本文選題：獨(dú)立分量分析 + 盲源分離�。� 參考：《山東大學(xué)》2012年博士論文

【摘要】：獨(dú)立分量分析(ICA)是二十世紀(jì)九十年代發(fā)展起來(lái)的一種多元統(tǒng)計(jì)和計(jì)算技術(shù),目的是用來(lái)分離或提取隨機(jī)變量、觀測(cè)數(shù)據(jù)或信號(hào)混合物中具有獨(dú)立特性的隱藏分量。ICA可以看作是主分量分析(PCA)和因子分析(FA)的擴(kuò)展。與PCA和FA相比,ICA是一種更強(qiáng)有力的技術(shù)。當(dāng)PCA和FA等經(jīng)典方法失效時(shí),ICA仍然能從具有統(tǒng)計(jì)獨(dú)立特性的觀測(cè)信號(hào)中挖掘出支撐數(shù)據(jù)的內(nèi)在分量或因子。對(duì)于通常是以大型樣本數(shù)據(jù)庫(kù)形式給出的多元觀測(cè)數(shù)據(jù),ICA定義了一個(gè)生成模型,該模型假設(shè)所觀測(cè)到的數(shù)據(jù)變量是未知源信號(hào)的線性或非線性混合。事實(shí)上,ICA模型中原始的源信號(hào)和實(shí)現(xiàn)混合的系統(tǒng)都是未知的。ICA還假設(shè)那些潛在變量是非高斯的且相互獨(dú)立,并稱它們?yōu)橛^測(cè)數(shù)據(jù)的獨(dú)立分量。這些獨(dú)立分量也可以稱作為源信號(hào)或因子,它們可以通過(guò)ICA相關(guān)方法分離或提取出來(lái)。 近年來(lái),由于在語(yǔ)音處理、生物醫(yī)學(xué)信號(hào)處理、圖像特征提取和無(wú)線通信等領(lǐng)域潛在的影響力,基于ICA的盲源分離(BSS)和盲源提取(BSE)已經(jīng)引起了社會(huì)各界高度的關(guān)注。許多科研機(jī)構(gòu)都在致力于盲源分離/盲源提取方法的開(kāi)發(fā)和應(yīng)用,并已在ICA相關(guān)理論和應(yīng)用中取得了很多有價(jià)值的研究成果。然而,ICA的研究目前尚處于發(fā)展階段,ICA算法和應(yīng)用中仍然存在若干尚未解決的問(wèn)題,這就限制了ICA技術(shù)的發(fā)展和應(yīng)用。總的來(lái)說(shuō),ICA技術(shù)仍然需要進(jìn)一步加強(qiáng)和完善。 本文介紹了國(guó)內(nèi)外ICA的發(fā)展歷史、研究現(xiàn)狀以及應(yīng)用情況,闡述了ICA的理論基礎(chǔ),包括ICA的數(shù)學(xué)定義、基本假設(shè)以及相關(guān)的數(shù)學(xué)理論基礎(chǔ)和實(shí)現(xiàn)途徑等,并針對(duì)擴(kuò)展ICA現(xiàn)存的幾個(gè)問(wèn)題。例如：對(duì)具有時(shí)間結(jié)構(gòu)特性感興趣信號(hào)的盲源提取、噪聲環(huán)境下基于高斯矩和參考信號(hào)的盲源提取和基于感興趣信號(hào)歸一化峭度值范圍的盲源提取等進(jìn)行了比較深入的研究,提出了幾個(gè)較為有效的算法。 本文的核心內(nèi)容概括如下： 提出了一種針對(duì)源信號(hào)具有時(shí)間結(jié)構(gòu)特性的基于極大似然估計(jì)技術(shù)的盲源提取算法。該算法可以有效地從線性混合的源信號(hào)混合物中提取出具有特定時(shí)間結(jié)構(gòu)特性的感興趣信號(hào)�；跁r(shí)間結(jié)構(gòu)特性的盲源提取(TBSE)可以看作是標(biāo)準(zhǔn)ICA的擴(kuò)展。在生物醫(yī)學(xué)信號(hào)測(cè)量中,很多感興趣信號(hào)具有不同程度的周期特性。因此,TBSE將有非常廣闊的應(yīng)用空間。為了彌補(bǔ)現(xiàn)有的基于時(shí)間結(jié)構(gòu)特性盲源提取算法的計(jì)算需求量大和提取精度低等缺陷,本文提出一種改良的基于源信號(hào)時(shí)間結(jié)構(gòu)特性的盲源提取算法。 