基于核估计的超定混合共轭盲信号分离方法

当混合信号的个数多于源信号时,盲源分离模型中的混合矩阵被描述为一个超定矩阵,因此不能直接通过估计逆矩阵的方法来得到分离矩阵。针对该线性超定混合情况提出了一种基于共轭梯度的盲源分离方法。该方法基于最小互信息准则,通过对行满秩分离矩阵的奇异值分解而引入了超定盲源分离的代价函数。利用共轭梯度优化算法推导出了迭代计算分离矩阵的更新公式。在每次迭代计算中,利用随机变量概率密度估计的核函数法在线估计分离信号的评价函数。避免了诸多传统盲分离算法中只能凭经验选取特定的非线性函数来代替评价函数的问题。仿真结果验证了所提算法的有效性。     

Adaptive weighted orthogonal constrained algorithm for blind source separation

Blind source separation (BSS) consists of recovering the statistically independent source signals from their linear mixtures without knowing the mixing coefficients. Pre-whitening is a useful pre-processing technique in BSS. However, BSS algorithms based on the pre-whitened data lack the equivariance property, one of the significant properties in BSS. By transforming the pre-whitening into a weighted orthogonal constraint condition, this paper proposes a new definition of the contrast function. In light of the constrained optimization method, various weighted orthogonal constrained BSS algorithms with equivariance property are developed. Simulations on man-made signals and practical speech signals show the proposed weighted orthogonal constrained BSS algorithms have better separation ability, convergent speed and steady state performance.     

Mixing matrix estimation using discriminative clustering for blind source separation

Mixing matrix estimation in instantaneous blind source separation (BSS) can be performed by exploiting the sparsity and disjoint orthogonality of source signals. As a result, approaches for estimating the unknown mixing process typically employ clustering algorithms on the mixtures in a parametric domain, where the signals can be sparsely represented. In this paper, we propose two algorithms to perform discriminative clustering of the mixture signals for estimating the mixing matrix. For the case of overdetermined BSS, we develop an algorithm to perform linear discriminant analysis based on similarity measures and combine it with K-hyperline clustering. Furthermore, we propose to perform discriminative clustering in a high-dimensional feature space obtained by an implicit mapping, using the kernel trick, for the case of underdetermined source separation. Using simulations on synthetic data, we demonstrate the improvements in mixing matrix estimation performance obtained using the proposed algorithms in comparison to other clustering methods. Finally we perform mixing matrix estimation from speech mixtures, by clustering single source points in the time-frequency domain, and show that the proposed algorithms achieve higher signal to interference ratio when compared to other baseline algorithms.     

适用于时变系统的在线盲源分离算法研究

针对传统EASI算法收敛速率与稳态误差之间的矛盾,提出了一种基于估计函数期望的步长自适应算法（New Adaptive EASI）,为了使这种算法能够更好地解决时变系统中不同条件下的盲源分离问题,提高信号的分离精度,建立了一种混合矩阵变化的在线检测机制,并将这种在线检测机制加入步长自适应算法中,对算法进行了改进。仿真实验表明,这种改进的步长自适应算法能够提高盲源分离初始阶段或是信道变化后分离初始阶段的信号恢复质量,解决源信号为非零均值信号时的盲源分离问题,并且能够准确地在线估计源信号的个数,实现信源数变化条件下的盲源分离。     

Sparse representation and blind source separation of ill-posed mixtures

Bofill et al. discussed blind source separation (BSS) of sparse signals in the case of two sensors. However, as Bofill et al. pointed out, this method has some limitation. The potential function they introduced is lack of theoretical basis. Also the method could not be extended to solve the problem in the case of more than three sensors. In this paper, instead of the potential function method, a K-PCA method (combining K-clustering with PCA) is proposed. The new method is easy to be used in the case of more than three sensors. It is easy to be implemented and can provide accurate estimation of mixing matrix. Some criterion is given to check the effect of the mixing matrix A . Some simulations illustrate the availability and accuracy of the method we proposed.     

