独立分量分析算法及其在信号处理中的应用研究

发布时间：2018-05-04 00:33

本文选题：独立分量分析 + 盲源分离　；参考：《山东大学》2012年博士论文

【摘要】：独立分量分析(ICA)是二十世纪九十年代发展起来的一种多元统计和计算技术,目的是用来分离或提取随机变量、观测数据或信号混合物中具有独立特性的隐藏分量。ICA可以看作是主分量分析(PCA)和因子分析(FA)的扩展。与PCA和FA相比,ICA是一种更强有力的技术。当PCA和FA等经典方法失效时,ICA仍然能从具有统计独立特性的观测信号中挖掘出支撑数据的内在分量或因子。对于通常是以大型样本数据库形式给出的多元观测数据,ICA定义了一个生成模型,该模型假设所观测到的数据变量是未知源信号的线性或非线性混合。事实上,ICA模型中原始的源信号和实现混合的系统都是未知的。ICA还假设那些潜在变量是非高斯的且相互独立,并称它们为观测数据的独立分量。这些独立分量也可以称作为源信号或因子,它们可以通过ICA相关方法分离或提取出来。近年来,由于在语音处理、生物医学信号处理、图像特征提取和无线通信等领域潜在的影响力,基于ICA的盲源分离(BSS)和盲源提取(BSE)已经引起了社会各界高度的关注。许多科研机构都在致力于盲源分离/盲源提取方法的开发和应用,并已在ICA相关理论和应用中取得了很多有价值的研究成果。然而,ICA的研究目前尚处于发展阶段,ICA算法和应用中仍然存在若干尚未解决的问题,这就限制了ICA技术的发展和应用。总的来说,ICA技术仍然需要进一步加强和完善。本文介绍了国内外ICA的发展历史、研究现状以及应用情况,阐述了ICA的理论基础,包括ICA的数学定义、基本假设以及相关的数学理论基础和实现途径等,并针对扩展ICA现存的几个问题。例如：对具有时间结构特性感兴趣信号的盲源提取、噪声环境下基于高斯矩和参考信号的盲源提取和基于感兴趣信号归一化峭度值范围的盲源提取等进行了比较深入的研究,提出了几个较为有效的算法。本文的核心内容概括如下：提出了一种针对源信号具有时间结构特性的基于极大似然估计技术的盲源提取算法。该算法可以有效地从线性混合的源信号混合物中提取出具有特定时间结构特性的感兴趣信号。基于时间结构特性的盲源提取(TBSE)可以看作是标准ICA的扩展。在生物医学信号测量中,很多感兴趣信号具有不同程度的周期特性。因此,TBSE将有非常广阔的应用空间。为了弥补现有的基于时间结构特性盲源提取算法的计算需求量大和提取精度低等缺陷,本文提出一种改良的基于源信号时间结构特性的盲源提取算法。在实际应用中,传统的基于信号时间结构特性的盲源提取算法会遇到若干与观测数据有关的问题。例如：时间相关关系不能得到完全满足；尽管感兴趣信号在特定的时间滞延处有强烈的时间相关性,有时其它信号也会在该时间滞延处有较弱的相关性,其它信号甚至也会在该时间滞延处时间相关。因此,传统的基于信号时间结构特性的盲源提取算法所提取的信号经常混杂有其它不感兴趣的信号或者噪声。极大似然估计是统计估计领域中的一种流行的高阶统计(HOS)技术。如果源信号是非高斯的且具有时间相关特性,极大似然估计可以开发有效地盲源提取方法。该类算法可以从信号混合物中提取出潜在的信号,但由于局部最大化或算法随机初始化等因素的影响,基于极大似然估计的盲源提取算法常常收敛到某一个局部极大值,所提取的信号不能保证是感兴趣信号。为了从测量到的源信号混合物中排他性地提取出感兴趣信号,本文提出一种基于源信号时间结构特性和极大似然估计技术的综合性盲源提取算法。整个提取过程分为两个阶段。第一阶段利用感兴趣信号的周期性信息从其线性混合物中提取出具有特定时间结构特性的信号。所提取的信号虽然逼近了感兴趣信号,但常混杂有若干其它信号甚至噪声。因此,该阶段只能看作是对感兴趣信号的粗略提取。第二阶段,基于源信号的统计独立特性,我们把第一阶段所提取的信号在极大似然估计框架下通过引进一个参数密度模型进行优化处理。所设计的指数密度函数束能与源信号的边际概率密度相匹配,因而可以对第一阶段所提取的信号在未知源信号概率密度分布情况下实施优化处理,从而提取出稳定有效的感兴趣信号。基于生物医学信号的计算机仿真实验验证了本文提出算法的有效性,与其它盲源提取算法的对比进一步说明了算法的可靠性和鲁棒性。与传统的盲源分离方法相比,盲源提取具有许多优良特性,如计算负载少和处理速度快。因此,盲源提取广泛应用于解决源信号众多而感兴趣信号很少情况下的盲信号分离问题。在实际应用中,感兴趣信号总是被其它信号甚至噪声所干扰。例如：在现实世界中,许多测得的生物医学信号不但包含众多源信号而且感兴趣信号还常常被其它信号甚至噪声所污染。噪声经常会造成错误的临床诊断,有时甚至会造成死亡事件的发生。作为一种重要的非高斯性量度,归一化峭度广泛用于设计解决盲源分离／盲源提取问题的目标函数。尽管在理论和应用上已经证明了该类目标函数的有效性,目前的基于归一化峭度的盲源提取方法大多是在无噪声环境下推导出来的,这在实际应用中是不现实的。近年来,学者们提出了几个从噪声环境下的信号混合物中根据归一化峭度提取感兴趣信号的方法,然而这些算法大都需要事先知道感兴趣信号的归一化峭度值。