盲分离算法的研究
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摘要
盲信号处理是当今信号处理领域的一个研究热点。它在无线通信、医学信号的智能化处理和分析、特征提取、语音和图像的增强及识别等方面有广泛的应用。相关的论文提出了众多有效的算法。在已有算法的基础上，本文做了以下几个方面的工作：
1．有些基于互累积量准则的算法不能够分离超高斯、亚高斯与高斯信号的混合信号。有些神经网络算法虽然能够分离超高斯、亚高斯与高斯信号中的任意一类信号，但是需要人为地选择相应的非线性函数作为评价函数的估计。有些算法先估计信号概率密度，进而估计出评价函数，但是算法的复杂度高。本文算法的着眼点在自适应地估计评价函数。评价函数的形式由一个参数的值决定，通过在线估计这个参数，从而使评价函数变成适合分离的信号所需要的形式。估计评价函数的算法需要调整的参数只有一个，因此算法的复杂度低，实验证明算法对参数初始值的选取也不敏感，算法的稳定性好。同时提出了几个基于累积量的分离算法。
2．后非线性盲分离系统中的非线性部分用一个多层感知器模拟。在盲解卷模型的参数空间里，代表代价函数最陡下降方向的不是传统的梯度而是自然梯度。基于传统梯度的BP算法的收敛速度慢，容易陷入局部最优点。本文采用自然梯度法估计盲解卷模型中的参数。相对而言，基于自然梯度的学习算法收敛的速度更快，分离的效果更好。
3．提出了一个基于核函数的后非线性盲分离算法。本算法先将有非线性失真的观测数据变换到特征空间中，求两个不同数据集合(都属于观测信号)的协方差矩阵，然后解一个广义特征值问题，就可以恢复出源信号。这个方法比基于神经网络的算法简单。针对卷积混合的情况，本文将线性混合情况下的解相关方法推广到特征空间中，提出了一个同样是基于核函数的后非线性盲解卷算法。
4．提出了一个基于集成学习方法的盲解卷算法。基于最大似然的盲解卷算法容易陷入局部最优解，集成学习方法有效地克服了最大似然方法的这个缺点。因而，算法的估计效果更好。
5．讨论了在Bayesian方法盲分离/解卷算法中，考虑先验信息以后与没有考虑先验的算法的性能差别。在基于源信号独立假设条件的算法的基础上，以先验形式引入二阶统计信息，使算法适用于源信号不完全独立但是满足不相关条件的情况。
In recent years, Blind Signal Processing has become one of the hottest areas in Signal Processing. The problem is relevant in various applications, especially in wireless communication, biomedical engineering, speech and image enhancement, speech and image recognition, feature extraction, etc. A large number of papers have been published on the problem of blind signal processing. The main contributions of this dissertation are:
1.Some cross-cumulant-based algorithms can't recover sources from the mixtures of super-Gaussian, sub-Gaussian and Gaussian signals. In some neural network approaches, the signs of the kurtosises of sources are assumed to be known. Some blind signal separation algorithms estimate the probability density function of the sources, with which then calculate the score function. But the method is often costly in computation and suffers from instability. In this dissertation, we propose a simple method to adaptively estimate the score function. In this method, only one parameter needs to be estimated. The simulations show the stability and effectiveness of the method.
2. The nonlinear sub-system of the post-linear blind source separation structure is modeled by a multilayer perceptron. It is well known that the natural gradient learning has ideal performances for on-line training of multilayer peceptrons. The natural gradient rather than conventional one gives the steepest descent direction of loss function in the parameter space of blind source separation. The conventional backpropagation method based on the ordinary gradient suffers from the plateaus which give rise to slow convergence. The natural gradient based algorithm gives better performance and faster convergence speed than the conventional algorithm.
3.We derive a new method based on kernel to solve the post-linear blind signal separation problem. We first project the observed data into feature space, and then apply the blind source separation algorithms developed for linear mixture model for separating the signals in feature space. In addition to the generalized eigenvalue method, we give the decorrelation method for source separation in the feature space.
