一种新的基于伪提取矢量的欠定盲分离方法

针对独立信号源的欠定盲分离,通过一定的理论分析,提出了一种基于伪提取矢量的欠定盲源分离方法。该方法通过判断采样点处取值占优的源信号,然后在观测信号采样点处选取对应的伪提取矢量,以恢复取值占优的源信号采样点的值,来实现欠定盲源分离。将该算法与经典的基于线性规划的欠定盲源分离方法进行了仿真,结果表明该方法由于在信号的各采样点处无需优化,因此大大提高了信号分离的速度,信号的分离速度要比基于线性规划的方法快数十倍。     

基于贪婪稀疏优化的欠定语音盲分离方法

提出一种基于语音信号稀疏特征的稀疏分量分析两步法,力图提高欠定情况下的语音信号盲分离性能.不同于传统的两步法,所提方法需要获取语音信号在变换域中的稀疏特征,将贪婪最优化思想引入至稀疏分量分析方法中,重构欠定盲分离语音源信号.通过仿真对比实验,展示了该方法应用于平稳声音信号和非平稳语音信号的盲分离效果,它能较好恢复语音源信号.与现有的最短路径法相比,所提算法可以提高两路以上观测信号的分离性能.相较于平滑L0范数算法,所提算法可以有效提高来波方向较近的语音盲信号分离性能.该方法具有更广阔的适用范围.     

一种加权增强的欠定盲辨识方法

针对欠定盲源分离混合矩阵问题,提出了一种基于二阶统计量平行因子分解,加权增强最小二乘法的欠定混合盲辨识方法。该算法不需要源信号满足稀疏性要求,仅在源信号满足相互独立和最多一个高斯信号的条件下,将独立源信号的空间协方差矩阵构建三阶张量,采用加权增强最小二乘法实现张量的标准分解,完成混合矩阵的估计。由于平行因子分解的唯一性在欠定条件下依然成立,该算法可以解决欠定盲源分离问题。仿真实验结果表明:提出的算法在计算欠定混合时具有很好的辨识效果,而且实现简单,可满足实际应用的要求。     

欠定情形下语音信号盲分离的新方法

提出了一种新的两步法来实现欠定情形下语音信号的盲分离。第一步,采用一种重构观测信号采样点搜索法来估计混合矩阵;第二步,提出了一种伪提取矢量的概念,通过伪提取矢量来提取取值占优的源信号的采样值来恢复源信号。在源信号的恢复过程中,还使用了经典的基于线性规划的欠定盲源分离方法。结果表明：该方法由于在信号的各采样点处无须优化,在源信号的分离过程中,分离速度要比基于线性规划的方法快数倍,且分离精度不低于基于线性规划的方法。仿真结果表明了该算法的良好性能。     

基于超平面法矢量的欠定盲信号分离算法

探讨欠定情况下(观测信号少于源数目)的盲信号分离. 首先给出了 m 维超平面的法矢量的计算公式, 提出了一个基于超平面法矢量的矩阵恢复算法. 其次针对语音分离, 提出了 k 源区间及其检测方法, 从而使 k-SCA 条件下的算法推广到了非稀疏信号的盲分离. 在源信号重建上, 提出了一个简化 l1 范数解的新算法. 几个仿真实验 (含语音信号实验) 证实了所提出算法的性能.     

基于EEMD和ICA的单通道列车信号盲分离

针对列车混合故障的诊断,提出了一种基于集合平均经验分解（EEMD）和独立分量分析（ICA）的盲分离诊断方法。通过EEMD算法将混合信号分解为包含不同源信号特征的本征模态函数（IMF）,组成新的多维信号;用主成分分析准确估计源信号个数,解决了单通道信号盲分离的欠定问题;利用快速独立分量分析（Fast-ICA）算法实现了信号的盲分离。实验信号分别采用仿真信号和列车实验信号进行实验,实验结果表明,该算法可以有效地分离出列车的单故障信号。     

基于奇异值分解的欠定ICA算法研究

从奇异值分解出发,研究欠定独立分量分析(ICA)盲分离的新算法,给出了欠定ICA算法的代价函数,推导出分离矩阵的计算公式.在此基础上,提出了将基于奇异值分解的欠定ICA算法与普通ICA算法相结合的二次盲信号分离算法.利用此盲分离算法,能够较好地分离出部分源信号.仿真实验说明了此方法的有效性.     

