A simplified approach to independent component analysis

Independent Component Analysis (ICA) is one of the fastest growing fields in the area of neural networks and signal processing. Blind Source Separation (BSS) is one of the applications of ICA. In this paper, ICA has been used for separating unknown source signals. BSS is used to extract independent signal components from their observed linear mixtures at an array of sensors. Various statistical techniques based on information theoretic and algebraic approaches exist for performing ICA. In this paper, we have used an objective function based on independence criterion of the signals. Optimisation of this objective function yields a neural algorithm along with a non-linear function for signal separation. Performance of the algorithm for artificially generated signals as well as audio signals has been evaluated.     

基于语音信号稀疏性的FDICA初始化和后处理方法

目前解决语音信号盲源分离(Blind source separation,BSS)的两大类方法分别为频域独立成分分析(Frequency domain independent component analysis,FDICA)和基于稀疏性的时频掩蔽(Time frequency masking,TF masking).为此将两类方法优点相结合,利用TF masking方法的结果,对FDICA做初始化,在加快FDICA收敛速度的同时也避免了次序不确定性问题.此外还提出了一种新的基于语音稀疏性FDICA的BSS后处理方法:基于局部最小比例控制(Local minimum ratio controlled,LMRC)谱减法,比常规的TF masking、维纳滤波等后处理方法,能够更有效地控制音乐噪声,提高分离性能.合成数据和实际采集数据的实验结果验证了所提方法的有效性.     

基于独立分量分析的电磁场信号工频干扰消除

为了解决电磁场信号测量中的工频及其谐波干扰问题,将盲源分离(BSS)应用于电磁场信号的工频干扰消除.从盲源分离和独立分量分析(ICA)的统一模型出发,分析了快速ICA算法和最大信噪比ICA算法的目标函数选择及算法推导,并分别对计算机随机产生不同波形信号和实测的电磁场信号进行分离,结果显示:无论从相似系数还是运算时间上看,最大信噪比ICA算法明显优于快速ICA算法.     

基于核独立成分分析的盲源信号分离

独立成分分析(ICA)已经广泛用于盲源信号的分离(BSS)。论文介绍了基于核空间的ICA的原理和基本算法,然后介绍了该算法与典型ICA和主成分分析(PCA)在盲源信号分离中的比较。实验表明在盲源信号分离中,基于核空间的ICA与其他典型ICA和PCA算法相比更具有准确性和鲁棒性。     

基于fMRI瞬时功率的独立成分分析

独立成分分析(independent component analysis,ICA)采用一种统计隐变量模型,假设信号是由各信源线性叠加构成.为了解决功能磁共振数据(functional magnetic resonance imaging,fMRI)中由于信源非线性叠加造成的ICA检测误差,提出了基于瞬时功率的ICA方法.首先,由电流能量形式将fMRI数据推广为fMRI能量信号;然后,由血氧水平依赖(blood oxygenation level dependent,BOLD)信号与T2*信号的关系,给出了两种反映BOLD能量变化的瞬时功率fMRI信号;最后,采用空间ICA分析fMRI瞬时功率信号,得到与各脑部活跃区域能量相关的独立成分.从理论和仿真试验两个方面阐明了新方法的合理性和优越性,同时应用于实际癫痫fMRI数据,经与传统ICA方法比较,该方法能够在静息态下鲁棒地检测脑部能量异常区域.     

Adaptive blind separation of underdetermined mixtures based on sparse component analysis

The independence priori is very often used in the conventional blind source separation （BSS）. Naturally, independent component analysis （ICA） is also employed to perform BSS very often. However, ICA is difficult to use in some challenging cases, such as underdetermined BSS or blind separation of dependent sources. Recently, sparse component analysis （SCA） has attained much attention because it is theoretically available for underdetermined BSS and even for blind dependent source separation sometimes. However, SCA has not been developed very sufficiently. Up to now, there are only few existing algorithms and they are also not perfect as well in practice. For example, although Lewicki-Sejnowski＇s natural gradient for SCA is superior to K-mean clustering, it is just an approximation without rigorously theoretical basis. To overcome these problems, a new natural gradient formula is proposed in this paper. This formula is derived directly from the cost function of SCA through matrix theory. Mathematically, it is more rigorous. In addition, a new and robust adaptive BSS algorithm is developed based on the new natural gradient. Simulations illustrate that this natural gradient formula is more robust and reliable than Lewicki-Sejnowski＇s gradient.     

