Blind Source Separation of Instantaneous Mixture of Delayed Sources Using High‐Order Taylor Approximation

This paper deals with the problem of blind source separation (BSS), where observed signals are a mixture of delayed sources. In reference to a previous work, when the delay time is small such that the first‐order Taylor approximation holds, delayed observations are transformed into an instantaneous mixture of original sources and their derivatives, for which an extended second‐order blind identification (SOBI) approach is used to recover sources. Inspired by the results of this previous work, we propose to generalize its first‐order Taylor approximation to suit higher‐order approximations in the case of a large delay time based on a similar version of its extended SOBI. Compared to SOBI and its extended version for a first‐order Taylor approximation, our method is more efficient in terms of separation quality when the delay time is large. Simulation results verify the performance of our approach under different time delays and signal‐to‐noise ratio conditions, respectively.     

基于时频域单源区域的延迟欠定混合非平稳信号盲分离

针对衰减-延迟欠定混合信号的盲分离问题,提出了基于子空间分解的时频域上单源区域检测方法,估计出信号在时频域上的单源区域以及相应的特征向量,然后利用系统聚类法对单源区域对应的特征向量进行聚类分析,估计出源信号数目以及混合矩阵,最后通过改进的基于子空间投影算法完成源信号的恢复.仿真结果表明本文算法提高了混合矩阵和源信号的估...     

Blind Separation of Noisy Multivariate Data Using Second-Order Statistics: Remote-Sensing Applications

In this paper a second-order method for blind source separation of noisy instantaneous linear mixtures is presented for the case where the signal order k is unknown. Its performance advantages are illustrated by simulations and by application to Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) multichannel visible/infrared data. The model assumes that m mixtures x of dimension n are observed, where x = Ap + Gw, and the underlying signal vector p has k < n/3 independent unit-variance elements. A is the mixing matrix, G is diagonal, and w is a normalized white-noise vector. The algorithm estimates the Second-Order separation matrix A, signal Order k, and Noise and is therefore designated as SOON. SOON first iteratively estimates k and G using a scree metric, singular-value decomposition, and the expectation-maximization algorithm, and then determines the values of AP and W. The final step estimates A and the set of m signal vectors p using a variant of the joint-diagonalization method used in the Second-Order Blind Identification (SOBI) and Second-Order NonStationary (SONS) source-separation algorithms. The SOON extension of SOBI and SONS significantly improves their separation of simulated sources hidden in noise. SOON also reveals interesting thermal dynamics within AVIRIS multichannel visible/infrared imaging data not found by noise-adjusted principal-component analysis.     

联合非高斯性和非线性自相关的有噪盲源分离算法

现有的盲源分离算法往往利用信号某一方面的统计特性来分离信号,例如:利用信号的非高斯特性,或者利用信号的时序特性。在实际应用中,信号往往是具有这两种特性信号的混合,采用信号某一方面的特性往往不能够成功的分离出信号。现有的盲源分离算法往往不考虑噪声的影响,但在实际应用中,噪声的影响是不可避免的。当源信号具有非高斯性和非线性自相关特性时,提出了联合非高斯性和非线性自相关特性的有噪盲源分离算法。计算机仿真表明了提出算法的有效性,和现有的基于非高斯性和非线性自相关特性的有噪盲源分离算法相比,提出算法具有更好的信号分离性能。      

MIMO-AR System Identification and Blind Source Separation for GMM-Distributed Sources

The problem of blind source separation (BSS) and system identification for multiple-input multiple-output (MIMO) auto-regressive (AR) mixtures is addressed in this paper. Two new time-domain algorithms for system identification and BSS are proposed based on the Gaussian mixture model (GMM) for sources distribution. Both algorithms are based on the generalized expectation-maximization (GEM) method for joint estimation of the MIMO-AR model parameters and the GMM parameters of the sources. The first algorithm is derived under the assumption of unstructured input signal statistics, while the second algorithm incorporates the prior knowledge about the structure of the input signal statistics due to the statistically independent source assumption. These methods are tested via simulations using synthetic and audio signals. The system identification performances are tested by comparison between the state transition matrix estimation using the proposed algorithms and the well-known multidimensional Yule-Walker solution followed by an instantaneous BSS method. The results show that the proposed algorithms outperform the Yule-Walker based approach. The BSS performances were compared to other convolutive BSS methods. The results show that the proposed algorithms achieve higher signal-to-interference ratio (SIR) compared to the other tested methods.     