Blind source separation based on high-resolution time-frequency distributions

Blind source separation (BSS) based on time-frequency distributions (TFDs) exploits the underlying diagonal or off-diagonal structure of TFD matrices to separate the source signals. In this paper, we propose a new signal-independent kernel which is defined in both the time-lag and the Doppler-lag domain and satisfies most of the desirable properties of a TFD. The main objective of this research is to achieve the high resolution and the maximum cross-term reduction with the preferable diagonal or off-diagonal structure of TFD matrices in BSS applications. Moreover, a BSS approach is developed which includes first whitening mixed signals, then constructing a set of TFD matrices using the proposed TFD and the Hough transform, finally a joint diagonalization of a combined set of TFD matrices to estimate the mixing matrix and the source signals. By use of the techniques proposed in this paper, the improved performance of BSS of nonstationary signals has been achieved.     

Blind source separation with time series variational Bayes expectation maximization algorithm

This paper presents a variational Bayes expectation maximization algorithm for time series based on Attias? variational Bayesian theory. The proposed algorithm is applied in the blind source separation (BSS) problem to estimate both the source signals and the mixing matrix for the optimal model structure. The distribution of the mixing matrix is assumed to be a matrix Gaussian distribution due to the correlation of its elements and the inverse covariance of the sensor noise is assumed to be Wishart distributed for the correlation between sensor noises. The mixture of Gaussian model is used to approximate the distribution of each independent source. The rules to update the posterior hyperparameters and the posterior of the model structure are obtained. The optimal model structure is selected as the one with largest posterior. The source signals and mixing matrix are estimated by applying LMS and MAP estimators to the posterior distributions of the hidden variables and the model parameters respectively for the optimal structure. The proposed algorithm is tested with synthetic data. The results show that: (1) the logarithm posterior of the model structure increases with the accuracy of the posterior mixing matrix; (2) the accuracies of the prior mixing matrix, the estimated mixing matrix, and the estimated source signals increase with the logarithm posterior of the model structure. This algorithm is applied to Magnetoencephalograph data to localize the source of the equivalent current dipoles.     

Markov and Semi-Markov switching of source appearances for nonstationary independent component analysis.

Independent component analysis (ICA) is currently the most popularly used approach to blind source separation (BSS), the problem of recovering unknown source signals when their mixtures are observed but the actual mixing process is unknown. Many ICA algorithms assume that a fixed set of source signals consistently exists in mixtures throughout the time-series to be examined. However, real-world signals often have such difficult nonstationarity that each source signal abruptly appears or disappears, thus the set of active sources dynamically changes with time. In this paper, we propose switching ICA (SwICA), which focuses on such situations. The proposed approach is based on the noisy ICA formulated as a generative model. We employ a special type of hidden Markov model (HMM) to represent such prior knowledge that the source may abruptly appear or disappear with time. The special HMM setting t hen provides an effect ofvariable selection in a dynamic way. We use the variational Bayes (VB) method to derive an effective approximation of Bayesian inference for this model. In simulation experiments using artificial and realistic source signals, the proposed method exhibited performance superior to existing methods, especially in the presence of noise. The compared methods include the natural-gradient ICA with a nonholonomic constraint, and the existing ICA method incorporating an HMM source model, which aims to deal with general nonstationarities that may exist in source signals. In addition, the proposed method could successfully recover the source signals even when the total number of true sources was overestimated or was larger than that of mixtures. We also propose a modification of the basic Markov model into a semi-Markov model, and show that the semi-Markov one is more effective for robust estimation of the source appearance.     

基于二阶统计和时间结构的盲信号分离方法

盲源分离(BSS)的目标就是在混合过程未知的情况下,仅仅依据观测得到的混合信号,恢复出不能直接观测的源信号。针对具有时间结构的源信号,即各个源信号分量满足空间上不相关但时间上相关,提出了一种基于二阶统计量的盲源分离方法。该方法首先对混合信号进行鲁棒预白化处理,其中依据最小描述长度准则对源信号的维数进行估计;然后通过对白化信号的时延协方差矩阵进行奇异值分解(SVD),从而实现源信号的盲分离。仿真中通过对一组语音信号的分离验证了算法的效果,并利用信号干扰比(SIR)和性能指标函数(PI)两个指标定量地对算法的性能进行了度量。     

Maximum contrast analysis for nonnegative blind source separation

In this paper, we propose a maximum contrast analysis (MCA) method for nonnegative blind source separation, where both the mixing matrix and the source signals are nonnegative. We first show that the contrast degree of the source signals is greater than that of the mixed signals. Motivated by this observation, we propose an MCA-based cost function. It is further shown that the separation matrix can be obtained by maximizing the proposed cost function. Then we derive an iterative determinant maximization algorithm for estimating the separation matrix. In the case of two sources, a closed-form solution exists and is derived. Unlike most existing blind source separation methods, the proposed MCA method needs neither the independence assumption, nor the sparseness requirement of the sources. The effectiveness of the new method is illustrated by experiments using X-ray images, remote sensing images, infrared spectral images, and real-world fluorescence microscopy images.     