在實(shí)際應(yīng)用中,傳統(tǒng)的基于信號(hào)時(shí)間結(jié)構(gòu)特性的盲源提取算法會(huì)遇到若干與觀測(cè)數(shù)據(jù)有關(guān)的問(wèn)題。例如：時(shí)間相關(guān)關(guān)系不能得到完全滿足；盡管感興趣信號(hào)在特定的時(shí)間滯延處有強(qiáng)烈的時(shí)間相關(guān)性,有時(shí)其它信號(hào)也會(huì)在該時(shí)間滯延處有較弱的相關(guān)性,其它信號(hào)甚至也會(huì)在該時(shí)間滯延處時(shí)間相關(guān)。因此,傳統(tǒng)的基于信號(hào)時(shí)間結(jié)構(gòu)特性的盲源提取算法所提取的信號(hào)經(jīng)�；祀s有其它不感興趣的信號(hào)或者噪聲。極大似然估計(jì)是統(tǒng)計(jì)估計(jì)領(lǐng)域中的一種流行的高階統(tǒng)計(jì)(HOS)技術(shù)。如果源信號(hào)是非高斯的且具有時(shí)間相關(guān)特性,極大似然估計(jì)可以開(kāi)發(fā)有效地盲源提取方法。該類算法可以從信號(hào)混合物中提取出潛在的信號(hào),但由于局部最大化或算法隨機(jī)初始化等因素的影響,基于極大似然估計(jì)的盲源提取算法常常收斂到某一個(gè)局部極大值,所提取的信號(hào)不能保證是感興趣信號(hào)。 為了從測(cè)量到的源信號(hào)混合物中排他性地提取出感興趣信號(hào),本文提出一種基于源信號(hào)時(shí)間結(jié)構(gòu)特性和極大似然估計(jì)技術(shù)的綜合性盲源提取算法。整個(gè)提取過(guò)程分為兩個(gè)階段。第一階段利用感興趣信號(hào)的周期性信息從其線性混合物中提取出具有特定時(shí)間結(jié)構(gòu)特性的信號(hào)。所提取的信號(hào)雖然逼近了感興趣信號(hào),但�；祀s有若干其它信號(hào)甚至噪聲。因此,該階段只能看作是對(duì)感興趣信號(hào)的粗略提取。第二階段,基于源信號(hào)的統(tǒng)計(jì)獨(dú)立特性,我們把第一階段所提取的信號(hào)在極大似然估計(jì)框架下通過(guò)引進(jìn)一個(gè)參數(shù)密度模型進(jìn)行優(yōu)化處理。所設(shè)計(jì)的指數(shù)密度函數(shù)束能與源信號(hào)的邊際概率密度相匹配,因而可以對(duì)第一階段所提取的信號(hào)在未知源信號(hào)概率密度分布情況下實(shí)施優(yōu)化處理,從而提取出穩(wěn)定有效的感興趣信號(hào)�；谏镝t(yī)學(xué)信號(hào)的計(jì)算機(jī)仿真實(shí)驗(yàn)驗(yàn)證了本文提出算法的有效性,與其它盲源提取算法的對(duì)比進(jìn)一步說(shuō)明了算法的可靠性和魯棒性。 與傳統(tǒng)的盲源分離方法相比,盲源提取具有許多優(yōu)良特性,如計(jì)算負(fù)載少和處理速度快。因此,盲源提取廣泛應(yīng)用于解決源信號(hào)眾多而感興趣信號(hào)很少情況下的盲信號(hào)分離問(wèn)題。在實(shí)際應(yīng)用中,感興趣信號(hào)總是被其它信號(hào)甚至噪聲所干擾。例如：在現(xiàn)實(shí)世界中,許多測(cè)得的生物醫(yī)學(xué)信號(hào)不但包含眾多源信號(hào)而且感興趣信號(hào)還常常被其它信號(hào)甚至噪聲所污染。噪聲經(jīng)常會(huì)造成錯(cuò)誤的臨床診斷,有時(shí)甚至?xí)斐伤劳鍪录陌l(fā)生。 作為一種重要的非高斯性量度,歸一化峭度廣泛用于設(shè)計(jì)解決盲源分離／盲源提取問(wèn)題的目標(biāo)函數(shù)。盡管在理論和應(yīng)用上已經(jīng)證明了該類目標(biāo)函數(shù)的有效性,目前的基于歸一化峭度的盲源提取方法大多是在無(wú)噪聲環(huán)境下推導(dǎo)出來(lái)的,這在實(shí)際應(yīng)用中是不現(xiàn)實(shí)的。近年來(lái),學(xué)者們提出了幾個(gè)從噪聲環(huán)境下的信號(hào)混合物中根據(jù)歸一化峭度提取感興趣信號(hào)的方法,然而這些算法大都需要事先知道感興趣信號(hào)的歸一化峭度值。