一单元ICA-R快速算法

一单元参考独立成分分析是一种有效的利用先验信息抽取一个期望源信号的方法。峭度是随机变量非高斯性的一个经典度量。基于约束独立成分分析理论,以峭度的绝对值为对比函数推导出一种快速一单元ICA-R算法。并针对该算法的收敛特点,给出一个优选初值去提升算法的收敛速度。最后,通过计算机模拟实验验证了该算法的有效性,同时所给优选初值加快算法收敛的性能也得到验证。     

新CICA一单元ICA-R固定点算法

一单元参考独立成分分析是一种有效地利用先验信息抽取一个期望源信号的方法。针对基于峭度的快速算法抽取正确率较低的缺点,在两种常用近似性量度下对快速算法进行了理论分析,指出该方法抽取正确率低的原因,通过避免不等式约束失效的方法,基于新CICA提出了一种一单元ICA-R固定点算法。大量计算机模拟实验表明所提算法抽取性能和快速算法相当,但具有更快的收敛速度和更高的抽取正确率。     

基于LabWindows2010的统计信息处理及仿真分析

介绍峭度基本算法,利用LabWindows进行编程产生四阶统计量的回调函数,并利用高性能的模块化数据显示运行结果。最后将该程序的C语言转换成MATLAB的M语言,对LabWindows及MATLAB产生的图形进行对比分析,两条峭度曲线显示完全吻合。     

L-DACS中的信号分离算法的研究

L波段数字航空通信系统(L-DACS)是未来20年乃至更长时间航空通信需求的航空通信系统。为了解决接收机更好地区别有用信号,通过研究固定步长EASI算法和变步长EASI(VS-EASI)算法,提出一种基于优选估计函数的EASI峭度变步长(Q-EASI)算法。该算法根据信号的分离状态与峭度方差的关系,使步长随峭度方差的变化而变化,从而使收敛速度与稳态误差之间的矛盾得以缓解,并在信号分离的不同阶段使用不同的估计函数,使稳态误差得以减小。仿真验证,新算法相对于传统算法在稳定性和收敛速度上都有较大提高。     

基于LabWindows2010的统计信息处理及仿真分析

介绍峭度基本算法，利用LabWindows进行编程产生四阶统计量的回调函数，并利用高性能的模块化数据显示运行结果。最后将该程序的C语言转换成MATLAB的M语言，对LabWindows及MATLAB产生的图形进行对比分析，两条峭度曲线显示完全吻合。     

基于CSR-ICA模型的隐写信息盲提取算法

针对加性隐写模型,提出一种基于CSR-ICA的隐写信息盲提取算法。算法仅需一幅隐写图像,在满足ICA模型线性约束条件下得到载体信号的估计信号,通过Contourlet稀疏性表示（CSR）对模型输入信号进行前置处理,优化选取归一化峭度性较大的信号作为模型输入信号,将归一化峭度作为分离算法学习的目标函数,避免异常值给分离算法带来的误差。算法具有较好的综合性能,并且克服了Chandramouli算法的局限性,提取正确率平均为90％。仿真实验结果给出了算法的有效性验证。     

水声信道盲均衡的最小平方峭度恒模算法

用误差信号峭度定义了平方峭度代价函数，提出了盲均衡器权系数更新的最小平方峭度恒模算法，该算法更新方程中含有的误差信号峰度因子有效地消除了高斯性误差信号的影响，加快了收敛，减小了收敛后的均方误差和码间干扰。用负声速梯度水声信道，对算法的性能进行了仿真研究。结果表明：该算法在收敛速度，收敛后的均方误差及码间干扰等方面的性能优于常数模算法与最小平均峭度恒模算法。     