一种任意信号源盲分离的高效算法

提出了信号源盲分离的DBBSS算法.利用随机变量概率密度函数非参数估计的核函数法,对混合信号的概率密度函数及其导数进行估计,并由此估计信号的评价函数(score function).解决了现有信号源盲分离算法中,普遍存在的非线性函数只能凭经验选取,以及混合信号同时包含超高斯信号和亚高斯信号时,算法失效的问题.该方法非常简单,可以直接应用于所有以非线性函数代替评价函数的信号源盲分离算法.仿真结果验证了算法的有效性.     

基于凸优化的抗旋转图像盲源分离算法研究

盲源分离是指在没有源信号任何先验知识的情况下,只根据多个观测信号实现对源信号的恢复。本文在CAMNS算法的基础上提出了一种抗旋转的图像盲源分离新算法,该算法首先对观测图像进行预处理,提取图像旋转不变因子,然后利用图像空间局部显著性的假设将旋转后的图像盲源分离转化为可解的凸优化问题,进而求出分离矩阵,最后反解混合方程组确定源图像。实验结果表明:新算法有效地消除了旋转对盲源分离的影响,算法性能指标较ICA算法、NMF算法和CAMNS算法提高了近80%以上。      

Blind source separation for convolutive mixtures based on the joint diagonalization of power spectral density matrices

This paper studies the problem of blind separation of convolutively mixed source signals on the basis of the joint diagonalization (JD) of power spectral density matrices (PSDMs) observed at the output of the separation system. Firstly, a general framework of JD-based blind source separation (BSS) is reviewed and summarized. Special emphasis is put on the separability conditions of sources and mixing system. Secondly, the JD-based BSS is generalized to the separation of convolutive mixtures. The definition of a time and frequency dependent characteristic matrix of sources allows us to state the conditions under which the separation of convolutive mixtures is possible. Lastly, a frequency-domain approach is proposed for convolutive mixture separation. The proposed approach exploits objective functions based on a set of PSDMs. These objective functions are defined in the frequency domain, but are jointly optimized with respect to the time-domain coefficients of the unmixing system. The local permutation ambiguity problems, which are inherent to most frequency-domain approaches, are effectively avoided with the proposed algorithm. Simulation results show that the proposed algorithm is valid for the separation of both simulated and real-word recorded convolutive mixtures.     

A near real-time approach for convolutive blind source separation

In this paper, we propose an algorithm for real-time signal processing of convolutive blind source separation (CBSS), which is a promising technique for acoustic source separation in a realistic environment, e.g., room/office or vehicle. First, we apply an overlap-and-save (sliding windows with overlapping) strategy that is most suitable for real-time CBSS processing; this approach can also aid in solving the permutation problem. Second, we consider the issue of separating sources in the frequency domain. We introduce a modified correlation matrix of observed signals and perform CBSS by diagonalization of the matrix. Third, we propose a method that can diagonalize the modified correlation matrix by solving a so-called normal equation for CBSS. One desirable feature of our proposed algorithm is that it can solve the CBSS problem explicitly, rather than stochastically, as is done with conventional algorithms. Moreover, a real-time separation of the convolutive mixtures of sources can be performed. We designed several simulations to compare the effectiveness of our algorithm with its counterpart, the gradient-based approach. Our proposed algorithm displayed superior convergence rates relative to the gradient-based approach. We also designed an experiment for testing the efficacy of the algorithm in real-time CBSS processing aimed at separating acoustic sources in realistic environments. Within this experimental context, the convergence time of our algorithms was substantially faster than that of the gradient-based algorithms. Moreover, our algorithm converges to a much lower value of the cost function than that of the gradient-based algorithm, ensuring better performance.     