我们在现实世界中经常会碰到这样的情况：不能事先确定感兴趣信号准确的归一化峭度值,但可以事先获取到感兴趣信号归一化峭度所在的区间范围,且其它信号的归一化峭度值不在该区间范围内。到目前为止,尚没有相应的盲源提取算法能在噪声环境下使用该类区间范围作为前验信息提取出感兴趣信号。本文首先设计出一个基于信号归一化峭度的目标函数,然后使用拉格郎日乘子法最大化该目标函数,进而构建出一个基于感兴趣信号归一化峭度值区间范围的盲源提取算法。只要事先获取到感兴趣信号归一化峭度值所在的区间范围,且其它信号的归一化峭度值不在该区间范围内,即使当多个信号的归一化峭度值非常接近,该算法也可以从噪声环境下具有统计独立特性的源信号混合物中提取出感兴趣信号。在许多BSS/BSE应用中,人们经常可以事先获取到感兴趣信号的某些前验信息。例如：感兴趣信号的形态、相位、踪迹或发生时间等。这些前验信息是与感兴趣信号紧密相关的,如果它们携带的信息能够把感兴趣信号从观测到的信号混合物中有效区分出来,就称其为参考信号。总的来说,参考信号被认为是根据某一距离量度离感兴趣信号最近的信号。近年来,学者们提出了若干基于参考信号的盲源提取算法。例如：Lu等人提出一种称作为ICA with reference(ICA-R)或constrained ICA(cICA)的盲源提取方法。ICA-R是通过最小化一个欠完备的目标函数和最大化利用参考信号中的前验信息而构建的。通过把部分前验信息以参考信号形式嵌入到著名的FastlCA算法中,ICA-R可以从大量的源信号混合物中提取出距离参考信号最近的感兴趣信号。作为一种经典地利用参考信号的盲源提取算法,ICA-R已经成功地应用到了功能磁共振成像(fMRI)处理领域中。然而,ICA-R在设计时并未考虑到噪声的存在。在很多情况下由于噪声污染的影响,算法的性能并不是很好。参考信号携带着足够的前验信息能够从源信号混合物中排他性地区分出感兴趣信号。在实际应用中,感兴趣信号通常总是被各种噪声所污染。本文提出一种改进的基于参考信号的盲源提取算法。我们首先把参考信号作为限制性条件系统化地嵌入到一个适用于噪声数据的目标函数中,从而构建出一个限制性最优化问题,然后使用拉格郎日乘子法和梯度最优化技术求解该最优化问题,进而导出一个噪声环境下基于参考信号的盲源提取算法。计算机仿真实验验证了算法的有效性和可靠性。
[Abstract]:Independent component analysis (ICA) is a multivariate statistical and computational technique developed in 1990s. The purpose is to separate or extract random variables. The hidden component.ICA with independent characteristics in the observation data or signal mixture can be regarded as the extension of the principal component analysis (PCA) and factor analysis (FA). Compared with PCA and FA, ICA It is a more powerful technology. When the classical methods such as PCA and FA fail, ICA can still excavate the intrinsic component or factor of the supporting data from the observational signals with statistical independence. For the multivariate observation data which is usually given in the form of large sample database, ICA defines a generation model, which is assumed to be observed. The data variable is a linear or nonlinear mixture of unknown source signals. In fact, the original source signal and the implementation of the hybrid system in the ICA model are unknown.ICA and assume that those potential variables are non Gauss and are independent of each other, and call them independent components of the observed data. They can be separated or extracted by ICA correlation.