基于改进源信号数目估计算法的欠定盲分离

两步法是解决稀疏信号欠定盲分离的一种常用方法,通常首先利用K-means聚类算法估计混叠矩阵,然后利用最短路径法恢复源信号。在使用K-means聚类算法时要求知道源信号的数目,而现实中往往不知道源信号的数目,需要对其进行估计。因此研究了聚类有效性评价指标——BWP指标,结合粒子群算法,提出了一种改进的确定源信号数目的算法,并将这种算法引入到欠定盲分离。实验表明,提出的算法在保证分离精度的同时能缩短分离时间,并可节省一定的内存,在观测信号数据量大时,这种优势更加明显。     

抑制边缘效应的自适应单通道盲源分离

单入多出的盲源分离SIMO_BSS是一种特殊的欠定盲源分离。针对单信道问题,通常采用总体经验模态分解和独立成分分析联合使用EEMD_ICA算法。然而,以EEMD为基础的盲源分离算法,会产生边缘效应降低信号分离准确率。因此,提出了一种在端点处增加预测极值点的方法来抑制边缘效应,在时间、空间复杂度上要明显优于基于周期延拓源信号的方法,而且适用于长序列信号的分离。在不同的信噪比SNR下,通过心电ECG混合信号仿真,该方法比EEMD_ICA方法,以及EEMD_PCA_ICA方法分离出的信号相似度高。最后将该算法实际应用到周期压电信号中,结果表明该方法具有明显的去噪分离效果。     

改进的分段盲源分离方法及其应用

针对传统盲源分离算法大多存在收敛速度慢、分离精度低的缺点,提出了一种改进的分段盲源分离算法。将整个信号分离过程分为快速分离和精细分离两个阶段。在快速分离阶段,采用基于粒子群优化(PSO)的分离算法,通过较少的迭代次数实现信号较好的初步分离;在精细分离阶段,通过选择适当的学习速率,进一步提高信号的分离精度。通过数值仿真及试验分析,将改进的分段盲源分离算法与现有的分离性能较好的基于人工蜂群(ABC)的分离算法进行了对比分析。结果表明,改进的分段盲源分离算法具有更优异的分离速度、分离精度和稳定性。     

松弛稀疏性条件下的欠定盲分离

采用2步法研究松弛稀疏性条件下的欠定盲信号分离。在矩阵恢复上,将时域检索平均法从时域扩展到小波域,得到单源区间矩阵恢复算法。在源信号恢复上,分析最短路径法和l1范数算法,提出基于任意观测信号数的统计稀疏分解准则算法。仿真结果表明,相比l1范数解算法,该算法具有较低的计算复杂度,且可提高恢复信号的信噪比。     

Analysis of sparse representation and blind source separation

In this letter, we analyze a two-stage cluster-then-l(1)-optimization approach for sparse representation of a data matrix, which is also a promising approach for blind source separation (BSS) in which fewer sensors than sources are present. First, sparse representation (factorization) of a data matrix is discussed. For a given overcomplete basis matrix, the corresponding sparse solution (coefficient matrix) with minimum l(1) norm is unique with probability one, which can be obtained using a standard linear programming algorithm. The equivalence of the l(1)-norm solution and the l(0)-norm solution is also analyzed according to a probabilistic framework. If the obtained l(1)-norm solution is sufficiently sparse, then it is equal to the l(0)-norm solution with a high probability. Furthermore, the l(1)- norm solution is robust to noise, but the l(0)-norm solution is not, showing that the l(1)-norm is a good sparsity measure. These results can be used as a recoverability analysis of BSS, as discussed. The basis matrix in this article is estimated using a clustering algorithm followed by normalization, in which the matrix columns are the cluster centers of normalized data column vectors. Zibulevsky, Pearlmutter, Boll, and Kisilev (2000) used this kind of two-stage approach in underdetermined BSS. Our recoverability analysis shows that this approach can deal with the situation in which the sources are overlapped to some degree in the analyzed domain and with the case in which the source number is unknown. It is also robust to additive noise and estimation error in the mixing matrix. Finally, four simulation examples and an EEG data analysis example are presented to illustrate the algorithm's utility and demonstrate its performance.     

