非线性盲源分离的原理及算法综述

本文主要阐述了非线性盲源分离(BSS)/独立成分分析(ICA)模型的基本数学原理、分离算法、算法性能及其应用。首先对线性和非线性BSS/ICA的数学模型作了介绍,重点介绍了非线性BSS/ICA解的不确定性,然后在此基础上对近十年来出现的各种非线性BSS/ICA算法进行简单综述,着重分析了一类可解且应用比较广泛的非线性BSS/ICA模型-后非线性BSS/ICA模型及其分离算法。最后对非线性BSS/ICA存在的问题和发展趋势进行了总结。     

盲信号分离

阵列处理和数据分析的一个典型问题是从混合的观测数据向量中恢复不可观测的各个源信号.盲信号分离是解决这一问题的一门新技术,近几年吸引了信号处理学界和神经网络学界众多学者的研究兴趣.本文将以独立分量分析和非线性主分量分析为主要对象,综述盲信号分离技术的理论、方法及应用等方面的发展,并作有关展望.     

引入参考信号的新峭度快速不动点算法

在盲源分离和独立成分分析中,峭度是衡量随机信号非高斯性的常用对比准则,通过不同类型的算法对其进行优化,找到非高斯性极大值点,即实现了源信号的提取或分离。例如,基于峭度的快速不动点算法,它是一种收敛速度很快的算法。最近,Marc Castella等人提出了一类基于所谓“参考信号”的对比准则,以及对应的梯度最大化优化算法,这些算法具有很好的收敛性能。受其启发,文章以一种类似的方式将“参考信号”思想应用到峭度中,得到一种新颖的对比函数,并基于该新峭度对比函数,提出了一种新的快速不动点算法。与经典的基于峭度的快速不动点算法相比,该算法极大地提高了收敛速度,尤其是随着信号样值点数的增加,该算法的优势会更加明显。文章分析和证明了该新峭度对比函数的局部收敛性,给出了新算法的详细推导过程,仿真实验验证了该算法的性能,并与经典算法进行了比较分析。      

Convolutive blind source separation algorithms applied to the electrocardiogram of atrial fibrillation: study of performance

The analysis of the surface electrocardiogram (ECG) is the most extended noninvasive technique in medical diagnosis of atrial fibrillation (AF). In order to use the ECG as a tool for the analysis of AF, we need to separate the atrial activity (AA) from other cardioelectric signals. In this matter, statistical signal processing techniques, like blind source separation (BSS), are able to perform a multilead statistical analysis with the aim to obtain the AA. Linear BSS techniques can be divided in two groups depending on the mixing model: algorithms where instantaneous mixing of sources is assumed, and convolutive BSS (CBSS) algorithms. In this work, a comparison of performance between one relevant CBSS algorithm, namely Infomax, and one of the most effective independent component analysis (ICA) algorithms, namely FastICA, is developed. To carry out the study, pseudoreal AF ECGs have been synthesized by adding fibrillation activity to normal sinus rhythm. The algorithm performances are expressed by two indexes: the signal to interference ratio (SIRAA) and the cross-correlation (RAA) between the original and the estimated AA. Results empirically prove that the instantaneous mixing model is the one that obtains the best results in the AA extraction, given that the mean SIRAA obtained by the FastICA algorithm (37.6 +/- 17.0 dB) is higher than the main SIRAA obtained by Infomax (28.5 +/- 14.2 dB). Also the RAA obtained by FastICA (0.92 +/- 0.13) is higher than the one obtained by Infomax (0.78 +/- 0.16).     

Extracting Epileptic Feature Spikes Using Independent Component Analysis

In recent years, blind source separation （BSS） by independent component analysis （ICA） has been drawing much attention because of its potential applications in signal processing such as in speech recognition systems, telecommunication and medical signal processing. In this paper, two algorithms of independent component analysis （fixed-point IC,4 and natural gradient-flexible ICA） are adopted to extract human epileptic feature spikes from interferential signals. Experiment results show that epileptic spikes can be extracted from noise successfully. The kurtosis of the epileptic component signal separated is much better than that of other noisy signals. It shows that ICA is an effective tool to extract epileptic spikes from patients＇ electroencephalogram EEG and shows promising application to assist physicians to diagnose epilepsy and estimate the epileptogenic region in clinic.     