In recent years, due to the potential influence in the fields of speech processing, biomedical signal processing, image feature extraction and wireless communication, ICA based blind source separation (BSS) and blind source extraction (BSE) have attracted great attention from all walks of life. Many research institutions have been developing and applying the method of blind source separation / blind source extraction. Many valuable research achievements have been obtained in the ICA related theories and applications. However, the research of ICA is still at the stage of development. There are still some unsolved problems in the ICA algorithm and application, which restricts the development and application of the ICA technology. In general, the ICA technology still needs to be further strengthened and improved.
This paper introduces the history of the development of ICA at home and abroad, the status of the research and its application, and expounds the theoretical basis of the ICA, including the mathematical definition of ICA, the basic hypothesis, the basis of the related mathematical theory and the ways to realize it, and the existing problems of the extended ICA. For example, the blind source extraction of the time structure special interest signal, The blind source extraction based on the Gauss moment and the reference signal and the blind source extraction based on the normalized kurtosis range of the interest signal are studied in the noisy environment, and several more effective algorithms are proposed.
The core content of this article is summarized as follows:
A blind source extraction algorithm based on maximum likelihood estimation for source signal with time structure is proposed. This algorithm can effectively extract interesting signals with specific time structure characteristics from the mixture of linear mixed source signals. Blind source extraction (TBSE) based on time structure characteristics can be considered as a standard ICA In biomedical signal measurement, many interesting signals have different degree of periodic characteristics. Therefore, TBSE will have a very wide application space. In order to make up for the large amount of computing demand and low extraction precision of the existing blind source extraction algorithm based on time structure characteristics, this paper proposes an improved source signal based on the source signal. A blind source extraction algorithm for inter structural characteristics.
In practical applications, the traditional blind source extraction algorithm based on the time structure characteristics of the signal will encounter some problems related to the observed data. For example, the time correlation can not be fully satisfied; although the signal of interest has a strong temporal correlation at a specific time delay, sometimes the other signals are also delayed at that time. There is a weak correlation, and the other signals may even be dependent on the time delay. Therefore, the signals extracted from the traditional blind source extraction algorithm based on the characteristic of the signal time structure are often mixed with other signals or noises that are not interested. The maximum likelihood estimation is a popular high order statistics in the field of statistical estimation (HOS If the source signal is non Gauss and has time dependent characteristics, the maximum likelihood estimation can develop an effective blind source extraction method. This kind of algorithm can extract potential signals from the signal mixture, but the blind source extraction based on maximum likelihood estimation is based on the influence of local maximization or random initialization of the algorithm. The law often converges to a local maximum, and the extracted signal can not be guaranteed to be an interested signal.
