with that obtained analytically. The self-similar states at the band edges show a multifractal behaviour and they are energy dependent in the case of blocks of atoms arranged in a Fibonacci sequence. For non-self-similar states we obtain a non-monotonic behaviour off(α) as a function of the chain length. We also show that in cases where extended states exist, the cross-over from extended to non-self-similar states in gradual.     

Multifractal analysis of fracture morphology of poly(ethylene-co-vinyl acetate)/carbon black conductive composite

In this paper, based on scanning electron microscope (SEM), the fracture morphology of poly(ethylene-co-vinyl acetate)/carbon black (EVA/CB) conductive composite with various cross-linkers 2,4-di(2-phenylisopropyl) phenol (DCP) contents were analysed by multifractal analysis. The relationship among the multifractal spectrum, cross-linker DCP content, the fracture morphology, fracture process and some mechanical property were discussed. The results showed that the larger the width Δα (Δα = α_max − α_min) of the multifractal spectra f(α), the more nonuniform the fracture surface morphology, in other words, the more the roughness. Moreover, the width Δα (Δα = α_max − α_min) of the multifractal spectra f(α) is the result of competition between ductile fracture and brittle fracture. Also, some mechanical property will correspondingly change when various cross-linker DCP contents were added. Multifractal analysis showed that the spectrum width Δα (Δα = α_max − α_min) of the multifractal spectra f(α) could be used to characterize the surface morphology and mechanical property of EVA/CB conductive composite, quantitatively.     

Essentially different distributions of current in the inverse problem for the Grad-Shafranov equation

The paper answers a question debated by physicists for many years. It is proved that, for almost equal gradients of the magnetic flux u at its zero-level curve ∂ω, which is the piecewise smooth boundary of a simply-connected domain ω ⋐ ℝ², the inverse problem for the Grad-Shafranov equation of plasma equilibrium in a tokamak (in the cylindrical approximation) admits essentially different profiles of distributions f _u : ω ∋ (x, y) ↦ f(u(x, y)) = u _xx (x, y) + u _yy (x, y) ⩾ 0 in the class of third-order polynomials f(u) = Σ _m=0³ a _m u ^m .     

Low Temperature Properties for Correlation Functions in Classical N-Vector Spin Models

We obtain convergent multi-scale expansions for the one-and two-point correlation functions of the low temperature lattice classical N - vector spin model in d S 3 dimensions, N S 2. The Gibbs factor is taken as exp[-b(1/2 ||?f||² +l/8 || |f|² - 1 ||² + v/2||f- h||²)], \exp [-\beta (1/2 ||\partial \phi||^2 +\lambda/8 ||\, |\phi|^2 - 1 ||^2 + v/2||\phi - h||^2)], where f(x), h ? R^N\phi(x), h \in R^N, x ? Z^dx \in Z^d, |h|=1, b < ￥|h|=1, \beta < \infty, l 3 ￥\lambda \geq \infty are large and 0 < v h 1. In the thermodynamic and v ˉ 0v \downarrow 0 limits, with h = e₁, and j L ‘^½ ‘, the expansion gives áf₁(x)? = 1+0(1/b^1/2)\langle \phi_1(x)\rangle = 1+0(1/\beta^{1/2}) (spontaneous magnetization), áf₁(x)f_i(y)? = 0\langle \phi_1(x)\phi_i(y)\rangle=0, áf_i (x)f_i (y)? = c₀ D^-1(x,y)+R(x,y)\langle \phi_i (x)\phi_i (y)\rangle = c_0 \Delta^{-1}(x,y)+R(x,y) (Goldstone Bosons), i = 2, 3, ?, Ni= 2, 3,\,\ldots, N, and áf₁(x)f₁(y)?^T=R￠(x,y)\langle \phi_1(x)\phi_1(y)\rangle^T=R'(x,y), where |R(x,y)||R(x,y)|, |R￠(x,y)| < 0(1)(1+|x-y|)^d-2+r|R'(x,y)|< 0(1)(1+|x-y|)^{d-2+\rho} for some „ > 0, and c₀ is aprecisely determined constant.     

Invariant curves for area-preserving twist maps far from integrable

One-parameter families of area-preserving twist maps of the formF (x, y)=(x +y +f(x),y +f(x)) are considered. Various invariant curves, for the maps corresponding tof(x)=sin andf(x)=sinx+(1/50) sin(5x), are rigorously constructed forlarge values of the nonlinearity parameter . For larger values of , close to critical, some numerical experiments are briefly discussed.     

New enhancement of infrared image based on human visual system

Infrared images are firstly analyzed using the multifractal theory so that the singularity of each pixel can be extracted from the images. The multifractal spectrum is then estimated, which can reflect overall characteristic of an infrared image. Thus the edge and texture of an infrared image can be accurately extracted based on the singularity of each pixel and the multifractal spectrum. Finally the edge pixels are classified and enhanced in accordance with the sensitivity of human visual system to the edge profile of an infrared image. The experimental results obtained by this approach are compared with those obtained by other methods. It is found that the proposed approach can be used to highlight the edge area of an infrared image to make an infrared image more suitable for observation by human eyes.