基于仿射投影-独立分量分析的盲源分离

仿射投影算法(APA)重复利用数据,可提高算法的收敛速度。本文以盲源分离(BSS)的独立分量分析(ICA)为基础,结合APA思想,设计出BSS的APA-ME、APA-MMI、APA-EASI新算法。在这些新算法中,输出向量数据被重复利用,向量式数据转变成矩阵式数据,从而加快了BSS的收敛速度。仿真结果表明,APA-ICA类BSS算法是有效的。     

ICA,kernel methods and nonnegativity: New paradigms for dynamical component analysis of fMRI data

In the last decades, functional magnetic resonance imaging (fMRI) has been introduced into clinical practice. As a consequence of this advanced noninvasive medical imaging technique, the analysis and visualization of medical image time-series data poses a new challenge to both research and medical application. But often, the model data for a regression or generalized linear model-based analysis are not available. Hence exploratory data-driven techniques, i.e. blind source separation (BSS) methods are very popular in functional nuclear magnetic resonance imaging (fMRI) data analysis since they are neither based on explicit signal models nor on a priori knowledge of the underlying physiological process. The independent component analysis (ICA) represents a main BSS method which searches for stochastically independent signals from the multivariate observations. In this paper, we introduce a new kernel-based nonlinear ICA method and compare it to standard BSS techniques. This kernel nonlinear ICA (kICA) overcomes the restrictions of linearity of the mixing process usually encountered with ICA. Dimension reduction is an important preprocessing step for this nonlinear technique and is performed in a novel way: a genetic algorithm is designed which determines the optimal number of basis vectors for a reduced-order feature space representation as an optimization problem of the condition number of the resulting basis. For the fMRI data, a comparative quantitative evaluation is performed between kICA with different kernels, nonnegative matrix factorization (NMF) and other BSS algorithms. The comparative results are evaluated by task-related activation maps, associated time courses and ROC study. The comparison is performed on fMRI data from experiments with 10 subjects. The external stimulus was a visual pattern presentation in a block design. The most important obtained results in this paper represent that kICA and sparse NMF (sNMF) are able to identify signal components with high correlation to the fMRI stimulus, and kICA with a Gaussian kernel is comparable to standard ICA algorithms and even more, it yields spatially focused results.     

融合极点对称模态分解与时频分析的单通道振动信号盲分离方法

针对单通道振动信号盲源分离的观察信号少于源信号,且传统的盲源分离方法往往忽视信号非平稳性的问题,提出一种基于极点对称模态分解和时频分析的盲分离算法（ESMD-TFA-BSS）。首先,采用极点对称模态分解方法将观察信号分解成不同的模态,采用贝叶斯信息准则（BIC）估计源信号个数并利用相关系数法选取最优观察信号,由原观察信号与最优观察信号组成新的观察信号;其次,根据新的观察信号计算白化矩阵并将其白化,利用平滑伪Wigner-Ville分布将白化后的信号拓展到时频域,采用矩阵联合对角化方法计算酉矩阵;最后,根据白化矩阵和酉矩阵估计源信号。在盲源分离仿真实验中,ESMD-TFA-BSS的估计源信号与仿真信号的相关系数分别为0.9771、0.9784、0.9660,基于经验模态分解和时频分析的盲分离算法（EMD-TFA-BSS）的相关系数分别为0.8697、0.9706、0.8548,ESMD-TFA-BSS比EMD-TFA-BSS的相关系数分别提高了12.35%、0.80%、13.00%。实验结果表明,ESMD-TFA-BSS在实际工程中能够有效地提高源信号分离精度。     

