扩展独立成分分析的若干算法及其应用研究
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摘要
独立成分分析(Independent Component Analysis,ICA)是一种新兴的数据处理与分析方法,主要用于在源信号和混合信道未知的情况下,从观测数据来提取原始的独立源信号。近年来,该方法已经成功地应用于语音信号处理、生物医学信号处理、神经计算、图像特征提取、远程通信、人脸识别等众多领域。ICA具有广阔的应用前景,吸引了众多的科研工作者献身其中,因此近些年获得了长足的发展。然而,ICA的研究尚处于发展阶段,仍有许多问题有待进一步深入研究和解决。
本文首先对ICA的国内外研究现状以及应用作了较详细的介绍,然后介绍了标准ICA和扩展ICA的相关知识。最后,针对ICA现有的几个问题,例如按顺序输出独立成分、只提取一个或多个感兴趣信号的盲抽取问题以及带噪观测信号的盲信号分离问题等进行了研究,提出了几个较为有效的算法。本文的主要工作概括如下:
1.针对独立成分输出顺序的不确定性问题,提出了一种基于约束ICA模型的排序算法。由于现有的标准ICA算法往往仅探求独立成分的方向,认为所得到的源信号的顺序对于通常所考虑的问题影响不大,从而忽略了这种不确定性。然而,在某些特殊应用中,确定输出成分的顺序是必需的。针对这种需要,本文提出了一种基于投影方法的约束ICA模型,根据某些统计量的大小来规定输出成分的顺序,并结合NewFP算法得到了相应的约束不动点算法。由于算法是不动点型算法,从而避免了其它梯度型算法中学习率的选择问题。基于模拟信号、语音信号的仿真实验以及实际的胎儿心电数据的处理结果证实了算法的有效性。
2.针对时间ICA的盲源抽取问题,提出了两个基于待抽取信号时间结构特性的盲抽取算法。首先,利用待抽取信号的广义自相关性以及其新息的非高斯性,提出了基于两者的凸组合模型,得到了梯度型的盲抽取算法,并在理论上给出了算法的稳定性分析。与一般的只利用非高斯性或只利用时间结构性的算法不同,该算法有效结合了这两个特性,从而能够较大限度地挖掘数据中的隐含的信息。在图像数据以及胎儿心电信号的抽取实验中,取得了较好的抽取效果。其次,以待抽取信号的先验参考信息为基础,将待抽取信号的参考信号和广义自相关性相结合,构造了基于两者的目标函数并提出了一种新的盲抽取算法。与现有的盲抽取算法相比,新算法更充分利用了待抽取信号的先验参考信息。需要指出的是,该算法并不过分地依赖于参考信号,即使选取的参考信号较一般时,也能得到较为满意的效果。基于胎儿心电数据的实验证实了算法的较好性能。
3.针对带噪数据的抽取及分离问题,提出了两个基于源信号时间结构特性的去噪算法。首先,将待抽取信号广义自相关性与高斯矩函数相结合,通过最大化这种广义自相关性,给出了感兴趣信号的去噪盲抽取算法。该算法采用偏差移除技术,是对无噪ICA算法的修正,以去除或减少由噪声引起的偏差。与现有的一些噪声盲抽取算法相比,即使在噪声协方差较大时,也能得到较满意的效果。而且本算法对时间延迟的估计误差不敏感。基于模拟信号、图像数据以及胎儿心电数据的实验结果证实了算法的有效性。其次,将源信号的非线性新息表示与高斯矩函数相结合,提出了一种适用于源信号协方差非平稳情况的去噪盲源分离算法。并针对现有噪声方法较少考虑噪声未知这一问题,进一步将其推广到噪声协方差未知情况,实验证实了算法的有效性和实用性。
Independent component analysis(ICA) is a new promising method for data processing and analysis.The aim of the ICA is to extract original independent components from observed data that are mixtures of the unknown sources without any knowledge of the mixed channel.Recently,ICA has received great attention due to its potential signal processing applications such as speech signal processing,biomedical signal processing,neural computation,image feature extraction,telecommunications and face recognition etc.Due to its wide and attractive applications,many researchers have studied ICA in the past twenty years and made this technique considerable developed.However,ICA is still in an initial stage of development,some problems about its theory and application need to be enhanced and improved further.
In this dissertation,we first provide an introduction about the research status and applications of ICA both at home and abroad.Then,preliminary knowledge of basic and extended ICA are given.In addition,some problems of extended ICA,for example,the ordering of independent components,the blind extraction of one or a set of interesting signals and the noisy blind source separation,are investigated deeply and several novel efficient methods are proposed.The main works in this dissertation can be introduced as follows:
1.Based on the constrained independent component analysis model,we propose a method for eliminating the indeterminacy on permutation of the ICA.Most Of traditional ICA algorithms only exploit the direction of independent components but ignore these inherent indeterminacy,which is considered as unimportant impact factors in the signal processing.However,in many special applications,this inherent indeterminacy needs to be determined.Concerning this case,we propose an algorithm for constrained independent component analysis model based on projection methods and incorporate the new fixed-point(NewFP) algorithm into this constrained ICA model to construct a new constrained fixed-point algorithm.This method is applied to order the independent components in a specific statistical measures.Moreover,it is more simple to implement than other existing algorithms due to its independence of the learning rate.Computation simulations on synthesized signals,speech signals and real-world fetal electrocardiograph (ECG) data demonstrate that this method not only systematically eliminates the indeterminacy of ICA on permutation but also performs better.