4.Maximum likelihood scheme is widely used to learn the parameters in the latent variable model. It has some drawbacks such as overfitting and sensitivity to local optimization. In order to circumvent the drawbaks, we use ensemble learning to
1．有些基于互累积量准则的算法不能够分离超高斯、亚高斯与高斯信号的混合信号。有些神经网络算法虽然能够分离超高斯、亚高斯与高斯信号中的任意一类信号，但是需要人为地选择相应的非线性函数作为评价函数的估计。有些算法先估计信号概率密度，进而估计出评价函数，但是算法的复杂度高。本文算法的着眼点在自适应地估计评价函数。评价函数的形式由一个参数的值决定，通过在线估计这个参数，从而使评价函数变成适合分离的信号所需要的形式。估计评价函数的算法需要调整的参数只有一个，因此算法的复杂度低，实验证明算法对参数初始值的选取也不敏感，算法的稳定性好。同时提出了几个基于累积量的分离算法。
2．后非线性盲分离系统中的非线性部分用一个多层感知器模拟。在盲解卷模型的参数空间里，代表代价函数最陡下降方向的不是传统的梯度而是自然梯度。基于传统梯度的BP算法的收敛速度慢，容易陷入局部最优点。本文采用自然梯度法估计盲解卷模型中的参数。相对而言，基于自然梯度的学习算法收敛的速度更快，分离的效果更好。
3．提出了一个基于核函数的后非线性盲分离算法。本算法先将有非线性失真的观测数据变换到特征空间中，求两个不同数据集合(都属于观测信号)的协方差矩阵，然后解一个广义特征值问题，就可以恢复出源信号。这个方法比基于神经网络的算法简单。针对卷积混合的情况，本文将线性混合情况下的解相关方法推广到特征空间中，提出了一个同样是基于核函数的后非线性盲解卷算法。
4．提出了一个基于集成学习方法的盲解卷算法。基于最大似然的盲解卷算法容易陷入局部最优解，集成学习方法有效地克服了最大似然方法的这个缺点。因而，算法的估计效果更好。
5．讨论了在Bayesian方法盲分离/解卷算法中，考虑先验信息以后与没有考虑先验的算法的性能差别。在基于源信号独立假设条件的算法的基础上，以先验形式引入二阶统计信息，使算法适用于源信号不完全独立但是满足不相关条件的情况。
In recent years, Blind Signal Processing has become one of the hottest areas in Signal Processing. The problem is relevant in various applications, especially in wireless communication, biomedical engineering, speech and image enhancement, speech and image recognition, feature extraction, etc. A large number of papers have been published on the problem of blind signal processing. The main contributions of this dissertation are:
1.Some cross-cumulant-based algorithms can't recover sources from the mixtures of super-Gaussian, sub-Gaussian and Gaussian signals. In some neural network approaches, the signs of the kurtosises of sources are assumed to be known. Some blind signal separation algorithms estimate the probability density function of the sources, with which then calculate the score function. But the method is often costly in computation and suffers from instability. In this dissertation, we propose a simple method to adaptively estimate the score function. In this method, only one parameter needs to be estimated. The simulations show the stability and effectiveness of the method.
2. The nonlinear sub-system of the post-linear blind source separation structure is modeled by a multilayer perceptron. It is well known that the natural gradient learning has ideal performances for on-line training of multilayer peceptrons. The natural gradient rather than conventional one gives the steepest descent direction of loss function in the parameter space of blind source separation. The conventional backpropagation method based on the ordinary gradient suffers from the plateaus which give rise to slow convergence. The natural gradient based algorithm gives better performance and faster convergence speed than the conventional algorithm.
3.We derive a new method based on kernel to solve the post-linear blind signal separation problem. We first project the observed data into feature space, and then apply the blind source separation algorithms developed for linear mixture model for separating the signals in feature space. In addition to the generalized eigenvalue method, we give the decorrelation method for source separation in the feature space.
4.Maximum likelihood scheme is widely used to learn the parameters in the latent variable model. It has some drawbacks such as overfitting and sensitivity to local optimization. In order to circumvent the drawbaks, we use ensemble learning to
引文
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