关于盲信号自适应分离中非线性函数的讨论

This paper proposes a new algorithm of blind source separation (BSS). The algorithm can overcome the difficulty known as “the sensors are less than the source signals” and works effectively when the sensors are less. Then, the paper discusses the nonlinear functions used in the new algorithm. A uniform nonlinear function is proposed and some criterion are given to choose its parameters. Finally, some simulations are presented to show the effectness of the algorithm and the correctness of the criterion.     

基于仿射投影-非线性主分量分析的盲源分离

仿射投影算法(APA)重复利用数据,可提高算法的收敛速度。针对现有盲源分离收敛速度慢的问题,以盲源分离的非线性主分量分析(PCA)为基础,结合仿射投影算法,提出了盲源分离的非线性APA-PCA准则,并设计出盲源分离的APA-Kalman,APA-RLS,APA-LMS新算法。在这些新算法中,预白化后的观测向量数据被重复利用,向量式数据转变成矩阵式数据,从而加快了盲源分离的收敛速度。仿真结果表明,非线性APA-PCA准则是有效的。     

FastICA算法及其在地震信号去噪中的应用*

ICA算法是求解盲源分离问题的有效算法。建立了ICA算法的数学模型,对模型的求解条件及多解性进行了分析。给出一种基于负熵极大的FastICA算法,讨论该算法在地震信号去噪中的应用。仿真实验验证了该算法的有效性。     

Independent component analysis based on nonparametric density estimation

In this paper, we introduce a novel independent component analysis (ICA) algorithm, which is truly blind to the particular underlying distribution of the mixed signals. Using a nonparametric kernel density estimation technique, the algorithm performs simultaneously the estimation of the unknown probability density functions of the source signals and the estimation of the unmixing matrix. Following the proposed approach, the blind signal separation framework can be posed as a nonlinear optimization problem, where a closed form expression of the cost function is available, and only the elements of the unmixing matrix appear as unknowns. We conducted a series of Monte Carlo simulations, involving linear mixtures of various source signals with different statistical characteristics and sample sizes. The new algorithm not only consistently outperformed all state-of-the-art ICA methods, but also demonstrated the following properties: 1) Only a flexible model, capable of learning the source statistics, can consistently achieve an accurate separation of all the mixed signals. 2) Adopting a suitably designed optimization framework, it is possible to derive a flexible ICA algorithm that matches the stability and convergence properties of conventional algorithms. 3) A nonparametric approach does not necessarily require large sample sizes in order to outperform methods with fixed or partially adaptive contrast functions.     

一种盲源分离的优先进化自适应遗传算法

盲分离技术与独立分量分析(ICA)由于不需要知道信号的先验信息而得到广泛应用.ICA是信号处理的一种新技术.其基本目标是寻找线性变换矩阵,将观测的多维混合信号进行变换,变换后的输出信号各分量之间尽可能统计独立.将改进的遗传算法(GA)与ICA相结合,提出基于优先进化自适应GA的盲源分离算法,并与传统的遗传算法进行了比较,证实了其具有更好的收敛性和稳态性能.对3段声音信号进行了仿真,仿真结果证明了算法的有效性.     

基于奇异值分解的欠定ICA算法研究

从奇异值分解出发,研究欠定独立分量分析(ICA)盲分离的新算法,给出了欠定ICA算法的代价函数,推导出分离矩阵的计算公式.在此基础上,提出了将基于奇异值分解的欠定ICA算法与普通ICA算法相结合的二次盲信号分离算法.利用此盲分离算法,能够较好地分离出部分源信号.仿真实验说明了此方法的有效性.     

