盲源分离算法及相关理论研究
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摘要
盲源分离或者盲信号分离（BSS）是指在各个源信号本身均未知的情况下，根据某种条件和假设，从混合的观察信号中分离出这些源信号的方法。在过去的几十年中，盲源分离技术由于其潜在的应用价值，得到了国内外众多学者的关注，发展极为迅速。目前，盲源分离技术已经在诸如语音增强与识别，生物工程，信息安全等领域中得到广泛应用。
本文首先介绍了盲源分离背景及国内外对于盲源分离的研究概况，接着讨论了盲源分离中经常用到的一些基本理论知识，这些知识包括盲源分离的约束条件，信号数据的中心化和白化等预处理技术，概率统计基础包括概率密度变换、峭度、高阶累积量等，另外介绍了信息论相关的知识，给出了一些必要的信息论方面的知识，如熵、负熵、互信息等。为了加深理解，介绍了几种常用的盲源分离算法。本文主要研究了瞬时线性混合盲源分离算法及其相关理论，主要成果如下：
1.研究利用图像的局部光滑特性实现盲源分离。结合图像本身的性质恢复混合图像是当前的研究热点之一。通过把图像信号和声音信号进行对比，可以发现在图像上一个较小的区域内，图像像素的变化程度很小，也就是说图像是局部光滑的，根据图像的这一现象，我们构造了一个适当的类熵函数表示图像局部区域的光滑程度，该类熵函数可以使源图像的熵值最小，同时使混合图像的熵值介于源图像极大熵值和极小熵值之间，然后把这个类熵函数作为遗传算法的目标函数，在整个图像空间搜索该类熵函数的极小值，取得了满意的分离效果，仿真实验表明了该方法的有效性。
2.研究基于二阶统计的频率域上的盲源分离算法。分析了Duarte提出的SOFI算法存在的累积误差问题，在此基础上提出一个逆向的二阶频率识别算法RSOFI，通过理论分析，证明了RSOFI算法的可行性。与SOFI算法相反，RSOFI首先提取的是光滑度最低的信号。但是RSOFI算法仍然存在累积误差问题，因此本文把SOFI算法和RSOFI算法结合起来，得到一个基于二阶统计量的改进的频域盲源分离算法ISOFI，在无噪声环境和有噪声环境下分别进行的仿真实验验证了ISOFI算法具有不错的分离性能。
3.次元或次分量（MCA）是数据具有最小方差的方向，也就是说，次元分析是寻找最小特征值所对应的特征向量的特征值分解（EVD）问题。特征值分解技术在盲源分离问题中有着广泛的应用，比如慢特征分析（SFA）方法，SOFI方法和我们提出的ISOFI方法都需要计算协方差矩阵的最小广义特征值对应的广义特征向量即次元，因此研究如何提取输入数据的次元是有意义的。本文通过研究现有的MCA神经网络学习算法，从广义特征分解的角度出发，提出了一种新颖的次元提取算法。对算法的理论分析证明了该算法的收敛性，通过与OJA+MCA学习算法和M LLER的MCA学习算法比较表明，我们提出的算法在实际应用中是一个很好的选择。
本文的研究工作始终与目前BSS理论研究方向相联系，对于推进BSS理论和算法的研究，具有一定的理论意义和应用价值。
Blind source separation (BSS) or blind signal separation is the techniquewhich canseparate out original signals from some observed mixed signals according to certainconditions and assumptions without knowing any priori information on the all thesource signals themselves. In the past decades, the techniques of blind signal separationhavegainedmore and more attentions from domestic and foreign scholars, and haveobtained extremely rapid development because of its potential numerous applications.At the present, BSS methods have been applied to the areas of speech enhancement andrecognition, bio-engineering, information security, etc. The linear instantaneous mixtureblind source separation algorithms and its related theory which bewidely used in thearea of BSS isto be researched in this dissertation.