基于峭度准则的稀疏编码算法与仿真研究

针对自然图像压缩收敛速度慢的问题,提出一种新的基于峭度的绝对值和固定系数方差的稀疏编码SC(Sparse Coding)算法。该算法采用稀疏性惩罚函数来表示峭度大小,同时保证了图像特征系数的分散性与独立性,并维持图像重构误差和稀疏惩罚函数之间的平衡,能够更有效地提取图像的边缘特征和局部特征。通过选取合适的特征基函数,有利于加快所提出的SC网络的收敛速度。应用该算法可以成功地提取自然图像的特征基向量,进一步利用特征系数的稀疏性,有效实现自然图像的压缩。仿真实验结果表明,与基于标准独立分量分析(ICA)和离散余弦变换(DCT)的图像压缩方法相比,基于峭度准则的稀疏编码图像压缩方法具有较快的收敛速度及较好的有效性和实用性。     

偏度在独立元分析模型中的作用分析及算法设计

相对于峭度(kurtosis),偏度(skewness)历来在独立元分析(ICA)的研究中就没有得到充分重视.尤其是当关于峭度符号的一比特匹配定理在理论上被证明了以后,偏度似乎更是变成了ICA模型中的一个无用统计量.但当信号的峭度很小或者其非Gauss性主要源自于偏度时,仅仅利用峭度信息是不足够的.本文目的就在于分析和讨论在此种情况下独立元分析如何利用偏度信息.首先从理论上分析了偏度在ICA模型中的作用,结果表明在偏度上并不存在与峭度类似的一比特匹配定理,也就是说,算法中模型密度函数的选择无需考虑其偏度与源信号偏度的符号匹配问题.在此基础上,本文进一步提出了一套灵活的模型密度函数设计方法,并提出了一个算法实例,它可以适用于具有任意偏度和峭度组合的信号.     

一种改进的发动机曲柄连杆机构的可靠性分配算法

为了对发动机曲柄连杆机构的可靠性进行更合理的分配,提出了一种改进的可靠性分配算法。在对曲柄连杆机构进行可靠性分析的基础上,根据可靠性工程中可靠性成本函数的规律,构建了发动机曲柄连杆机构的可靠性预估成本函数,建立了曲柄连杆机构可靠性的分配模型,并根据可靠性与成本的微分性质,构建了以重要度最大单元为搜索单元逐步迭代的算法,该算法简单、易用。最后结合一个实例,验证了模型和方法的有效性与可行性。     

改进的一单元复数参考独立成分分析算法

一单元复数参考独立成分分析算法存在阈值参数难以确定的问题。通过将算法的目标优化函数巧妙地调整为期望提取信号的幅值和参考信号的近似性量度，基于机器学习原理和经典的Kuhn-Tucker条件提出一种改进的固定点算法，有效避免人为选取选择阈值参数和步长参数，降低了计算复杂度，并提高了算法收敛的稳定性和收敛速率。针对复数合成数据的仿真实验证实了所提算法的有效性。     

An improved method for independent component analysis with reference

Through incorporating a priori information available in some applications for independent component analysis (ICA) as the reference into the negentropy contrast function for FastICA, ICA with reference (ICA-R) or constrained ICA (cICA) is obtained as a constrained optimization problem. ICA-R achieves some advantages over earlier methods, whereas its computation load is somewhat high and its performance is strongly dependent on the threshold parameter. By alternately optimizing the negentropy contrast function for FastICA and the closeness measure for ICA-R, an improved method for ICA-R is proposed in this paper which can avoid the inherent drawbacks of ICA-R. The validity of the proposed method is demonstrated by simulation experiments.     

参考独立分量的正则化方法

参考独立分量分析（ICA with Reference,ICA-R）充分利用先验知识或参考信号,取得了很好的分离效果,但其中的阈值参数很难选取,且计算量很大。理论分析和实验表明,若阈值选取不当,算法甚至不收敛。通过在FastICA算法的负熵对比度函数中引入ICA-R算法中的接近性度量函数作为正则化项,得到一个简单的改进算法。针对合成数据和实际的ECG数据的仿真实验表明,算法收敛快、提取效果好,同时正则化参数取值非常灵活。     

A class of complex ICA algorithms based on the kurtosis cost function.