病态混叠下语音信号的盲源分离

针对稀疏信号盲源分离势函数法需要过多参数,以及聚类算法需要知道源信号个数的缺陷,采用基于拉普拉斯模型的势函数法估计源信号数目和混合矩阵。将混合信号重新聚类,对每一类信号的协方差矩阵进行奇异值分解,混合矩阵得到更精确的估计,进而源信号也得到更精确的估计。通过计算机仿真,表明了该算法的优越性。     

Nonlinear blind source separation using a radial basis functionnetwork

This paper proposes a novel neural-network approach to blind source separation in nonlinear mixture. The approach utilizes a radial basis function (RBF) neural-network to approximate the inverse of the nonlinear mixing mapping which is assumed to exist and able to be approximated using an RBF network. A contrast function which consists of the mutual information and partial moments of the outputs of the separation system, is defined to separate the nonlinear mixture. The minimization of the contrast function results in the independence of the outputs with desirable moments such that the original sources are separated properly. Two learning algorithms for the parametric RBF network are developed by using the stochastic gradient descent method and an unsupervised clustering method. By virtue of the RBF neural network, this proposed approach takes advantage of high learning convergence rate of weights in the hidden layer and output layer, natural unsupervised learning characteristics, modular structure, and universal approximation capability. Simulation results are presented to demonstrate the feasibility, robustness, and computability of the proposed method.     

NGA实现互信息量最小化的盲源分离

提出了一种新的盲源分离算法,该算法通过自然梯度算法实现互信息量最小化,从而达到盲源分离的最佳效果。由于互信息量具有度量分离信号的循环相关矩阵和单位阵的相似程度的特性,最小互信量标志着分离矩阵最佳的状态。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。仿真结果表明算法对具有循环平稳特性的源信号分离效果显著,且收敛速度快。     

Blind source separation based on constant modulus criterion and signal mutual information

We address the problem of adaptive blind source separation (BSS) from instantaneous multi-input multi-output (MIMO) channels. It is known that the constant modulus (CM) criterion can be used to extract unknown source signals. However, the existing CM-based algorithms normally extract the source signals in a serial manner. Consequently, the accuracy in extracting each source signal, except for the first one, depends on the accuracy of previous source extraction. This estimation error propagation (accumulation) will cause severe performance degradation. In this letter, we propose a new adaptive separation algorithm that can separate all source signals simultaneously by directly updating the separation matrix. The superior performance of the new algorithm is demonstrated by simulation examples.     

融合极点对称模态分解与时频分析的单通道振动信号盲分离方法

针对单通道振动信号盲源分离的观察信号少于源信号,且传统的盲源分离方法往往忽视信号非平稳性的问题,提出一种基于极点对称模态分解和时频分析的盲分离算法（ESMD-TFA-BSS）。首先,采用极点对称模态分解方法将观察信号分解成不同的模态,采用贝叶斯信息准则（BIC）估计源信号个数并利用相关系数法选取最优观察信号,由原观察信号与最优观察信号组成新的观察信号;其次,根据新的观察信号计算白化矩阵并将其白化,利用平滑伪Wigner-Ville分布将白化后的信号拓展到时频域,采用矩阵联合对角化方法计算酉矩阵;最后,根据白化矩阵和酉矩阵估计源信号。在盲源分离仿真实验中,ESMD-TFA-BSS的估计源信号与仿真信号的相关系数分别为0.9771、0.9784、0.9660,基于经验模态分解和时频分析的盲分离算法（EMD-TFA-BSS）的相关系数分别为0.8697、0.9706、0.8548,ESMD-TFA-BSS比EMD-TFA-BSS的相关系数分别提高了12.35%、0.80%、13.00%。实验结果表明,ESMD-TFA-BSS在实际工程中能够有效地提高源信号分离精度。     

具有非奇异约束的线性卷积混合信号盲分离联合对角化方法

联合对角化能够成功解决盲分离问题, 但在求解时会得到非期望的奇异解, 从而无法完全分离出源信号. 鉴于此, 提出一种用于线性卷积混合盲分离的联合对角化方法, 将卷积混合模型变换为瞬时模型, 并对变换后的模型应用联合对角化求取分离矩阵. 在求解过程中, 引入约束条件对解的范围进行限定, 避免了奇异解的出现. 仿真结果表明, 所提出的方法能够成功实现卷积混合信号盲分离.