2.We further study the issue of blind source extraction(BSE) on temporal ICA (TICA) and present two BSE algorithms for extracting the desired signal with temporal structures.
Firstly,through combining the generalized autocorrelations of the desired signal and the non-Gaussianity of its innovations,we develop an objective function,which is formulated as the convex combination of these priori special temporal characteristics.Maximizing this objective function,we obtain an efficient gradient BSE algorithm and further give its stability analysis in this paper.Note that ICA with its basic form ignores the time structure and uses only the non-Gaussianity criteria.However,the proposed algorithm combines both of these estimation criteria(non-Gaussianity and time-correlations) in order to exploit the data information as much as possible.Simulations on image data and ECG data indicate its better performance.
Secondly,based on the temporal characteristics and other prior information of desired signals,we develop an objective function for extracting the interesting signals,which combines the generalized autocorrelations and reference information of desired signals. Maximizing this objective function,a BSE fixed-point algorithm is proposed.Comparing with other BSE method,this method makes full use of more priori information of the desired signal.It should be pointed out that the good performance of the proposed algorithm may attribute to the application of a properly reference signal.Fortunately, the proposed method does not excessively depend on the selection of the reference signals, which generalizes this method for broader applicability.Simulations on artificial ECG signals and the real-world ECG data demonstrate the better performance of the new algorithm.
3.We study the problem of extracting or separating source signals with temporal structures.Moreover,we propose two noisy algorithms based on these priori special characteristics and Gaussian moments.
Firstly,we address the extraction of the noisy model based on the temporal characteristics of sources.An objective function,which combines Gaussian moments to generalized autocorrelations,is proposed.Maximizing this objective function,we present a fixed-point noisy blind source extraction algorithm,which is given by bias removal techniques.This means that ordinary(noise-free) ICA methods are modified so that the bias due to Gaussian noise is removed,or at least reduced.Comparing with other existing extraction algorithms,the proposed algorithm shows its robustness to the estimated error of time delay even to high noise level.Simulations on synthesized signals,images and ECG data demonstrate the better performance of the proposed method.
Secondly,we present a noisy blind source separation algorithm which incorporates Gaussian moments into the nonlinear innovation of original sources.This method is applicable to the situation when the noise covariance is known and source signals are nonstationary in the sense that the variance of each is assumed to change smoothly as a function of time.Furthermore,this method is extended to the case of noise covariance unknown in advance.Validity and performance of the described approaches are demonstrated by computer simulations.
本文首先对ICA的国内外研究现状以及应用作了较详细的介绍,然后介绍了标准ICA和扩展ICA的相关知识。最后,针对ICA现有的几个问题,例如按顺序输出独立成分、只提取一个或多个感兴趣信号的盲抽取问题以及带噪观测信号的盲信号分离问题等进行了研究,提出了几个较为有效的算法。本文的主要工作概括如下:
1.针对独立成分输出顺序的不确定性问题,提出了一种基于约束ICA模型的排序算法。由于现有的标准ICA算法往往仅探求独立成分的方向,认为所得到的源信号的顺序对于通常所考虑的问题影响不大,从而忽略了这种不确定性。然而,在某些特殊应用中,确定输出成分的顺序是必需的。针对这种需要,本文提出了一种基于投影方法的约束ICA模型,根据某些统计量的大小来规定输出成分的顺序,并结合NewFP算法得到了相应的约束不动点算法。由于算法是不动点型算法,从而避免了其它梯度型算法中学习率的选择问题。基于模拟信号、语音信号的仿真实验以及实际的胎儿心电数据的处理结果证实了算法的有效性。
2.针对时间ICA的盲源抽取问题,提出了两个基于待抽取信号时间结构特性的盲抽取算法。首先,利用待抽取信号的广义自相关性以及其新息的非高斯性,提出了基于两者的凸组合模型,得到了梯度型的盲抽取算法,并在理论上给出了算法的稳定性分析。与一般的只利用非高斯性或只利用时间结构性的算法不同,该算法有效结合了这两个特性,从而能够较大限度地挖掘数据中的隐含的信息。在图像数据以及胎儿心电信号的抽取实验中,取得了较好的抽取效果。其次,以待抽取信号的先验参考信息为基础,将待抽取信号的参考信号和广义自相关性相结合,构造了基于两者的目标函数并提出了一种新的盲抽取算法。与现有的盲抽取算法相比,新算法更充分利用了待抽取信号的先验参考信息。需要指出的是,该算法并不过分地依赖于参考信号,即使选取的参考信号较一般时,也能得到较为满意的效果。基于胎儿心电数据的实验证实了算法的较好性能。
3.针对带噪数据的抽取及分离问题,提出了两个基于源信号时间结构特性的去噪算法。首先,将待抽取信号广义自相关性与高斯矩函数相结合,通过最大化这种广义自相关性,给出了感兴趣信号的去噪盲抽取算法。该算法采用偏差移除技术,是对无噪ICA算法的修正,以去除或减少由噪声引起的偏差。与现有的一些噪声盲抽取算法相比,即使在噪声协方差较大时,也能得到较满意的效果。而且本算法对时间延迟的估计误差不敏感。基于模拟信号、图像数据以及胎儿心电数据的实验结果证实了算法的有效性。其次,将源信号的非线性新息表示与高斯矩函数相结合,提出了一种适用于源信号协方差非平稳情况的去噪盲源分离算法。并针对现有噪声方法较少考虑噪声未知这一问题,进一步将其推广到噪声协方差未知情况,实验证实了算法的有效性和实用性。
Independent component analysis(ICA) is a new promising method for data processing and analysis.The aim of the ICA is to extract original independent components from observed data that are mixtures of the unknown sources without any knowledge of the mixed channel.Recently,ICA has received great attention due to its potential signal processing applications such as speech signal processing,biomedical signal processing,neural computation,image feature extraction,telecommunications and face recognition etc.Due to its wide and attractive applications,many researchers have studied ICA in the past twenty years and made this technique considerable developed.However,ICA is still in an initial stage of development,some problems about its theory and application need to be enhanced and improved further.
