基于循环平衡理论的盲源分离算法
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摘要
盲源分离是二十世纪九十年代末期提出的一种新的信号处理方法,是在源信号及传输信道未知的情况下,仅利用接收滤波器输出的观测数据恢复源信号的方法。主要用于恢复和提取多通道混合信号中的潜在成分,进而在混合信号中分析出有用信号。盲源分离由于不需要训练序列就能实现对混合源信号的分离,已被广泛应用于通信、图像处理、生物医学、地质勘探等领域,成为目前信号处理领域的重要热点研究课题之一。
传统的盲源分离算法是以接收信号为平稳信号为前提进行处理的,但自然界中的多数信号却具有循环平稳特性。本文以循环平稳理论为基础对接收信号进行处理,从接收混合信号中提取有用信息,使算法的运算量大大减小,仿真实验表明了新算法具有较好分离效果。
本文所做的主要工作有：
(1)研究了循环平稳理论及其在信号分离中的应用,阐述了盲源分离算法的基本原理、算法类型、发展现状等,重点分析了高阶统计量盲源分离算法和二阶统计量盲源分离算法。
(2)阐述了利用循环平稳度控制分离矩阵的原理,推导了二阶循环平稳度准则,提出了基于该准则的盲源分离算法。同时,将二阶循环平稳度扩展到高阶循环平稳度,推导了三阶循环累积量的循环平稳度准则,证明了该准则对于信号分离的有效性,提出了基于三阶循环平稳度准则的盲源分离算法。
(3)阐述了通过优化规则求解目标函数极值的盲源分离算法原理,分析了联合矩阵近似对角化过程,提出了基于循环平稳理论的联合矩阵近似对角化盲源分离算法。首先对接收信号进行鲁棒白化处理,根据二阶统计量实现混合信号的去相关,在对各分量进行正交变换后实现混合信号的盲源分离。同时,将循环累积量引入矩阵联合近似对角化原理中,提出了基于循环累积量的联合近似对角化盲源分离算法。
(4)根据信息论相关理论,分析了KL散度和最小互信量及其性质,提出了基于互信息量最小化的循环平稳信号盲源分离算法。该算法利用互信息量来度量分离信号的循环相关矩阵和单位阵的相似程度,通过自然梯度寻优算法来实现互信息量的最小化,从而得到理想的分离矩阵。
Blind Source Separation (BSS) was proposed at the end of 1990s, which is a completely new way of signal processing, and it can recover the desired signal without the priori channel information and the source signals. This technology is mainly used to recover and extract the Potential components in the multi-channel, then analyze the desried signal from the mixed signals. BSS can separate the desired signal from the mixed signals without the Training sequence, it has been widely used in such fields as: communication, image processing, Biomedical, geological exploration, and etc. BSS has become an important hot research topic in the fields of signal processing.
The traditional blind source separation algorithm was proposed on the basis of the transmitted signal stationary. But most of the natrual signals have the characteristics of cyclostationary (CS). This paper is mainly to process the mixed signal based on cyclostationary theory, and extract the useful information from the received mixed signals, which greatly reduced the computation complexity, the simulation experiments show that the new algorithms have better separation results.
The major contribution of this paper is summarized as follow:
1.Comprehensive analyzed the cyclostationary theory and its application in the field of signal separation. Introduced the Concepts, principles and techniques, and the classification of blind source separation algorithm, mainly analyzed the BSS algorithms based on the second order and the high order cyclostatistics.
2. Described the principle of controlling the BSS matrix based on degree of cyclostationary (DCS), derived the second-order DCS criterion, and a new BSS algorithm based on the criterion was proposed. Then, extend the concept of DCS to high-order statistics, derived the 3-order cyclic cumulant DCS criterion, proved the effection of the new criterion for the signal separation, and proposed a new BSS algorithm based on the 3-order cyclic cumulant.
3. Described the optimization rules to establish objective function extremum and analyzed the joint approximate diagonalization matrix (JADE), and proposed a new BSS algorithm of CS JADE. This algorithm whitening processed the received mixed signals firstly and orthogonal transformated the components according to decorrelation principle to transformated the components according to decorrelation principle to realize the separation effect. Simultaneously, introduced the cyclic cumulant matrix into the JADE principle, proposed the blind source separation algorithm of cyclic cumulant JADE principle.
