基于贝塞尔函数的莱斯因子矩估计算法改进

针对传统的莱斯K因子一二阶矩估计方法因贝塞尔函数存在计算复杂度大、实用性低的问题，提出一种基于贝塞尔函数阶数的莱斯因子矩估计算法。该算法首先根据原矩估计公式计算◢K◣值对应的矩估计值，然后根据不同阶数的贝塞尔近似公式计算矩估计值并求解对应的◢K◣值，计算估计准确率，进而确定贝塞尔函数阶数的选择，简化矩估计算法。实验研究表明，所提方法与原方法相比降低了时耗，在◢K◣值较小时效果更优。     

基于AR模型和ZMNL变换的K分布海杂波仿真方法

海杂波统计模型的研究对最优检测算法设计和雷达性能预估有重要作用。文章介绍了一种基于AR模型和ZMNL变换的K分布海杂波仿真方法,结合ACI准则和Yule-Walker方程,利用Levinson-Durbin递推关系式求解AR模型的阶数和参数,将生成的高斯序列通过线性滤波器产生服从K分布的相关序列。仿真结果表明,无论是功率谱还是概率分布都与理想分布相吻合。     

船载高频地波雷达一阶海杂波仿真模型研究

船载高频地波雷达(High Frequency Surface Wave Radar, HFSWR)海杂波仿真模型的建立对于有效海杂波抑制方法的提出具有重要指导意义。针对目前一阶海杂波模型存在的问题，提出了改进的船载HFSWR一阶海杂波空时分布模型。首先分析了船载平台在相参积累周期内前向运动对海杂波回波入射角的影响，提出了不同距离元海杂波子块入射角随时间变化的规律，并由此导出新的一阶海杂波时空分布模型、海杂波回波信号模型、以及目标回波模型。仿真结果表明，生成的海杂波数据的分布特性比传统模型更加接近实测海杂波的分布特性，为以后船载HFSWR海杂波有效抑制算法的研究提供较好的仿真数据支持。     

基于时频分析的海杂波背景下舰船目标检测

为了克服基于小波尺度谱重排的时频分析方法中时、频分辨率不佳及时频分布可读性较差等问题,本文提出了一种基于参数优化Morlet小波变换和奇异值分解的海杂波背景下舰船目标检测算法。算法首先利用Shannon小波熵作为目标函数,根据高频地波雷达信号的特点自适应地优化Morlet小波变换的时间带宽积参数,使得后续重排尺度谱的时、频分辨率同时达到最佳。然后再对重排小波尺度谱进行基于奇异值分解的降噪处理,以抑制环境噪声的影响,进一步提高时频分布的可读性。实验结果表明：与传统的时频分析算法相比,本文提出的算法具有更好的时频聚集性和较强的噪声抑制能力,能有效地检测海杂波背景下缓慢运动的匀速和匀加速舰船目标。     

海杂波复合K分布模型的参数估计

海杂波幅度分布特性对雷达海面目标检测与识别、信号处理以及性能评估均有重要意义。在高分辨率雷达中,复合K分布模型对海杂波的实测数据具有很好的拟合效果。采用粒子群优化算法进行海杂波模型的参数估计,重点研究粒子群算法中的惯性权重和学习因子的选择以及边界问题的处理,并利用CSIR组织公布的雷达实测数据进行仿真,估计结果通过均方差检验评估参数估计效果,结果表明:粒子群优化算法具有良好的适应性和估计精度,验证了改进算法的有效性。     

分数阶Fourier域低分辨雷达飞机回波的分形特性分析与目标分类

常规低分辨雷达体制下的目标分类与辨识是雷达目标识别领域的一个研究难点。研究表明,地、海、空等雷达杂波具有分形特性,不同类型目标会对回波分形特性产生不同的影响,但在强杂波背景下,回波的分形特性更多地表现为杂波的特性。作为一种非平稳信号分析工具,分数阶Fourier变换可以有效地获取目标回波信号的细节特征并充分抑制杂波,且具有快速算法。为此,论文立足于分形及其相关理论,拟从分数阶Fourier域对常规雷达飞机目标回波的分形特性进行分析,估计和分析其分形参数,并对分数阶Fourier域回波分形特征在飞机目标分类中的应用进行探讨。研究结果表明,在最优变换阶数下,分数阶Fourier域飞机目标回波具有显著的分形特性,且充分反映了目标的特性,分形测度分析可以揭示回波的动力学演化机制,且最优变换域回波分形特征可以有效用于飞机目标的分类和识别。     