This dissertation introduces the background of blind source separation and theresearch status of domestic and foreign at the beginning. And then, some basictheoretical knowledgeincluding the constraints,central processing and pre-whiteningprocessing are introduced. At the same time, theknowledge related to information theoryconsists of entropy, negative entropy,mutual information,kurtosis and higher-ordercumulants are presented.Some classical algorithms of BSS have also been provided.The main results of this thesis are as follows:
1.A novel algorithm which can separate themixed smooth images by utilizing localsmoothness which attracts more and more attentions at the present is proposed. Thedegree of variations of pixels where a smaller area is very slowwhich can be discoveredby comparing image with wave signal. In other words, the image is of locally smooth.Based on this discovery, a proper like entropy function which can represent the localsmoothness of an image is formulated. The entropy of source images are the lowestbased on the like entropy function, at the same time, the entropy value of mixed imagesis between the highest entropy of the source images and the lowest entropy of the sourceimages. Accordingly, the separation weight vector associated with the lowest entropyvalues canbe obtained. Compared with the conventional independent componentanalysis algorithm, the original signals in theproposed algorithm are not required to be independent. Simulation results on mixed images are employed to furtherillustrate theadvantages of the proposed method.
2.The blind separation algorithm based on second-order statistics is studied.Thedisadvantages existing in the method proposed by Duarte is analyzed.On that basis,areversed second-order frequency indentification algorithm is proposed. Bytheoreticalanalysis, the feasibility of the reversed algorithm is proven. However, the reversedalgorithm still has the shortcoming of cumulative errors. To overcome the disadvantagesof cumulative errors existing in the both of SOFI and RSOFI algorithm, an improvedmethod is proposed by using symmetric mode. Theoretical analysis and simulationresults show the effectiveness of the improved method compared with the originalalgorithm in both noisy and noise-free scenarios.
3. Minor component analysis (MCA) are widely used in many applications such ascurve and surface fitting, robustbeamforming, and blind signal separation. Based on thegeneralized eigen-decomposition, completely different approach that leads to derive anovel MCA algorithm is presented. First, in the sense ofgeneralizedeigen-decomposition, by using gradient ascent approach, we derive analgorithm for extractingthe first minor eigenvector. Then, the algorithm used to extractmultiple minor eigenvectors is proposedby using the orthogonality property. The proofsand rigorous theoretical analysis show that the proposedalgorithm is convergent to theircorresponding minor eigenvectors. Three important characteristicsof these algorithmsare identified. The first is that the algorithm for extracting minor eigenvectors canbeextended to generalized minor eigenvectors easily. The second is that thecorresponding eigenvalues canbe computed simultaneously as a byproduct of thisalgorithm. The third is that the algorithm is globallyconvergent. The simulations havebeen conducted for illustration of the efficiency and effectiveness ofthe proposedalgorithm.
This research of the thesis is closely linked with the present BSS theoreticalresearch, which has a certain instructional significance to the study of BSS theory andalgorithm.
本文首先介绍了盲源分离背景及国内外对于盲源分离的研究概况，接着讨论了盲源分离中经常用到的一些基本理论知识，这些知识包括盲源分离的约束条件，信号数据的中心化和白化等预处理技术，概率统计基础包括概率密度变换、峭度、高阶累积量等，另外介绍了信息论相关的知识，给出了一些必要的信息论方面的知识，如熵、负熵、互信息等。为了加深理解，介绍了几种常用的盲源分离算法。本文主要研究了瞬时线性混合盲源分离算法及其相关理论，主要成果如下：
1.研究利用图像的局部光滑特性实现盲源分离。结合图像本身的性质恢复混合图像是当前的研究热点之一。通过把图像信号和声音信号进行对比，可以发现在图像上一个较小的区域内，图像像素的变化程度很小，也就是说图像是局部光滑的，根据图像的这一现象，我们构造了一个适当的类熵函数表示图像局部区域的光滑程度，该类熵函数可以使源图像的熵值最小，同时使混合图像的熵值介于源图像极大熵值和极小熵值之间，然后把这个类熵函数作为遗传算法的目标函数，在整个图像空间搜索该类熵函数的极小值，取得了满意的分离效果，仿真实验表明了该方法的有效性。
2.研究基于二阶统计的频率域上的盲源分离算法。分析了Duarte提出的SOFI算法存在的累积误差问题，在此基础上提出一个逆向的二阶频率识别算法RSOFI，通过理论分析，证明了RSOFI算法的可行性。与SOFI算法相反，RSOFI首先提取的是光滑度最低的信号。但是RSOFI算法仍然存在累积误差问题，因此本文把SOFI算法和RSOFI算法结合起来，得到一个基于二阶统计量的改进的频域盲源分离算法ISOFI，在无噪声环境和有噪声环境下分别进行的仿真实验验证了ISOFI算法具有不错的分离性能。
3.次元或次分量（MCA）是数据具有最小方差的方向，也就是说，次元分析是寻找最小特征值所对应的特征向量的特征值分解（EVD）问题。特征值分解技术在盲源分离问题中有着广泛的应用，比如慢特征分析（SFA）方法，SOFI方法和我们提出的ISOFI方法都需要计算协方差矩阵的最小广义特征值对应的广义特征向量即次元，因此研究如何提取输入数据的次元是有意义的。本文通过研究现有的MCA神经网络学习算法，从广义特征分解的角度出发，提出了一种新颖的次元提取算法。对算法的理论分析证明了该算法的收敛性，通过与OJA+MCA学习算法和M LLER的MCA学习算法比较表明，我们提出的算法在实际应用中是一个很好的选择。