MIMO型RFID的传感标签盲源分离防碰撞算法

针对传感标签密集的多输入多输出型射频识别(MIMO-RFID)系统中标签同时响应导致一系列的碰撞问题,提出了一种并行识别传感标签的欠定盲分离的防碰撞算法(BFast-ICA).在快速独立分量分析(Fast-ICA)算法的基础上,采用更高阶次的迭代方法,实现碰撞传感标签信号的欠定盲分离.在分离性能和吞吐量两个方面进行性能仿真,实验结果表明:改进的防碰撞算法能够更快地分离传感标签信号;在阅读器天线数目相同的情况下,最大吞吐量比当前的盲分离标签防碰撞算法提高了40％以上.     

基于约束NMF的欠定盲信号分离算法*

提出一种约束非负矩阵分解方法用于解决欠定盲信号分离问题。非负矩阵分解直接用于求解欠定盲信号分离时,分解结果不唯一,无法正确分离源信号。本文在基本非负矩阵分解算法基础上,对分解得到的混合矩阵施加行列式约束,保证分解结果的唯一性;对分解得到的源信号同时施加稀疏性约束和最小相关约束,实现混合信号的唯一分解,提高源信号分离性能。仿真实验证明了本文算法的有效性。     

基于线性阵列的欠定盲源分离几何分析

采用线性阵列对欠定盲源分离问题进行建模,研究源信号的空间分布对欠定盲源分离的影响.利用二步法和稀疏分量分析解决欠定盲源分离问题,其中,混合矩阵的估计主要利用稀疏源信号的线性混合信号沿混合矩阵列向量方向线性聚类的特性.理论分析和仿真实验结果表明,当源信号在空间处于某些特定区域时,若采用线性聚类方法,混合矩阵是不可估计的,...     

功率谱估计和扩展子空间下的欠定盲分离

研究了欠定情形下的信号盲分离。充分利用信号的时频特性,提出了AR模型功率谱估计法滑动估计信号频率,设计带通滤波器近似获取源信号和欠定混合矩阵,以及扩展子空间向量基构造完备观测信号的方法,将问题转化为完备情况下的盲分离,最后运用FastICA方法实现了信号盲分离。仿真实验数据表明方法的可行性和有效性,为欠定盲分离问题研究提供了新的思路。     

Equivalence Probability and Sparsity of Two Sparse Solutions in Sparse Representation

This paper discusses the estimation and numerical calculation of the probability that the 0-norm and 1-norm solutions of underdetermined linear equations are equivalent in the case of sparse representation. First, we define the sparsity degree of a signal. Two equivalence probability estimates are obtained when the entries of the 0-norm solution have different sparsity degrees. One is for the case in which the basis matrix is given or estimated, and the other is for the case in which the basis matrix is random. However, the computational burden to calculate these probabilities increases exponentially as the number of columns of the basis matrix increases. This computational complexity problem can be avoided through a sampling method. Next, we analyze the sparsity degree of mixtures and establish the relationship between the equivalence probability and the sparsity degree of the mixtures. This relationship can be used to analyze the performance of blind source separation (BSS). Furthermore, we extend the equivalence probability estimates to the small noise case. Finally, we illustrate how to use these theoretical results to guarantee a satisfactory performance in underdetermined BSS.      

A spectral clustering approach to underdetermined postnonlinear blind source separation of sparse sources

This letter proposes a clustering-based approach for solving the underdetermined (i.e., fewer mixtures than sources) postnonlinear blind source separation (PNL BSS) problem when the sources are sparse. Although various algorithms exist for the underdetermined BSS problem for sparse sources, as well as for the PNL BSS problem with as many mixtures as sources, the nonlinear problem in an underdetermined scenario has not been satisfactorily solved yet. The method proposed in this letter aims at inverting the different nonlinearities, thus reducing the problem to linear underdetermined BSS. To this end, first a spectral clustering technique is applied that clusters the mixture samples into different sets corresponding to the different sources. Then, the inverse nonlinearities are estimated using a set of multilayer perceptrons (MLPs) that are trained by minimizing a specifically designed cost function. Finally, transforming each mixture by its corresponding inverse nonlinearity results in a linear underdetermined BSS problem, which can be solved using any of the existing methods.     

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.