稀疏分量分析在欠定盲源分离问题中的研究进展及应用

伴随着国内外对盲源分离问题研究的日益深入,在独立分量分析等经典算法之外逐步发展出了许多新的算法.稀疏分量分析就是其中有效的方法之一,它利用信号的稀疏分解,克服了独立分量分析非欠定性的要求,解决了欠定情况下的盲源分离问题.本文将以稀疏分量分析为主要对象,归纳总结了近期的研究进展.     

MIMO-AR System Identification and Blind Source Separation for GMM-Distributed Sources

The problem of blind source separation (BSS) and system identification for multiple-input multiple-output (MIMO) auto-regressive (AR) mixtures is addressed in this paper. Two new time-domain algorithms for system identification and BSS are proposed based on the Gaussian mixture model (GMM) for sources distribution. Both algorithms are based on the generalized expectation-maximization (GEM) method for joint estimation of the MIMO-AR model parameters and the GMM parameters of the sources. The first algorithm is derived under the assumption of unstructured input signal statistics, while the second algorithm incorporates the prior knowledge about the structure of the input signal statistics due to the statistically independent source assumption. These methods are tested via simulations using synthetic and audio signals. The system identification performances are tested by comparison between the state transition matrix estimation using the proposed algorithms and the well-known multidimensional Yule-Walker solution followed by an instantaneous BSS method. The results show that the proposed algorithms outperform the Yule-Walker based approach. The BSS performances were compared to other convolutive BSS methods. The results show that the proposed algorithms achieve higher signal-to-interference ratio (SIR) compared to the other tested methods.     

On the use of simulated annealing to automatically assign decorrelated components in second-order blind source separation

In this paper, an automatic assignment tool, called BSS-AutoAssign,for artifact-related decorrelated components within a second-order blind source separation (BSS) is presented. The latter is based on the recently proposed algorithm dAMUSE, which provides an elegant solution to both the BSS and the denoising problem simultaneously. BSS-AutoAssign uses a local principal component analysis (PCA)to approximate the artifact signal and defines a suitable cost function which is optimized using simulated annealing. The algorithms dAMUSE plus BSS-AutoAssign are illustrated by applying them to the separation of water artifacts from two-dimensional nuclear overhauser enhancement (2-D NOESY)spectroscopy signals of proteins dissolved in water.     

Edge Effect Elimination in Single-Mixture Blind Source Separation

Blind source separation (BSS) of single-channel mixed recording is a challenging task that has applications in the fields of speech, audio and bio-signal processing. Ensemble empirical mode decomposition (EEMD)-based methods are commonly used for blind separation of single input multiple outputs. However, all of these EEMD-based methods appear in the edge effect problem when cubic spline interpolation is used to fit the upper and lower envelopes of the given signals. It is therefore imperative to have good methods to explore a more suitable design choice, which can avoid the problems mentioned above as much as possible. In this paper we present a novel single-mixture blind source separation method based on edge effect elimination of EEMD, principal component analysis (PCA) and independent component analysis (ICA). EEMD represents any time-domain signal as the sum of a finite set of oscillatory components called intrinsic mode functions (IMFs). In extreme point symmetry extension (EPSE), optimum values of endpoints are obtained by minimizing the deviation evaluation function of signal and signal envelope. Edge effect is turned away from signal by abandoning both ends’ extension parts of IMFs. PCA is applied to reduce dimensions of IMFs. ICA finds the independent components by maximizing the statistical independence of the dimensionality reduction of IMFs. The separated performance of edge EPSE-EEMD-PCA-ICA algorithm is compared with EEMD-ICA and EEMD-PCA-ICA algorithms through simulations, and experimental results show that the former algorithm outperforms the two latter algorithms with higher correlation coefficient and lower relative root mean square error (RRMSE).     