分数阶的Zernike矩

为改善Zernike矩的抗噪、重构等性能,将仅能取整数阶的传统Zernike矩推广为分数阶Zernike矩,提出一种分数阶Zernike矩构造算法.首先改造传统Zernike多项式的径向部分,以分数阶多项式替代传统Zernike矩中的整数阶多项式,使传统的Zernike矩仅是这种构造的特例;其次证明了所提分数阶Zernike矩的正交性和旋转不变性.实验结果表明,该算法可构造出比传统Zernike矩重构性能好、抗噪性能强的分数阶Zernike矩.     

一种基于自适应背景杂波模型的宽幅SAR图像CFAR舰船检测算法

利用海洋宽幅SAR图像进行大范围海域舰船检测在海洋监视、军事侦察等方面具有重要应用。由于海况的复杂性,宽幅SAR图像背景杂波特性随海域不同而变化。采用双参数CFAR检测算法和基于K分布CFAR检测算法在处理宽幅SAR图像时,由于在待检测的所有区域采用同种背景杂波模型,导致使用的杂波模型在不适应区域失配,使CFAR检测性能下降。针对这个问题,提出了一种基于自适应背景杂波模型的CFAR宽幅SAR图像舰船检测算法,该算法通过背景窗口的多尺度统计方差判断目标所处的杂波环境,自适应选择对应的背景杂波分布模型,最后根据已知的恒虚警率及选择的杂波概率密度函数进行CFAR检测。对20多幅宽幅SAR图像进行了试验,实验结果表明:该算法在检测精度上有明显的改善。     

基于非对称Lanczos 算法的线性分数阶系统模型降阶方法

采用非对称Lanczos 算法研究线性分数阶系统的模型降阶问题, 提出一种保持系统传递函数一定数量的分数阶矩的模型降阶方法. 根据Caputo 导数的运算法则给出线性分数阶系统的分数阶矩的计算方法; 利用非对称Lanczos 算法构造对应的非对称三对角矩阵; 根据非对称三对角矩阵的性质证明降阶系统与原系统具有相同的一定数量的分数阶矩; 给出降阶系统与原系统传递函数的误差估计, 为合理选择降阶系统的阶次提供理论依据. 数值实例的计算结果验证了所提出方法的有效性.

     

基于改进的布谷鸟搜索算法对分数阶生物系统的参数估计

近年来,非线性分数阶系统的参数估计问题已经在许多科学和工程领域特别是计算生物学中,引起了广泛的兴趣.本文针对分数阶生物系统的参数估计问题,将系统参数和分数阶导数同时作为独立的未知参数来进行估计,并提出了一种改进的布谷鸟搜索(improved cuckoo search, ICS)算法来求解该问题.在ICS算法中,通过引入一个自适应参数控制机制,同时结合反向学习方法,从而达到提高算法收敛速度和估计值精度的目的.最后,以三种经典的分数阶生物动力系统模型为例进行了数值仿真,其中还考虑了有测量误差和噪声数据的情形.仿真结果表明ICS算法具有良好的适应性、较高的收敛可靠性及精度,为求解非线性分数阶系统参数估计问题提供了一种有效工具.     