A unifying criterion for instantaneous blind source separation based on correntropy

Correntropy has recently been introduced as a generalized correlation function between two stochastic processes, which contains both high-order statistics and temporal structure of the stochastic processes in one functional form. Based on this blend of high-order statistics and temporal structure in a single functional form, we propose a unified criterion for instantaneous blind source separation (BSS). The criterion simultaneously exploits both spatial and spectral characteristics of the sources. Consequently, the new algorithm is able to separate independent, identically distributed (i.i.d.) sources, which requires high-order statistics; and it is also able to separate temporally correlated Gaussian sources with distinct spectra, which requires temporal information. Performance of the proposed method is compared with other popular BSS methods that solely depend on either high-order statistics (FastICA, JADE) or second-order statistics at different lags (SOBI). The new algorithm outperforms the conventional methods in the case of mixtures of sub-Gaussian and super-Gaussian sources.     

Blind separation of independent sources for virtually any sourceprobability density function

The blind source separation (BSS) problem consists of the recovery of a set of statistically independent source signals from a set of measurements that are mixtures of the sources when nothing is known about the sources and the mixture structure. In the BSS scenario, of two noiseless real-valued instantaneous linear mixtures of two sources, an approximate maximum-likelihood (ML) approach has been suggested in the literature, which is only valid under certain constraints on the probability density function (pdf) of the sources. In the present paper, the expression for this ML estimator is reviewed and generalized to include virtually any source distribution. An intuitive geometrical interpretation of the new estimator is also given in terms of the scatter plots of the signals involved. An asymptotic performance analysis is then carried out, yielding a closed-form expression for the estimator asymptotic pdf. Simulations illustrate the behavior of the suggested estimator and show the accuracy of the asymptotic analysis. In addition, an extension of the method to the general BSS scenario of more than two sources and two sensors is successfully implemented     

Blind source separation based on time-frequency signalrepresentations

Blind source separation consists of recovering a set of signals of which only instantaneous linear mixtures are observed. Thus far, this problem has been solved using statistical information available on the source signals. This paper introduces a new blind source separation approach exploiting the difference in the time-frequency (t-f) signatures of the sources to be separated. The approach is based on the diagonalization of a combined set of “spatial t-f distributions”. In contrast to existing techniques, the proposed approach allows the separation of Gaussian sources with identical spectral shape but with different t-f localization properties. The effects of spreading the noise power while localizing the source energy in the t-f domain amounts to increasing the robustness of the proposed approach with respect to noise and, hence, improved performance. Asymptotic performance analysis and numerical simulations are provided     

Separation of an instantaneous mixture of Gaussian autoregressive sources by the exact maximum likelihood approach

This paper deals with the problem of blind separation of an instantaneous mixture of Gaussian autoregressive sources, without additive noise, by the exact maximum likelihood approach. The maximization of the likelihood function is divided, using relaxation, into two suboptimization problems, solved by relaxation methods as well. The first one consists of the estimation of the separating matrix when the autoregressive structure of the sources is fixed. The second one aims at estimating this structure when the separating matrix is fixed. We show that the first problem is equivalent to the determinant maximization of the separating matrix under nonlinear constraints. We prove the existence and the consistency of the maximum likelihood estimator. We also give the expression of Fisher's information matrix. Then, we study, by computer simulations, the performance of our estimator and show the improvement of its achievements w.r.t. both quasimaximum likelihood and second-order blind identification (SOBI) estimators.     

基于时频分析的混合矩阵估计方法

在盲源分离信号处理中,尤其在欠定条件下(观测信号数目大于源信号数目),精确的估计混合矩阵是具有挑战性的问题。现存部分方法利用信号的稀疏性进行求解,并假设在时域或者时频域中源信号不重叠,然而这类方法在假设条件不满足,即源信号部分重叠情况下随着信号稀疏性降低性能恶化明显。本文针对具有较弱稀疏性的源信号,提出了一种基于时频分析的欠定盲源分离的混合矩阵估计方法。首先,利用源信号时频变换后系数实部与虚部比值的差异性选择单源点;其次,运用经典的聚类方法估计解混合矩阵的各向量。仿真结果表明:提出的方法简易可行并具有较好的估计性能。      

Experimental upper bound for the performance of convolutive source separation methods