     

基于多步分解算法的解盲源分离新方法

在利用二阶统计量实现盲源分离问题中,混迭矩阵经过白化以后转变成了酉矩阵。针对酉矩阵各列之间相互正交的特性,提出一种关于酉矩阵某一列的最小二乘对称代价函数。通过基于梯度下降法的三迭代算法,交替估计三二次代价函数中的各组待定参数,搜索代价函数最小点,从而得到对应能量最大信号源的酉矩阵的一列。利用系统化的多步分解算法（MSA）,依次估计酉矩阵的一列,最终得到整个酉矩阵的估计。仿真结果表明,与经典的通过连续Givens旋转求酉矩阵的SOBI算法相比,该算法全局拒噪水平至少改善了9 dB,而所需计算时间仅为SOBI的二分之一,更有效地解决了盲源分离问题。     

Blind separation of non-stationary sources using continuous density hidden Markov models

Blind source separation (BSS) has attained much attention in signal processing society due to its ‘blind’ property and wide applications. However, there are still some open problems, such as underdetermined BSS, noise BSS. In this paper, we propose a Bayesian approach to improve the separation performance of instantaneous mixtures with non-stationary sources by taking into account the internal organization of the non-stationary sources. Gaussian mixture model (GMM) is used to model the distribution of source signals and the continuous density hidden Markov model (CDHMM) is derived to track the non-stationarity inside the source signals. Source signals can switch between several states such that the separation performance can be significantly improved. An expectation-maximization (EM) algorithm is derived to estimate the mixing coefficients, the CDHMM parameters and the noise covariance. The source signals are recovered via maximum a posteriori (MAP) approach. To ensure the convergence of the proposed algorithm, the proper prior densities, conjugate prior densities, are assigned to estimation coefficients for incorporating the prior information. The initialization scheme for the estimates is also discussed. Systematic simulations are used to illustrate the performance of the proposed algorithm. Simulation results show that the proposed algorithm has more robust separation performance in terms of similarity score in noise environments in comparison with the classical BSS algorithms in determined mixture case. Additionally, since the mixing matrix and the sources are estimated jointly, the proposed EM algorithm also works well in underdetermined case. Furthermore, the proposed algorithm converges quickly with proper initialization.     

基于Givens矩阵和联合非线性不相关的盲源分离新算法

针对源信号统计独立的盲源分离(Blind Source Separation,BSS)问题,提出了一种基于Givens矩阵和联合非线性不相关的盲源分离新算法.由于分离信号独立性的度量是影响算法有效性的重要因素,因此首先提出了一种改进的度量独立性的方法,该方法以独立源信号的联合非线性不相关来度量独立性;其次,结合Givens矩阵可以对分离矩阵施加正交性约束且能减少要估计参数个数的性质,将盲源分离问题转化成无约束优化问题,并利用拟牛顿法中的BFGS算法求解该无约束优化问题,得到分离矩阵;最后,通过模拟混合信号和真实语音混合信号的分离实验验证了该算法的有效性.     

PID控制原理在语音信号盲源分离中的应用

语音信号在非平稳系统中是动态混合的,为了实时抑制盲源分离过程中的非平稳混合扰动,加快收敛速度,减小稳态误差,提出了一种应用PID控制原理的自适应盲源分离算法。依据一种无预处理的自适应盲源分离算法建立PID控制模型,调节学习速率,跟踪语音信号的分离过程,实时减小由非平稳混合引入的分离误差,动态更新分离矩阵。在混合矩阵缓变和突变两种情形下分别对PID参数整定和语音信号的分离进行仿真分析,结合经典算法对比提出算法的性能。仿真与对比结果表明,提出的算法适用于非平稳混合系统语音信号的分离,算法性能较经典算法有改善。