EMI-based classification of multiple closely spaced subsurface objects via independent component analysis

Previous work in subsurface object discrimination using electromagnetic induction data has shown that discrimination algorithms based on statistical signal processing techniques are effective for classifying data from objects that occur in isolation. However, for multiple closely spaced subsurface objects, the raw (unprocessed) measurement is a mixture of the responses from several objects and as such cannot be used directly to determine the identity of each of the individual objects. Thus, we propose to separate individual signatures from the mixture by posing the problem as a blind source separation (BSS) problem and effecting signature separation using independent component analysis. We propose to apply BSS to separate the mixed signatures and then follow the separation process with a Bayesian classifier. This approach is evaluated using both simulated data and data from unexploded ordnance items. The results show that this approach can be used to effectively classify multiple closely spaced objects.     

基于雷达系统抗干扰的卷积盲分离算法研究

如何提高雷达系统的抗干扰能力一直是雷达信号处理中比较关注的问题。卷积混合盲分离技术是当前盲分离研究的热点和难点。文中用卷积混合盲分离算法来分离雷达系统接收的信号,把卷积混合的干扰信号和有用信号分离开来,以实现雷达系统抗干扰的目的。该方法使用基于Householder变换的高阶累积量的联合对角化的频域方法来分离卷积混合的雷达接收信号。计算机仿真表明,该抗干扰方法可把卷积混合的雷达信号和干扰信号分离出来,且达到较好的分离效果。     

独立分量分析盲信号分离方法研究

盲源分离是指从多个相互独立的源信号的混合信号中分离出源信号来。独立分量分析法是盲源分离的一种新方法,由于其在语音信号处理、阵列信号处理、生物医学信号处理、移动通信及图象处理等领域的应用前景,越来越引起人们的关注,成为研究的热点。介绍一种基于四阶累积量的非高斯性最大化的ICA算法解决盲源分离的问题,并给出了该算法分离通信信号的计算机仿真结果,验证了算法的有效性。     

结合ICA和复数神经网络的二麦阵列盲源分离技术

为了降低语音信号盲源分离算法的延时,提高其准确性和稳定性,本文结合传统盲源分离技术和深度神经网络的优势,提出了一种基于ICA独立分量分析和复数神经网络的二麦阵列盲源分离技术。本文将复数递归神经网络和独立分量分析方法有机融合,提出一种基于时频域的双通道复数神经网络,同时解决了独立分量分析中的排列问题。所提方法利输入混合信号利用复数域神经网络计算初始化分离矩阵,神经网络输出采用复数域形式,利用复数学习标签估计复数矩阵,然后采用独立分量分析方法获得目标分离矩阵。实验数据表明,所提方法相较于其它独立分量分析方法提高了盲源分离的实时性和准确性。      

Testing for stochastic independence: application to blind source separation

In this paper, we address the issue of testing for stochastic independence and its application as a guide to selecting the standard independent component analysis (ICA) algorithms when solving blind source separation (BSS) problems. Our investigation focuses on the problem of establishing tests for the quality of separation among recovered sources obtained by ICA algorithms in an unsupervised environment. We review existing tests and propose two contingency table-based algorithms. The first procedure is based on the measure of goodness-of-fit of the observed signals to the model of independence provided by the power-divergence (PD) family of test statistics. We provide conditions that guarantee the validity of the independence test when the individual sources are nonstationary. When the sources exhibit significant time dependence, we show how to adopt Hotelling's T/sup 2/ test statistic for zero mean to create an accurate test of independence. Experimental results obtained from a variety of synthetic and real-life benchmark data sets confirm the success of the PD-based test when the individual source samples preserve the so-called constant cell probability assumption as well as the validity of the T/sup 2/-based test for sources with significant time dependence.     

