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。     

Source number estimation and separation algorithms of underdetermined blind separation

Recently, sparse component analysis （SCA） has become a hot spot in BSS research. Instead of independent component analysis （ICA）, SCA can be used to solve underdetermined mixture efficiently. Two-step approach （TSA） is one of the typical methods to solve SCA based BSS problems. It estimates the mixing matrix before the separation of the sources. K-means clustering is often used to estimate the mixing matrix. It relies on the prior knowledge of the source number strongly. However, the estimation of the source number is an obstacle. In this paper, a fuzzy clustering method is proposed to estimate the source number and mixing matrix simultaneously. After that, the sources are recovered by the shortest path method （SPM）. Simulations show the availability and robustness of the proposed method.     

A parametric density model for blind source separation

In this paper, a parametric mixture density model is employed to be the source prior in blind source separation (BSS). A strict lower bound on the source prior is derived by using a variational method, which naturally enables the intractable posterior to be represented as a gaussian form. An expectation-maximization (EM) algorithm in closed form is therefore derived for estimating the mixing matrix and inferring the sources. Simulation results show that the proposed variational expectation-maximization algorithm can perform blind separation of not only speech source of more sources than mixtures, but also binary source of more sources than mixtures.     

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。     

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.     

Blind source separation with unknown and dynamically changing number of source signals

The contrast function remains to be an open problem in blind source separation (BSS) when the number of source signals is unknown and/or dynamically changed. The paper studies this problem and proves that the mutual information is still the contrast function for BSS if the mixing matrix is of full column rank. The mutual information reaches its minimum at the separation points, where the random outputs of the BSS system are the scaled and permuted source signals, while the others are zero outputs. Using the property that the transpose of the mixing matrix and a matrix composed by m observed signals have the indentical null space with probability one, a practical method, which can detect the unknown number of source signals n, ulteriorly traces the dynamical change of the sources number with a few of data, is proposed. The effectiveness of the proposed theorey and the developed novel algorithm is verified by adaptive BSS simulations with unknown and dynamically changing number of source signals.     

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。     

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.     

基于EMD的单通道盲源分离跳频通信抗干扰方法

针对传统盲源分离算法无法在单路接收的跳频通信场景中使用的问题,提出一种结合经验模态分解的单通道盲源分离跳频通信抗干扰方法。首先通过理论分析和仿真确定了采用EMD对混有干扰的单路接收跳频信号进行增维的方法,将单通道盲分离的欠定问题转为正定问题,之后分别利用全盲盲源分离和半盲盲源分离实现扰信分离。在不同信干比、不同信噪比等多种条件下的仿真实验验证了本方法的有效性。     

盲源分离的一种时频比方法

在M.Puigt和Y.Deville提出的时频盲源分离算法基础上,引入S变换来获取非平稳信号的多分辨率特性。首先通过S变换将一维混叠信号映射到二维时频平面,然后构造不同混叠信号的时频比矩阵,通过在时频比矩阵范围内搜索单源分析域计算混合阵的每个元素,进而估计源信号。该方法能有效分离非平稳信号且具备多分辨率特性。     

Blind Separation of Mutually Correlated Sources Using Precoders

This paper studies the problem of blind source separation (BSS) from instantaneous mixtures with the assumption that the source signals are mutually correlated. We propose a novel approach to BSS by using precoders in transmitters. We show that if the precoders are properly designed, some cross-correlation coefficients of the coded signals can be forced to be zero at certain time lags. Then, the unique correlation properties of the coded signals can be exploited in receiver to achieve source separation. Based on the proposed precoders, a subspace-based algorithm is derived for the blind separation of mutually correlated sources. The effectiveness of the algorithm is illustrated by simulation examples.      

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.     

Convolutive Blind Source Separation in the Frequency Domain Based on Sparse Representation

Convolutive blind source separation (CBSS) that exploits the sparsity of source signals in the frequency domain is addressed in this paper. We assume the sources follow complex Laplacian-like distribution for complex random variable, in which the real part and imaginary part of complex-valued source signals are not necessarily independent. Based on the maximum a posteriori (MAP) criterion, we propose a novel natural gradient method for complex sparse representation. Moreover, a new CBSS method is further developed based on complex sparse representation. The developed CBSS algorithm works in the frequency domain. Here, we assume that the source signals are sufficiently sparse in the frequency domain. If the sources are sufficiently sparse in the frequency domain and the filter length of mixing channels is relatively small and can be estimated, we can even achieve underdetermined CBSS. We illustrate the validity and performance of the proposed learning algorithm by several simulation examples.     

小波去噪算法在含噪盲源分离中的应用

无噪模型下的盲源分离算法在信噪比较低的情况下并不适用。针对该情况一种解决方案就是先对含有高斯白噪声的混合信号进行去噪预处理,然后使用盲源分离算法进行分离。为此,本文提出了一种适用于信噪比较低条件下的基于平移不变量的小波去噪算法。该算法首先使用高频系数滑动窗口法准确估计含噪混合信号的噪声方差,然后使用Bayesshrink阈值估计算法 得到更加合理的阈值,最后在不降低去噪效果的同时缩小了平移不变量的范围,减少了运算量。实验仿真表明,在信噪比较低的情况下,与传统小波去噪算法相比,该算法可以更加有效地去除噪声,在很大程度上提升盲源分离算法的性能。     

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,...     

基于递归神经网络结构的非平稳信号自适应盲分离

基于递归网络分离结构并利用时间相关的评价函数，针对二输入二输出盲信号分离问题，提出了一种非平稳信号的自适应盲分离算法。该算法计算量小，可根据输出信号能量大小有选择地更新分离系数。并可扩展到多输入多输出盲分离问题。仿真验证对声音等非平稳信号具有良好的分离效果。     

Multichannel Nonnegative Matrix Factorization in Convolutive Mixtures for Audio Source Separation

We consider inference in a general data-driven object-based model of multichannel audio data, assumed generated as a possibly underdetermined convolutive mixture of source signals. We work in the short-time Fourier transform (STFT) domain, where convolution is routinely approximated as linear instantaneous mixing in each frequency band. Each source STFT is given a model inspired from nonnegative matrix factorization (NMF) with the Itakura–Saito divergence, which underlies a statistical model of superimposed Gaussian components. We address estimation of the mixing and source parameters using two methods. The first one consists of maximizing the exact joint likelihood of the multichannel data using an expectation-maximization (EM) algorithm. The second method consists of maximizing the sum of individual likelihoods of all channels using a multiplicative update algorithm inspired from NMF methodology. Our decomposition algorithms are applied to stereo audio source separation in various settings, covering blind and supervised separation, music and speech sources, synthetic instantaneous and convolutive mixtures, as well as professionally produced music recordings. Our EM method produces competitive results with respect to state-of-the-art as illustrated on two tasks from the international Signal Separation Evaluation Campaign (SiSEC 2008).      

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.     

基于稀疏性的欠定语音盲分离方法研究

针对源信号增多导致语音信号稀疏性变差的问题,提出一种新的基于稀疏性的混合矩阵估计方法,利用主分量分析(PCA)检测只有一个源信号存在的时频点并用于估计混合矩阵,从而提高了估计性能,特别适用于欠定语音盲分离。同时指出了影响基于稀疏性语音盲分离方法性能的因素。仿真结果验证了上述结论。     

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.