4. According to the theory of information theory, analyzed the nature of KL divergence and the minimum mutual Information (MMI), proposed a new blind source separation of minimum mutual Information. The proposed new algorithm takes the mutual information as the measurement to illustrate the similarity between cyclic correlation matrix and the matrix units. According to the natural gradient optimization algorithm to achieve a minimum of mutual information to get the ideal separation matrix.
传统的盲源分离算法是以接收信号为平稳信号为前提进行处理的,但自然界中的多数信号却具有循环平稳特性。本文以循环平稳理论为基础对接收信号进行处理,从接收混合信号中提取有用信息,使算法的运算量大大减小,仿真实验表明了新算法具有较好分离效果。
本文所做的主要工作有：
(1)研究了循环平稳理论及其在信号分离中的应用,阐述了盲源分离算法的基本原理、算法类型、发展现状等,重点分析了高阶统计量盲源分离算法和二阶统计量盲源分离算法。
(2)阐述了利用循环平稳度控制分离矩阵的原理,推导了二阶循环平稳度准则,提出了基于该准则的盲源分离算法。同时,将二阶循环平稳度扩展到高阶循环平稳度,推导了三阶循环累积量的循环平稳度准则,证明了该准则对于信号分离的有效性,提出了基于三阶循环平稳度准则的盲源分离算法。
(3)阐述了通过优化规则求解目标函数极值的盲源分离算法原理,分析了联合矩阵近似对角化过程,提出了基于循环平稳理论的联合矩阵近似对角化盲源分离算法。首先对接收信号进行鲁棒白化处理,根据二阶统计量实现混合信号的去相关,在对各分量进行正交变换后实现混合信号的盲源分离。同时,将循环累积量引入矩阵联合近似对角化原理中,提出了基于循环累积量的联合近似对角化盲源分离算法。
(4)根据信息论相关理论,分析了KL散度和最小互信量及其性质,提出了基于互信息量最小化的循环平稳信号盲源分离算法。该算法利用互信息量来度量分离信号的循环相关矩阵和单位阵的相似程度,通过自然梯度寻优算法来实现互信息量的最小化,从而得到理想的分离矩阵。
Blind Source Separation (BSS) was proposed at the end of 1990s, which is a completely new way of signal processing, and it can recover the desired signal without the priori channel information and the source signals. This technology is mainly used to recover and extract the Potential components in the multi-channel, then analyze the desried signal from the mixed signals. BSS can separate the desired signal from the mixed signals without the Training sequence, it has been widely used in such fields as: communication, image processing, Biomedical, geological exploration, and etc. BSS has become an important hot research topic in the fields of signal processing.
The traditional blind source separation algorithm was proposed on the basis of the transmitted signal stationary. But most of the natrual signals have the characteristics of cyclostationary (CS). This paper is mainly to process the mixed signal based on cyclostationary theory, and extract the useful information from the received mixed signals, which greatly reduced the computation complexity, the simulation experiments show that the new algorithms have better separation results.
The major contribution of this paper is summarized as follow:
1.Comprehensive analyzed the cyclostationary theory and its application in the field of signal separation. Introduced the Concepts, principles and techniques, and the classification of blind source separation algorithm, mainly analyzed the BSS algorithms based on the second order and the high order cyclostatistics.
2. Described the principle of controlling the BSS matrix based on degree of cyclostationary (DCS), derived the second-order DCS criterion, and a new BSS algorithm based on the criterion was proposed. Then, extend the concept of DCS to high-order statistics, derived the 3-order cyclic cumulant DCS criterion, proved the effection of the new criterion for the signal separation, and proposed a new BSS algorithm based on the 3-order cyclic cumulant.
3. Described the optimization rules to establish objective function extremum and analyzed the joint approximate diagonalization matrix (JADE), and proposed a new BSS algorithm of CS JADE. This algorithm whitening processed the received mixed signals firstly and orthogonal transformated the components according to decorrelation principle to transformated the components according to decorrelation principle to realize the separation effect. Simultaneously, introduced the cyclic cumulant matrix into the JADE principle, proposed the blind source separation algorithm of cyclic cumulant JADE principle.
4. According to the theory of information theory, analyzed the nature of KL divergence and the minimum mutual Information (MMI), proposed a new blind source separation of minimum mutual Information. The proposed new algorithm takes the mutual information as the measurement to illustrate the similarity between cyclic correlation matrix and the matrix units. According to the natural gradient optimization algorithm to achieve a minimum of mutual information to get the ideal separation matrix.
引文
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