有噪复杂度寻踪的新算法

复杂度寻踪是投影寻踪向时间序列数据,即具有时间结构信号的扩展。该方法是和具有时间依赖特性的源信号的盲分离和独立成分分析紧密联系的。在源信号是具有时间依赖特性和存在高斯噪声的情况下,现有的有噪复杂度寻踪算法没有给出自回归系数的估计方法,影响了算法的实际应用,提出了有噪复杂度寻踪的新算法,该算法给出了自回归系数的估计方法。对自然图像和人工信号的仿真表明了提出算法的有效性,和现有的盲源分离算法相比较,提出算法具有好的信号分离性能。      

盲信号分离在数字无线通信中的一种应用

本文提出了基于神经网络的盲信号分离在数字无线通信中的一种应用。利用本文中的天线阵,接收到的信号可以看作是由Ｎ个独立的信号源所激励的线性混合系统的输出,应用基于神经网络的鲁棒性很好的盲分离算法＾〖７〗,实现多用户信号的分离。我们还就其在数字无线通讯中的应用进行了计算机模拟,模拟结果显示分离效果是令人满意的。     

盲源信号分离技术

盲源信号分离是一种功能强大的信号处理方法，其处理的对象是相互统计独立的信号源经线性组合而产生的一组混合信号，最终目的是从混合信号中分离出独立的信号分量。本文简要介绍信号源分离的基本思想、算法、发展历程以及盲分离的应用领域。最后展望了盲信号分离问题研究的发展方向。     

Atrial activity extraction for atrial fibrillation analysis using blind source separation

This contribution addresses the extraction of atrial activity (AA) from real electrocardiogram (ECG) recordings of atrial fibrillation (AF). We show the appropriateness of independent component analysis (ICA) to tackle this biomedical challenge when regarded as a blind source separation (BSS) problem. ICA is a statistical tool able to reconstruct the unobservable independent sources of bioelectric activity which generate, through instantaneous linear mixing, a measurable set of signals. The three key hypothesis that make ICA applicable in the present scenario are discussed and validated: 1) AA and ventricular activity (VA) are generated by sources of independent bioelectric activity; 2) AA and VA present non-Gaussian distributions; and 3) the generation of the surface ECG potentials from the cardioelectric sources can be regarded as a narrow-band linear propagation process. To empirically endorse these claims, an ICA algorithm is applied to recordings from seven patients with persistent AF. We demonstrate that the AA source can be identified using a kurtosis-based reordering of the separated signals followed by spectral analysis of the sub-Gaussian sources. In contrast to traditional methods, the proposed BSS-based approach is able to obtain a unified AA signal by exploiting the atrial information present in every ECG lead, which results in an increased robustness with respect to electrode selection and placement.     

一种适用于微弱信号盲提取的白化方法

独立分量分析(ICA)算法是解决盲信号分离(BSS)问题的最有效方法之一.ICA中,对观测信号预白化处理的作用至关重要.通常采用主分量分析(PCA)来进行预白化处理.实际中,在利用广播、电视等作为照射源的被动雷达系统中,观测信号通常被强噪声和干扰严重污染,这很大程度上降低了BSS方法的性能.然而,传统的BSS方法中没有...     

Optimal Pairwise Fourth-Order Independent Component Analysis

Blind source separation (BSS) aims at the reconstruction of unknown mutually independent signals, so-called sources, from their mixtures observed at the output of a sensor array. The BSS of instantaneous linear mixtures, which finds application in numerous fields, can be solved through the statistical tool of independent component analysis (ICA). This paper concentrates on the analytic solutions for the fundamental two-signal ICA scenario. A novel estimation class, so-called general weighted fourth-order estimator (GWFOE), is put forward, which is based on the fourth-order statistics of the whitened sensor output. By means of a weight parameter, the GWFOE is able to unify a variety of apparently disparate estimation expressions previously scattered throughout the literature, including the well-known JADE method in the two-signal case. A theoretical asymptotic performance analysis is carried out, resulting in the GWFOE large-sample mean square error and the source-dependent weight value of the most efficient estimator in the class. To extend the pairwise estimators to the general scenario of more than two sources, an improved Jacobi-like optimization technique is proposed. The approach consists of calculating the necessary sensor-output fourth-order statistics at the initialization stage of the algorithm, which can lead to significant computational savings when large sample blocks are processed. Based on this idea, adaptive algorithms are also devised, showing very satisfactory convergence characteristics. Experiments illustrate the good performance of these optimal pairwise ICA strategies, in both off- and on-line processing modes.