Cross-weighted moments and affine invariants for image registrationand matching

A framework for deriving a class of new global affine invariants for both object matching and positioning based on a novel concept of cross-weighted moments with fractional weights is presented. The fractional weight factor allows for a more flexible range to balance between the capability to discriminate between objects that differ only in small shape details and the sensitivity of small shape details to the presence of the noise. Moreover, it makes it possible to arrive at low order (zero order) affine invariants that are more robust than those derived from higher order regular moments. The affine transformation parameters are recovered from the zero and the first order cross-weighted moments without requiring any feature point correspondence information. The equations used to find the affine transformation parameters are linear algebraic. The sensitivity of the cross-weighted moment invariants to noise, missing data, and perspective effects is shown on real images     

基于局部窗口K分布的快速舰船检测算法

针对局部窗口K分布检测算法运算速度慢、计算效率低的问题,提出了一种基于局部窗口K分布的快速舰船目标检测算法。该算法首先采用迭代分割算法对原始合成孔径雷达(SAR)图像进行预筛选处理,根据预筛选选出潜在目标,在原始SAR图像中剔除潜在目标像素;然后利用背景图像计算二阶和四阶积分图像,在每一个像素点处采用滑动窗口的方式,在积分图像中进行加减计算确定所在位置的二四阶矩并估计K分布的参数;其次,确定概率密度函数后,通过求解函数得到检测阈值,根据检测阈值确定感兴趣区域;最后,通过模糊差影的鉴别方法对目标中的虚警目标进行进一步剔除,进而完成检测。通过实测SAR图像检测实验,积分算法与局部窗口的K分布算法相比将运算所需时间降低了50%,基于模糊差影的鉴别算法将品质因素由44.4%提高到100%。所提算法既保证了算法的实时性,又提高了检测的精度,在进行SAR舰船自动检测方面具有一定的应用价值。     

Efficient computation of Zernike and Pseudo-Zernike moments for pattern classification applications

Two novel algorithms for the fast computation of the Zernike and Pseudo-Zernike moments are presented in this paper. The proposed algorithms are very useful, particularly in the case of using the computed moments, as discriminative features in pattern classification applications, where the computation of single moments of several orders is required. The derivation of the algorithms is based on the elimination of the factorial computations, by computing recursively the fractional terms of the orthogonal polynomials being used. The newly introduced algorithms are compared to the direct methods, which are the only methods that permit the computation of single moments of any order. The computational complexity of the proposed method is O(p ²) in multiplications, with p being the moment order, while the corresponding complexity of the direct method is O(p ³). Appropriate experiments justify the superiority of the proposed recursive algorithms over the direct ones, establishing them as alternative to the original algorithms, for the fast computation of the Zernike and Pseudo-Zernike moments.     

伪Zernike矩不变性分析及其改进研究

伪 Zernike矩是基于图象整个区域的形状描述算子 ,而基于轮廓的形状描述子 ,例如曲率描述子、傅立叶描述子和链码描述子等是不能正确描述由几个不连接区域组成的形状的 ,因为这些算子只能描述单个的轮廓形状 .同时 ,由于伪 Zernike矩的基是正交径向多项式 ,和 Hu矩相比 ,除了具有旋转不变性、高阶矩和低阶矩能表达不同信息等特征外 ,还具有冗余性小、可以任意构造高阶矩等特点 ,另外 ,伪 Zernike矩还可以用于目标重构 .目前 ,伪 Zernike矩没有得到广泛的应用 ,其中的一个主要原因是 ,它不具备真正意义上的比例不变性 .为了能使伪Zernike矩得到更广泛的应用 ,在详细分析伪 Zernike矩不变性的基础上 ,提出了伪 Zernike矩的改进方法 ,使改进后的伪 Zernike矩在保持旋转不变性的同时 ,还具有真正意义上的比例不变性 ,同时给出了部分的实验分析结果 .实验结果证明 ,该改进后的伪 Zernike矩较改进前的伪 Zernike矩 ,具有更好的旋转和比例不变性 .     

INFORMATION AND SELF-ORGANIZATION REVISITED VIA COMPLEX-VALUED FRACTIONAL BROWNIAN MOTION OF ORDER n

Haken obtained many interesting results on information and self-organization by using Jaynes' maximum entropy principle with constraints in the form of given values of state moments up to the fourth order. The basic contention of this approach lies on the selection of these constraints, for the very reason that the result so obtained depended heavily upon them. The mean values of the state moments are quite acceptable and understandable, but why not the fifth one? In this paper, it is shown that the use of complex valued fractional Brownian motion of order n can contribute to answering this question. In addition, one examines how Haken's results are modified when the disturbing random term is not a Gaussian white noise, but a fractional Gaussian white noise of order n. The effect of such a noise on the stability of dynamical systems is analyzed. The key is that one has to consider much more state moments than when one works with Gaussian white noise.     