In this paper, we introduce a novel way of performing real-valued optimization in the complex domain. This framework enables a direct complex optimization technique when the cost function satisfies the Brandwood's independent analyticity condition. In particular, this technique has been used to derive three algorithms, namely, kurtosis maximization using gradient update (KM-G), kurtosis maximization using fixed-point update (KM-F), and kurtosis maximization using Newton update (KM-N), to perform the complex independent component analysis (ICA) based on the maximization of the complex kurtosis cost function. The derivation and related analysis of the three algorithms are performed in the complex domain without using any complex-real mapping for differentiation and optimization. A general complex Newton rule is also derived for developing the KM-N algorithm. The real conjugate gradient algorithm is extended to the complex domain similar to the derivation of complex Newton rule. The simulation results indicate that the fixed-point version (KM-F) and gradient version (KM-G) are superior to other similar algorithms when the sources include both circular and noncircular distributions and the dimension is relatively high.     

A fast algorithm for one-unit ICA-R

Independent component analysis (ICA) aims to recover a set of unknown mutually independent source signals from their observed mixtures without knowledge of the mixing coefficients. In some applications, it is preferable to extract only one desired source signal instead of all source signals, and this can be achieved by a one-unit ICA technique. ICA with reference (ICA-R) is a one-unit ICA algorithm capable of extracting an expected signal by using prior information. However, a drawback of ICA-R is that it is computationally expensive. In this paper, a fast one-unit ICA-R algorithm is derived. The reduction of the computational complexity for the ICA-R algorithm is achieved through (1) pre-whitening the observed signals; and (2) normalizing the weight vector. Computer simulations were performed on synthesized signals, a speech signal, and electrocardiograms (ECG). Results of these analyses demonstrate the efficiency and accuracy of the proposed algorithm.     

一种参考独立成分分析算法在弱信号提取中的应用

独立成分分析(Independent Component Analysis,ICA)是解决盲源分离问题十分有效的方法。特别是Fast-ICA算法,它以中心极限定理为出发点,采用定点迭代的优化算法,收敛快速、稳健。但是在提取弱信号时,由于中心极限定理不再严格成立,FastICA算法也不再适用。因此从理论和实验两个方面着手验证了这个观点,并针对弱信号提取问题提出新的解决思路:在FastICA算法的基础上,引入源信号的部分先验信息作为约束,即参考独立成分分析(Independent Component Analysis with Reference,ICA-R)。若已知源信号的部分功率谱,结合加权范数最小化信号外推算法的思想,建立接近性度量,以约束的形式融入FastICA算法中,从而分离出要求的弱信号。实验结果表明,不管是对模拟信号还是真实的脑电信号,该算法都是有效的。     

A reference-based blind source extraction algorithm

By utilizing a priori information available as reference, constrained independent component analysis (cICA) or independent component analysis with reference (ICA-R) achieves some advantages over other methods. However, ICA-R is very time-consuming; moreover, it is very difficult to determine its threshold parameter, once the value is improperly chosen the algorithm will fail to converge. In order to overcome these drawbacks, a very simple blind source extraction method, whose optimization function is simply the closeness measure between the desired output and its corresponding reference in ICA-R, is proposed in this paper. Experiments with synthesized data and real-world electrocardiograph data confirm its validity and superiority.     

Principal kurtosis analysis and its application for remote-sensing imagery

Fast Independent Component Analysis (FastICA) is the commonly used feature extraction method for non-Gaussian structure data and it is often used in multispectral/hyperspectral image processing. However, FastICA requires all pixels to be involved at each iteration. Therefore, it is a very time-consuming method when the total number of iterations is large. In this study, we propose an equivalent algebraic method for FastICA when selecting kurtosis as a non-Gaussian index. We name this new method principal kurtosis analysis (PKA). The feature extraction result of PKA is equivalent to that of FastICA when considering kurtosis as the measurement of non-Gaussianity. Similar to FastICA, PKA also applies the fixed-point iteration method to search for extreme kurtosis directions. However, when computing the projected direction in the iteration process, PKA only requires a co-kurtosis tensor and not all of the pixels. Therefore, this reduces the time complexity. The proposed algorithm (PKA) has been applied on multispectral and hyperspectral images and shows its time advantage in the experiments.