本文選題：獨立分量分析 + 盲源分離　； 參考：《山東大學》2012年博士論文

【摘要】：獨立分量分析(ICA)是二十世紀九十年代發(fā)展起來的一種多元統(tǒng)計和計算技術,目的是用來分離或提取隨機變量、觀測數(shù)據(jù)或信號混合物中具有獨立特性的隱藏分量。ICA可以看作是主分量分析(PCA)和因子分析(FA)的擴展。與PCA和FA相比,ICA是一種更強有力的技術。當PCA和FA等經(jīng)典方法失效時,ICA仍然能從具有統(tǒng)計獨立特性的觀測信號中挖掘出支撐數(shù)據(jù)的內(nèi)在分量或因子。對于通常是以大型樣本數(shù)據(jù)庫形式給出的多元觀測數(shù)據(jù),ICA定義了一個生成模型,該模型假設所觀測到的數(shù)據(jù)變量是未知源信號的線性或非線性混合。事實上,ICA模型中原始的源信號和實現(xiàn)混合的系統(tǒng)都是未知的。ICA還假設那些潛在變量是非高斯的且相互獨立,并稱它們?yōu)橛^測數(shù)據(jù)的獨立分量。這些獨立分量也可以稱作為源信號或因子,它們可以通過ICA相關方法分離或提取出來。 近年來,由于在語音處理、生物醫(yī)學信號處理、圖像特征提取和無線通信等領域潛在的影響力,基于ICA的盲源分離(BSS)和盲源提取(BSE)已經(jīng)引起了社會各界高度的關注。許多科研機構都在致力于盲源分離/盲源提取方法的開發(fā)和應用,并已在ICA相關理論和應用中取得了很多有價值的研究成果。然而,ICA的研究目前尚處于發(fā)展階段,ICA算法和應用中仍然存在若干尚未解決的問題,這就限制了ICA技術的發(fā)展和應用�？偟膩碚f,ICA技術仍然需要進一步加強和完善。 本文介紹了國內(nèi)外ICA的發(fā)展歷史、研究現(xiàn)狀以及應用情況,闡述了ICA的理論基礎,包括ICA的數(shù)學定義、基本假設以及相關的數(shù)學理論基礎和實現(xiàn)途徑等,并針對擴展ICA現(xiàn)存的幾個問題。例如：對具有時間結構特性感興趣信號的盲源提取、噪聲環(huán)境下基于高斯矩和參考信號的盲源提取和基于感興趣信號歸一化峭度值范圍的盲源提取等進行了比較深入的研究,提出了幾個較為有效的算法。 本文的核心內(nèi)容概括如下： 提出了一種針對源信號具有時間結構特性的基于極大似然估計技術的盲源提取算法。該算法可以有效地從線性混合的源信號混合物中提取出具有特定時間結構特性的感興趣信號�；跁r間結構特性的盲源提取(TBSE)可以看作是標準ICA的擴展。在生物醫(yī)學信號測量中,很多感興趣信號具有不同程度的周期特性。因此,TBSE將有非常廣闊的應用空間。為了彌補現(xiàn)有的基于時間結構特性盲源提取算法的計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時間結構特性的盲源提取算法。 在實際應用中,傳統(tǒng)的基于信號時間結構特性的盲源提取算法會遇到若干與觀測數(shù)據(jù)有關的問題。例如：時間相關關系不能得到完全滿足；盡管感興趣信號在特定的時間滯延處有強烈的時間相關性,有時其它信號也會在該時間滯延處有較弱的相關性,其它信號甚至也會在該時間滯延處時間相關。因此,傳統(tǒng)的基于信號時間結構特性的盲源提取算法所提取的信號經(jīng)�；祀s有其它不感興趣的信號或者噪聲。極大似然估計是統(tǒng)計估計領域中的一種流行的高階統(tǒng)計(HOS)技術。如果源信號是非高斯的且具有時間相關特性,極大似然估計可以開發(fā)有效地盲源提取方法。該類算法可以從信號混合物中提取出潛在的信號,但由于局部最大化或算法隨機初始化等因素的影響,基于極大似然估計的盲源提取算法常常收斂到某一個局部極大值,所提取的信號不能保證是感興趣信號。 為了從測量到的源信號混合物中排他性地提取出感興趣信號,本文提出一種基于源信號時間結構特性和極大似然估計技術的綜合性盲源提取算法。整個提取過程分為兩個階段。第一階段利用感興趣信號的周期性信息從其線性混合物中提取出具有特定時間結構特性的信號。所提取的信號雖然逼近了感興趣信號,但常混雜有若干其它信號甚至噪聲。因此,該階段只能看作是對感興趣信號的粗略提取。第二階段,基于源信號的統(tǒng)計獨立特性,我們把第一階段所提取的信號在極大似然估計框架下通過引進一個參數(shù)密度模型進行優(yōu)化處理。