本文的研究工作始终与目前BSS理论研究方向相联系，对于推进BSS理论和算法的研究，具有一定的理论意义和应用价值。
Blind source separation (BSS) or blind signal separation is the techniquewhich canseparate out original signals from some observed mixed signals according to certainconditions and assumptions without knowing any priori information on the all thesource signals themselves. In the past decades, the techniques of blind signal separationhavegainedmore and more attentions from domestic and foreign scholars, and haveobtained extremely rapid development because of its potential numerous applications.At the present, BSS methods have been applied to the areas of speech enhancement andrecognition, bio-engineering, information security, etc. The linear instantaneous mixtureblind source separation algorithms and its related theory which bewidely used in thearea of BSS isto be researched in this dissertation.
This dissertation introduces the background of blind source separation and theresearch status of domestic and foreign at the beginning. And then, some basictheoretical knowledgeincluding the constraints,central processing and pre-whiteningprocessing are introduced. At the same time, theknowledge related to information theoryconsists of entropy, negative entropy,mutual information,kurtosis and higher-ordercumulants are presented.Some classical algorithms of BSS have also been provided.The main results of this thesis are as follows:
1.A novel algorithm which can separate themixed smooth images by utilizing localsmoothness which attracts more and more attentions at the present is proposed. Thedegree of variations of pixels where a smaller area is very slowwhich can be discoveredby comparing image with wave signal. In other words, the image is of locally smooth.Based on this discovery, a proper like entropy function which can represent the localsmoothness of an image is formulated. The entropy of source images are the lowestbased on the like entropy function, at the same time, the entropy value of mixed imagesis between the highest entropy of the source images and the lowest entropy of the sourceimages. Accordingly, the separation weight vector associated with the lowest entropyvalues canbe obtained. Compared with the conventional independent componentanalysis algorithm, the original signals in theproposed algorithm are not required to be independent. Simulation results on mixed images are employed to furtherillustrate theadvantages of the proposed method.
2.The blind separation algorithm based on second-order statistics is studied.Thedisadvantages existing in the method proposed by Duarte is analyzed.On that basis,areversed second-order frequency indentification algorithm is proposed. Bytheoreticalanalysis, the feasibility of the reversed algorithm is proven. However, the reversedalgorithm still has the shortcoming of cumulative errors. To overcome the disadvantagesof cumulative errors existing in the both of SOFI and RSOFI algorithm, an improvedmethod is proposed by using symmetric mode. Theoretical analysis and simulationresults show the effectiveness of the improved method compared with the originalalgorithm in both noisy and noise-free scenarios.
3. Minor component analysis (MCA) are widely used in many applications such ascurve and surface fitting, robustbeamforming, and blind signal separation. Based on thegeneralized eigen-decomposition, completely different approach that leads to derive anovel MCA algorithm is presented. First, in the sense ofgeneralizedeigen-decomposition, by using gradient ascent approach, we derive analgorithm for extractingthe first minor eigenvector. Then, the algorithm used to extractmultiple minor eigenvectors is proposedby using the orthogonality property. The proofsand rigorous theoretical analysis show that the proposedalgorithm is convergent to theircorresponding minor eigenvectors. Three important characteristicsof these algorithmsare identified. The first is that the algorithm for extracting minor eigenvectors canbeextended to generalized minor eigenvectors easily. The second is that thecorresponding eigenvalues canbe computed simultaneously as a byproduct of thisalgorithm. The third is that the algorithm is globallyconvergent. The simulations havebeen conducted for illustration of the efficiency and effectiveness ofthe proposedalgorithm.
This research of the thesis is closely linked with the present BSS theoreticalresearch, which has a certain instructional significance to the study of BSS theory andalgorithm.
引文
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