我們?cè)诂F(xiàn)實(shí)世界中經(jīng)常會(huì)碰到這樣的情況：不能事先確定感興趣信號(hào)準(zhǔn)確的歸一化峭度值,但可以事先獲取到感興趣信號(hào)歸一化峭度所在的區(qū)間范圍,且其它信號(hào)的歸一化峭度值不在該區(qū)間范圍內(nèi)。到目前為止,尚沒(méi)有相應(yīng)的盲源提取算法能在噪聲環(huán)境下使用該類區(qū)間范圍作為前驗(yàn)信息提取出感興趣信號(hào)。 本文首先設(shè)計(jì)出一個(gè)基于信號(hào)歸一化峭度的目標(biāo)函數(shù),然后使用拉格郎日乘子法最大化該目標(biāo)函數(shù),進(jìn)而構(gòu)建出一個(gè)基于感興趣信號(hào)歸一化峭度值區(qū)間范圍的盲源提取算法。只要事先獲取到感興趣信號(hào)歸一化峭度值所在的區(qū)間范圍,且其它信號(hào)的歸一化峭度值不在該區(qū)間范圍內(nèi),即使當(dāng)多個(gè)信號(hào)的歸一化峭度值非常接近,該算法也可以從噪聲環(huán)境下具有統(tǒng)計(jì)獨(dú)立特性的源信號(hào)混合物中提取出感興趣信號(hào)。 在許多BSS/BSE應(yīng)用中,人們經(jīng)�？梢允孪全@取到感興趣信號(hào)的某些前驗(yàn)信息。例如：感興趣信號(hào)的形態(tài)、相位、蹤跡或發(fā)生時(shí)間等。這些前驗(yàn)信息是與感興趣信號(hào)緊密相關(guān)的,如果它們攜帶的信息能夠把感興趣信號(hào)從觀測(cè)到的信號(hào)混合物中有效區(qū)分出來(lái),就稱其為參考信號(hào)�？偟膩�(lái)說(shuō),參考信號(hào)被認(rèn)為是根據(jù)某一距離量度離感興趣信號(hào)最近的信號(hào)。 近年來(lái),學(xué)者們提出了若干基于參考信號(hào)的盲源提取算法。例如：Lu等人提出一種稱作為ICA with reference(ICA-R)或constrained ICA(cICA)的盲源提取方法。ICA-R是通過(guò)最小化一個(gè)欠完備的目標(biāo)函數(shù)和最大化利用參考信號(hào)中的前驗(yàn)信息而構(gòu)建的。通過(guò)把部分前驗(yàn)信息以參考信號(hào)形式嵌入到著名的FastlCA算法中,ICA-R可以從大量的源信號(hào)混合物中提取出距離參考信號(hào)最近的感興趣信號(hào)。作為一種經(jīng)典地利用參考信號(hào)的盲源提取算法,ICA-R已經(jīng)成功地應(yīng)用到了功能磁共振成像(fMRI)處理領(lǐng)域中。然而,ICA-R在設(shè)計(jì)時(shí)并未考慮到噪聲的存在。在很多情況下由于噪聲污染的影響,算法的性能并不是很好。 參考信號(hào)攜帶著足夠的前驗(yàn)信息能夠從源信號(hào)混合物中排他性地區(qū)分出感興趣信號(hào)。在實(shí)際應(yīng)用中,感興趣信號(hào)通�？偸潜桓鞣N噪聲所污染。本文提出一種改進(jìn)的基于參考信號(hào)的盲源提取算法。我們首先把參考信號(hào)作為限制性條件系統(tǒng)化地嵌入到一個(gè)適用于噪聲數(shù)據(jù)的目標(biāo)函數(shù)中,從而構(gòu)建出一個(gè)限制性最優(yōu)化問(wèn)題,然后使用拉格郎日乘子法和梯度最優(yōu)化技術(shù)求解該最優(yōu)化問(wèn)題,進(jìn)而導(dǎo)出一個(gè)噪聲環(huán)境下基于參考信號(hào)的盲源提取算法。計(jì)算機(jī)仿真實(shí)驗(yàn)驗(yàn)證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.

【學(xué)位授予單位】：山東大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2012
【分類號(hào)】：R318.0

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本文編號(hào)：1840808