An important problem in the field of blind source separation (BSS) of real convolutive mixtures is the determination of the role of the demixing filter structure and the criterion/optimization method in limiting separation performance. This issue requires the knowledge of the optimal performance for a given structure, which is unknown for real mixtures. Herein, the authors introduce an experimental upper bound on the separation performance for a class of convolutive blind source separation structures, which can be used to approximate the optimal performance. As opposed to a theoretical upper bound, the experimental upper bound produces an estimate of the optimal separating parameters for each dataset in addition to specifying an upper bound on separation performance. Estimation of the upper bound involves the application of a supervised learning method to the set of observations found by recording the sources one at a time. Using the upper bound, it is demonstrated that structures other than the finite-impulse-response (FIR) structure should be considered for real (convolutive) mixtures, there is still much room for improvement in current convolutive BSS algorithms, and the separation performance of these algorithms is not necessarily limited by local minima.     

Second Order Nonstationary Source Separation

This paper addresses a method of blind source separation that jointly exploits the nonstationarity and temporal structure of sources. The method needs only multiple time-delayed correlation matrices of the observation data, each of which is evaluated at different time-windowed data frame, to estimate the demixing matrix. The method is insensitive to the temporally white noise since it is based on only time-delayed correlation matrices (with non-zero time-lags) and is applicable to the case of either nonstationary sources or temporally correlated sources. We also discuss the extension of some existing methods with the overview of second-order blind source separation methods. Extensive numerical experiments confirm the validity and high performance of the proposed method.     

Quadratic Higher Order Criteria for Iterative Blind Separation of a MIMO Convolutive Mixture of Sources

This paper deals with the problem of source separation in the case when the observations result from a multiple-input multiple-output convolutive mixing system. In a blind framework, higher order contrast functions have been proved to be efficient for extracting sources. Inspired by a semiblind approach, we propose new contrast functions for blind signal separation that make use of reference signals. The main advantage of this approach consists in the quadratic form of these criteria: the extraction of one source hence reduces to a simple optimization task for which fast and efficient algorithms are available. The separation of the other sources from the mixture is then carried out by an iterative deflation method. Furthermore, these contrasts are shown to be valid for both independent identically distributed (i.i.d.) and non-i.i.d. source signals. The performance offered by these criteria is investigated through simulations: they appear as very appealing tools compared with some classical contrast functions     

Blind detection of synchronous CDMA in non-Gaussian channels

Most blind source separation algorithms assume the channel noise to be Gaussian. This paper considers the problem of noncooperative blind detection of synchronous direct-sequence code-division multiple-access communications (no knowledge of the spreading sequences or training data) in non-Gaussian channels. Three iterative algorithms with different performance and complexity tradeoffs are proposed. Simulation results show that they significantly outperform Gaussian-optimal blind source separation algorithms in non-Gaussian channels. The Cramer-Rao lower bound for this problem is computed, and the performance of the proposed algorithms is shown to approach this bound for moderate signal-to-noise ratios.     

一种非平稳卷积混合信号的时域盲源分离算法

该文将卷积混合盲源分离模型中的向量进行重新规划并对联合近似对角化方法加以推广,提出一种非平稳卷积混合信号的时域盲源分离算法。该算法先将采集到的卷积混合信号进行重排,使之满足重新定义向量后的瞬时混合模型特征,然后考虑到信号的非平稳特性,采用空间白化和联合近似块对角化方法分离出源信号。由于没有使用域变换而是从新的角度将卷积混合问题简化为瞬时混合问题,避免了卷积运算或域映射过程,降低了算法的复杂度。仿真实验验证了该算法的有效性并就参数的变化对信号干扰比的影响进行了分析。     

有噪复杂度寻踪的新算法

复杂度寻踪是投影寻踪向时间序列数据,即具有时间结构信号的扩展。该方法是和具有时间依赖特性的源信号的盲分离和独立成分分析紧密联系的。在源信号是具有时间依赖特性和存在高斯噪声的情况下,现有的有噪复杂度寻踪算法没有给出自回归系数的估计方法,影响了算法的实际应用,提出了有噪复杂度寻踪的新算法,该算法给出了自回归系数的估计方法。对自然图像和人工信号的仿真表明了提出算法的有效性,和现有的盲源分离算法相比较,提出算法具有好的信号分离性能。