Blind Source Separation Using Quadratic form Innovation

Blind source separation (BSS) is an increasingly popular data analysis technique with many applications. Several methods for BSS using the statistical properties of original sources have been proposed, for a famous one, such as non-Gaussianity, which leads to independent component analysis (ICA). This paper proposes a blind source separation method based on a novel statistical property: the quadratic form innovation of original sources, which includes linear predictability and energy (square) predictability as special cases. A gradient learning algorithm is presented by minimizing a loss function of the quadratic form innovation. Also, we give the stability analysis of the proposed BSS algorithm. Simulations verify the efficient implementation of the proposed method.     

Effective Learning Rate Adjustment of Blind Source Separation Based on an Improved Particle Swarm Optimizer

Blind source separation (BSS) is a technique used to recover a set of source signals without prior information on the transformation matrix or the probability distributions of the source signals. In previous works on BSS, the choice of the learning rate would result in a competition between stability and speed of convergence. In this paper, a particle swarm optimization (PSO)-based learning rate adjustment method is proposed for BSS, and a simple decision-making method is introduced for how the learning rate should be applied in the current time slot. In the experiments, samples of four and ten source signals were mixed and separated and the results were compared with other related approaches. The proposed approach exhibits rapid convergence, and produces more efficient and more stable independent component analysis algorithms, than other related approaches.     

Atrial fibrillatory signal estimation using blind source extraction algorithm based on high-order statistics

The analysis and the characterization of atrial fibrillation （AF） requires, in a previous key step, the extraction of the atrial activity （AA） free from 12-lead electrocardiogram （ECG）. This contribution proposes a novel non-invasive approach for the AA estimation in AF episodes. The method is based on blind source extraction （BSE） using high order statistics （HOS）. The validity and performance of this algorithm are confirmed by extensive computer simulations and experiments on realworld data. In contrast to blind source separation （BSS） methods, BSE only extract one desired signal, and it is easy for the machine to judge whether the extracted signal is AA source by calculating its spectrum concentration, while it is hard for the machine using BSS method to judge which one of the separated twelve signals is AA source. Therefore, the proposed method is expected to have great potential in clinical monitoring.     

基于盲源分离的超声信号去噪的仿真研究

提出一种新的基于盲源分离的超声信号去噪方法.为了验证去噪方法的有效性,应用此方法处理了仿真的超声信号,并与小波去噪的效果进行了比较.实验结果表明:该去噪方法能极大提高超声信号的信噪比,且其效果能与小波去噪方法相媲美,其特点是通过超声信号和噪声信号的盲源分离实现噪声消除.     

Markov and Semi-Markov switching of source appearances for nonstationary independent component analysis.

Independent component analysis (ICA) is currently the most popularly used approach to blind source separation (BSS), the problem of recovering unknown source signals when their mixtures are observed but the actual mixing process is unknown. Many ICA algorithms assume that a fixed set of source signals consistently exists in mixtures throughout the time-series to be examined. However, real-world signals often have such difficult nonstationarity that each source signal abruptly appears or disappears, thus the set of active sources dynamically changes with time. In this paper, we propose switching ICA (SwICA), which focuses on such situations. The proposed approach is based on the noisy ICA formulated as a generative model. We employ a special type of hidden Markov model (HMM) to represent such prior knowledge that the source may abruptly appear or disappear with time. The special HMM setting t hen provides an effect ofvariable selection in a dynamic way. We use the variational Bayes (VB) method to derive an effective approximation of Bayesian inference for this model. In simulation experiments using artificial and realistic source signals, the proposed method exhibited performance superior to existing methods, especially in the presence of noise. The compared methods include the natural-gradient ICA with a nonholonomic constraint, and the existing ICA method incorporating an HMM source model, which aims to deal with general nonstationarities that may exist in source signals. In addition, the proposed method could successfully recover the source signals even when the total number of true sources was overestimated or was larger than that of mixtures. We also propose a modification of the basic Markov model into a semi-Markov model, and show that the semi-Markov one is more effective for robust estimation of the source appearance.