An LP-based hyperparameter optimization model for language modeling

In order to find hyperparameters for a machine learning model, algorithms such as grid search or random search are used over the space of possible values of the models’ hyperparameters. These search algorithms opt the solution that minimizes a specific cost function. In language models, perplexity is one of the most popular cost functions. In this study, we propose a fractional nonlinear programming model that finds the optimal perplexity value. The special structure of the model allows us to approximate it by a linear programming model that can be solved using the well-known simplex algorithm. To the best of our knowledge, this is the first attempt to use optimization techniques to find perplexity values in the language modeling literature. We apply our model to find hyperparameters of a language model and compare it to the grid search algorithm. Furthermore, we illustrate that it results in lower perplexity values. We perform this experiment on a real-world dataset from SwiftKey to validate our proposed approach.     

Multi‐Scale Kernels Using Random Walks

We introduce novel multi‐scale kernels using the random walk framework and derive corresponding embeddings and pairwise distances. The fractional moments of the rate of continuous time random walk (equivalently diffusion rate) are used to discover higher order kernels (or similarities) between pair of points. The formulated kernels are isometry, scale and tessellation invariant, can be made globally or locally shape aware and are insensitive to partial objects and noise based on the moment and influence parameters. In addition, the corresponding kernel distances and embeddings are convergent and efficiently computable. We introduce dual Green's mean signatures based on the kernels and discuss the applicability of the multi‐scale distance and embedding. Collectively, we present a unified view of popular embeddings and distance metrics while recovering intuitive probabilistic interpretations on discrete surface meshes.     

Methodology for shape optimization of ultrasonic amplifier using genetic algorithms and simplex method

Designing devices for ultrasonic vibration applications is mostly done by intuitively adjusting the geometry to obtain the desired mode of vibration at a specific operating frequency. Recent studies have shown that with optimization methods, new devices with improved performance can be easily found. In this investigation, a new methodology for designing an ultrasonic amplifier through shape optimization using genetic algorithms and simplex method with specific fitness functions is presented. Displacements at specific functional areas, main functionality, and mode frequency are considered to determine the properties of an individual shape to meet the stated criteria. Length, diameter, position of mountings, and further specific geometric parameters are set up for the algorithm search for an optimized shape. Beginning with genetic algorithms, the basic shape fitting the stated requirements is found. After that the simplex method further improves the found shape to most appropriately minimize the fitness function. At the end, the fittest individual is selected as the final solution. Finally, resulting shapes are experimentally tested to show the effectiveness of the methodology.     

A genetic algorithm and a particle swarm optimizer hybridized with Nelder–Mead simplex search

This paper integrates Nelder–Mead simplex search method (NM) with genetic algorithm (GA) and particle swarm optimization (PSO), respectively, in an attempt to locate the global optimal solutions for the nonlinear continuous variable functions mainly focusing on response surface methodology (RSM). Both the hybrid NM–GA and NM–PSO algorithms incorporate concepts from the NM, GA or PSO, which are readily to implement in practice and the computation of functional derivatives is not necessary. The hybrid methods were first illustrated through four test functions from the RSM literature and were compared with original NM, GA and PSO algorithms. In each test scheme, the effectiveness, efficiency and robustness of these methods were evaluated via associated performance statistics, and the proposed hybrid approaches prove to be very suitable for solving the optimization problems of RSM-type. The hybrid methods were then tested by ten difficult nonlinear continuous functions and were compared with the best known heuristics in the literature. The results show that both hybrid algorithms were able to reach the global optimum in all runs within a comparably computational expense.     

基于伪Zernike矩的图像识别

研究和分析了伪Zernike矩的位移及尺度不变特性。利用此特性，对图像识别中的一种情况，即不同位移及不同尺度下同一目标的识别提出了新的方法。通过计算目标图像的高阶伪Zernike矩模值，再利用聚类方法进行分类。实验结果表明，伪Zernike矩对于不同尺度目标的识别具有很好的作用。