In order to extract the interesting signals from the measured source mixture, a comprehensive blind source extraction algorithm based on the time structure characteristics of the source signal and the maximum likelihood estimation technique is proposed. The whole extraction process is divided into two stages. The first stage uses the periodic information of the signal of interest from its linear mixture. A signal with specific time structure characteristics is extracted. The extracted signal, although approximating the signal of interest, often mixed with a number of other signals and even noise. Therefore, this stage can only be regarded as a rough extraction of the signal of interest. The second phase, based on the statistical independence of the source signal, we take the first phase of the extracted letter. In the framework of maximum likelihood estimation, a parameter density model is introduced. The designed exponential density function beam can match the marginal probability density of the source signal, so the signal extracted from the first phase can be optimized under the probability density distribution of the unknown source signal, thus the stability is extracted. The validity of the proposed algorithm is verified by the computer simulation experiment based on biomedical signals. Compared with other blind source extraction algorithms, the reliability and robustness of the algorithm are further illustrated.
Compared with the traditional blind source separation method, blind source extraction has many excellent characteristics, such as less computing load and faster processing speed. Therefore, blind source extraction is widely used to solve the blind signal separation problem with many source signals and few interesting signals. In practical applications, the interesting signals are always dried by other signals and even noise. For example, in the real world, many measured biomedical signals not only contain a large number of source signals but also the signals of interest are often contaminated by other signals and even noise. Noise often causes a false clinical diagnosis and sometimes even the occurrence of death events.
As an important non Gauss measure, normalized kurtosis is widely used to design the target function for the problem of blind source separation / blind source extraction. Although the effectiveness of this kind of target function has been proved in theory and application, most of the blind source extraction methods based on normalized kurtosis are derived from the noise free environment. This is unrealistic in practical applications. In recent years, scholars have proposed several methods to extract interesting signals from the normalized kurtosis in noisy environment. However, most of these algorithms need to know the normalized kurtosis of the signal of interest beforehand. We often encounter such situations in the real world. The exact normalized kurtosis value of the signal of interest can not be determined in advance, but the interval range of the normalized kurtosis of the interested signal can be obtained beforehand, and the normalized kurtosis of other signals is not within the range. So far, no corresponding blind source extraction method can be used in the noise environment to make use of this class range. A signal of interest is extracted for the pre - test information.
In this paper, we first design a target function based on the normalized kurtosis of the signal, then use the Lagrange multiplier method to maximize the objective function, and then construct a blind source extraction algorithm based on the interval range of the normalized kurtosis value of the interest signal. And the normalized kurtosis of other signals is not within the range. Even when the normalized kurtosis values of multiple signals are very close, the algorithm can also extract the interesting signal from the source signal mixture with a statistical independent characteristic under the noise environment.
In many BSS/BSE applications, people can often get some prior information on the signal of interest, such as the form, phase, trace, or time of the interested signal, which are closely related to the signal of interest, if the information they carry can be enough to take the signal of interest from the observed signal mixture. In general, the reference signal is considered to be the closest signal from the interested signal according to a certain distance.
In recent years, scholars have proposed a number of blind source extraction algorithms based on reference signals. For example, Lu et al. Proposed a blind source extraction method called ICA with reference (ICA-R) or constrained ICA (cICA), which is constructed by minimizing an incomplete target function and maximizing the prior information in the reference signal. By embedding some of the forward information in a reference signal into the famous FastlCA algorithm, ICA-R can extract the nearest interesting signal from a large number of source signal mixtures. As a blind source extraction algorithm used for classical reference signals, ICA-R has been successfully applied to functional magnetic resonance imaging (fMRI). In the field of processing, however, ICA-R does not take into account the existence of noise when designing. In many cases, the performance of the algorithm is not very good due to the influence of noise pollution.
The reference signal carries sufficient prior information to separate the interesting signals from the exclusive area of the source mixture. In practical applications, the signals of interest are usually contaminated by various noises. In this paper, an improved blind source extraction algorithm based on reference signals is proposed. We first use the reference signal as a restrictive condition system. It is integrated into a target function suitable for noise data, thus constructing a restricted optimization problem, then using the Lagrange multiplier method and gradient optimization technique to solve the optimization problem, and then derives a blind source extraction algorithm based on the reference signal in a noisy environment. The computer simulation experiment proves the calculation. The validity and reliability of the method.

【学位授予单位】：山东大学
【学位级别】：博士
【学位授予年份】：2012
【分类号】：R318.0

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