所設計的指數(shù)密度函數(shù)束能與源信號的邊際概率密度相匹配,因而可以對第一階段所提取的信號在未知源信號概率密度分布情況下實施優(yōu)化處理,從而提取出穩(wěn)定有效的感興趣信號�；谏镝t(yī)學信號的計算機仿真實驗驗證了本文提出算法的有效性,與其它盲源提取算法的對比進一步說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,如計算負載少和處理速度快。因此,盲源提取廣泛應用于解決源信號眾多而感興趣信號很少情況下的盲信號分離問題。在實際應用中,感興趣信號總是被其它信號甚至噪聲所干擾。例如：在現(xiàn)實世界中,許多測得的生物醫(yī)學信號不但包含眾多源信號而且感興趣信號還常常被其它信號甚至噪聲所污染。噪聲經(jīng)常會造成錯誤的臨床診斷,有時甚至會造成死亡事件的發(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計解決盲源分離／盲源提取問題的目標函數(shù)。盡管在理論和應用上已經(jīng)證明了該類目標函數(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噪聲環(huán)境下推導出來的,這在實際應用中是不現(xiàn)實的。近年來,學者們提出了幾個從噪聲環(huán)境下的信號混合物中根據(jù)歸一化峭度提取感興趣信號的方法,然而這些算法大都需要事先知道感興趣信號的歸一化峭度值。我們在現(xiàn)實世界中經(jīng)常會碰到這樣的情況：不能事先確定感興趣信號準確的歸一化峭度值,但可以事先獲取到感興趣信號歸一化峭度所在的區(qū)間范圍,且其它信號的歸一化峭度值不在該區(qū)間范圍內(nèi)。到目前為止,尚沒有相應的盲源提取算法能在噪聲環(huán)境下使用該類區(qū)間范圍作為前驗信息提取出感興趣信號。 本文首先設計出一個基于信號歸一化峭度的目標函數(shù),然后使用拉格郎日乘子法最大化該目標函數(shù),進而構建出一個基于感興趣信號歸一化峭度值區(qū)間范圍的盲源提取算法。只要事先獲取到感興趣信號歸一化峭度值所在的區(qū)間范圍,且其它信號的歸一化峭度值不在該區(qū)間范圍內(nèi),即使當多個信號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)計獨立特性的源信號混合物中提取出感興趣信號。 在許多BSS/BSE應用中,人們經(jīng)�？梢允孪全@取到感興趣信號的某些前驗信息。例如：感興趣信號的形態(tài)、相位、蹤跡或發(fā)生時間等。這些前驗信息是與感興趣信號緊密相關的,如果它們攜帶的信息能夠把感興趣信號從觀測到的信號混合物中有效區(qū)分出來,就稱其為參考信號�？偟膩碚f,參考信號被認為是根據(jù)某一距離量度離感興趣信號最近的信號。 近年來,學者們提出了若干基于參考信號的盲源提取算法。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是通過最小化一個欠完備的目標函數(shù)和最大化利用參考信號中的前驗信息而構建的。通過把部分前驗信息以參考信號形式嵌入到著名的FastlCA算法中,ICA-R可以從大量的源信號混合物中提取出距離參考信號最近的感興趣信號。作為一種經(jīng)典地利用參考信號的盲源提取算法,ICA-R已經(jīng)成功地應用到了功能磁共振成像(fMRI)處理領域中。然而,ICA-R在設計時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。 參考信號攜帶著足夠的前驗信息能夠從源信號混合物中排他性地區(qū)分出感興趣信號。在實際應用中,感興趣信號通�？偸潜桓鞣N噪聲所污染。本文提出一種改進的基于參考信號的盲源提取算法。我們首先把參考信號作為限制性條件系統(tǒng)化地嵌入到一個適用于噪聲數(shù)據(jù)的目標函數(shù)中,從而構建出一個限制性最優(yōu)化問題,然后使用拉格郎日乘子法和梯度最優(yōu)化技術求解該最優(yōu)化問題,進而導出一個噪聲環(huán)境下基于參考信號的盲源提取算法。計算機仿真實驗驗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.

【學位授予單位】：山東大學
【學位級別】：博士
【學位授予年份】：2012
【分類號】：R318.0

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