In this dissertation,we first provide an introduction about the research status and applications of ICA both at home and abroad.Then,preliminary knowledge of basic and extended ICA are given.In addition,some problems of extended ICA,for example,the ordering of independent components,the blind extraction of one or a set of interesting signals and the noisy blind source separation,are investigated deeply and several novel efficient methods are proposed.The main works in this dissertation can be introduced as follows:
1.Based on the constrained independent component analysis model,we propose a method for eliminating the indeterminacy on permutation of the ICA.Most Of traditional ICA algorithms only exploit the direction of independent components but ignore these inherent indeterminacy,which is considered as unimportant impact factors in the signal processing.However,in many special applications,this inherent indeterminacy needs to be determined.Concerning this case,we propose an algorithm for constrained independent component analysis model based on projection methods and incorporate the new fixed-point(NewFP) algorithm into this constrained ICA model to construct a new constrained fixed-point algorithm.This method is applied to order the independent components in a specific statistical measures.Moreover,it is more simple to implement than other existing algorithms due to its independence of the learning rate.Computation simulations on synthesized signals,speech signals and real-world fetal electrocardiograph (ECG) data demonstrate that this method not only systematically eliminates the indeterminacy of ICA on permutation but also performs better.
2.We further study the issue of blind source extraction(BSE) on temporal ICA (TICA) and present two BSE algorithms for extracting the desired signal with temporal structures.
Firstly,through combining the generalized autocorrelations of the desired signal and the non-Gaussianity of its innovations,we develop an objective function,which is formulated as the convex combination of these priori special temporal characteristics.Maximizing this objective function,we obtain an efficient gradient BSE algorithm and further give its stability analysis in this paper.Note that ICA with its basic form ignores the time structure and uses only the non-Gaussianity criteria.However,the proposed algorithm combines both of these estimation criteria(non-Gaussianity and time-correlations) in order to exploit the data information as much as possible.Simulations on image data and ECG data indicate its better performance.
Secondly,based on the temporal characteristics and other prior information of desired signals,we develop an objective function for extracting the interesting signals,which combines the generalized autocorrelations and reference information of desired signals. Maximizing this objective function,a BSE fixed-point algorithm is proposed.Comparing with other BSE method,this method makes full use of more priori information of the desired signal.It should be pointed out that the good performance of the proposed algorithm may attribute to the application of a properly reference signal.Fortunately, the proposed method does not excessively depend on the selection of the reference signals, which generalizes this method for broader applicability.Simulations on artificial ECG signals and the real-world ECG data demonstrate the better performance of the new algorithm.
3.We study the problem of extracting or separating source signals with temporal structures.Moreover,we propose two noisy algorithms based on these priori special characteristics and Gaussian moments.
Firstly,we address the extraction of the noisy model based on the temporal characteristics of sources.An objective function,which combines Gaussian moments to generalized autocorrelations,is proposed.Maximizing this objective function,we present a fixed-point noisy blind source extraction algorithm,which is given by bias removal techniques.This means that ordinary(noise-free) ICA methods are modified so that the bias due to Gaussian noise is removed,or at least reduced.Comparing with other existing extraction algorithms,the proposed algorithm shows its robustness to the estimated error of time delay even to high noise level.Simulations on synthesized signals,images and ECG data demonstrate the better performance of the proposed method.
Secondly,we present a noisy blind source separation algorithm which incorporates Gaussian moments into the nonlinear innovation of original sources.This method is applicable to the situation when the noise covariance is known and source signals are nonstationary in the sense that the variance of each is assumed to change smoothly as a function of time.Furthermore,this method is extended to the case of noise covariance unknown in advance.Validity and performance of the described approaches are demonstrated by computer simulations.
引文
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