Fast nonlinear autocorrelation algorithm for source separation

Independent component analysis (ICA) and blind source separation (BSS) methods have been used for pattern recognition problems. It is well known that ICA and BSS depend on the statistical properties of original sources or components, such as non-Gaussianity. In the paper, using a statistical property—nonlinear autocorrelation and maximizing the nonlinear autocorrelation of source signals, we propose a fast fixed-point algorithm for BSS. We study its convergence property and show that its convergence speed is at least quadratic. Simulations by the artificial signals and the real-world applications verify the efficient implementation 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.     

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.     

Towards an intelligent multi-sensor satellite image analysis based on blind source separation using multi-source image fusion

In this paper we propose a new approach for land cover classification using blind sources separation (BSS) and satellite image fusion methods simultaneously. Satellite image pixels are represented by radiometric values where each pixel is considered as a mixture of several independent sources. The BSS methods were developed in order to extract maximum information from different statistical features such as spatial correlation and local high order statistics. The statistical independence of the sources can be obtained through the joint approximate diagonalization of eigen-matrix in two dimensions (JADE-2D) algorithm. A reduction of spatial correlation can be obtained using the second order blind identification in two dimensions (SOBI-2D) algorithm. Non-Gaussianity can be measured using the fast-independent component analysis in two dimensions (Fast-ICA-2D) algorithm. These algorithms allow extraction of features by estimating the source images, mixing and un-mixing the matrix. These source images will be used by our framework as secondary knowledge, which is useful for a supervised classification.     

Bayesian nonstationary source separation

A Bayesian nonstationary source separation algorithm is proposed in this paper to recover nonstationary sources from noisy mixtures. In order to exploit the temporal structure of the data, we use a time-varying autoregressive (TVAR) process to model each source signal. Then variational Bayesian (VB) learning is adopted to integrate the source model with blind source separation (BSS) in probabilistic form. Our separation algorithm makes full use of temporally correlated prior information and avoids overfitting in separation process. Experimental results demonstrate that our vbICA-TVAR algorithm learns the temporal structure of sources and acquires cleaner source reconstruction.     

Mixing Audiovisual Speech Processing and Blind Source Separation for the Extraction of Speech Signals From Convolutive Mixtures

Looking at the speaker's face can be useful to better hear a speech signal in noisy environment and extract it from competing sources before identification. This suggests that the visual signals of speech (movements of visible articulators) could be used in speech enhancement or extraction systems. In this paper, we present a novel algorithm plugging audiovisual coherence of speech signals, estimated by statistical tools, on audio blind source separation (BSS) techniques. This algorithm is applied to the difficult and realistic case of convolutive mixtures. The algorithm mainly works in the frequency (transform) domain, where the convolutive mixture becomes an additive mixture for each frequency channel. Frequency by frequency separation is made by an audio BSS algorithm. The audio and visual informations are modeled by a newly proposed statistical model. This model is then used to solve the standard source permutation and scale factor ambiguities encountered for each frequency after the audio blind separation stage. The proposed method is shown to be efficient in the case of 2 times 2 convolutive mixtures and offers promising perspectives for extracting a particular speech source of interest from complex mixtures     

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.     

统计相关源信号分离模型与算法综述

统计相关源信号分离理论不仅有着广泛的应用背景, 也为深入了解数据的本质结构提供了有效的分析工具. 首先, 重点分析和讨论一类特殊的相关源信号分离模型—–独立子空间分析模型的可分离性; 其次, 分别介绍基于源信号稀疏性、统计测度、独立子空间分析、源信号时序结构、源信号有界性和非负性的各种相关源信号分离算法; 再次, 通过将加性噪声中的盲源分离和高光谱解混问题建模为统计相关源信号分离模型, 表明了该方法的应用价值; 最后, 总结了相关源信号分离中存在的问题, 并对下一步的研究思路进行了分析和展望.

     

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.     

An Efficient Measure of Signal Temporal Predictability for Blind Source Separation

An efficient measure of signal temporal predictability is proposed, which is referred to as difference measure. We can prove that the difference measure of any signal mixture is between the maximal and minimal difference measure of the source signals. Previous blind source separation (BSS) problem is changed to a generalized eigenproblem by using Stone’s measure. However, by using difference measure, the BSS problem is furthermore simplified to a standard symmetric eigenproblem. And the separation matrix is the eigenvector matrix, which can be solved by using principal component analysis (PCA) method. Based on difference measure, a few efficient algorithms have been proposed, which are either in batch mode or in on-line mode. Simulations show that difference measure is competitive with Stone’s measure. Especially, the on-line algorithms derived from difference measure have better performance than those derived from Stone’s measure.     

Blind source separation with dynamic source number using adaptive neural algorithm

A difficult blind source separation (BSS) issue dealing with an unknown and dynamic number of sources is tackled in this study. In the past, the majority of BSS algorithms familiarize themselves with situations where the numbers of sources are given, because the settings for the dimensions of the algorithm are dependent on this information. However, such an assumption could not be held in many advanced applications. Thus, this paper proposes the adaptive neural algorithm (ANA) which designs and associates several auto-adjust mechanisms to challenge these advanced BSS problems. The first implementation is the on-line estimator of source numbers improved from the cross-validation technique. The second is the adaptive structure neural network that combines feed-forward architecture and the self-organized criterion. The last is the learning rate adjustment in order to enhance efficiency of learning. The validity and performance of the proposed algorithm are demonstrated by computer simulations, and are compared to algorithms with state of the art. From the simulation results, these have been confirmed that the proposed ANA performed better separation than others in static BSS cases and is feasible for dynamic BSS cases.     

Method to separate sparse components from signal mixtures

This paper addresses the blind source separation (BSS) problem where the input data are mixtures of sources that are “sparse”—that is each source has zero amplitude for some of the time. It is shown that, under certain conditions, it is possible to separate these sources by the analysis of localised segments of the phase space trajectory where one source dominates rather than applying statistical methods to the whole phase space plot. Results are presented for both simulated data, and thoracic and abdominal ECG data taken from an expectant mother. It is shown that when applied to the ECG data, the proposed technique has a comparable performance to the standard Fast ICA method. For the particular simulated data set, the proposed method gives better results for relatively low noise levels but is less robust than the FastICA for higher noise levels. Subsequently, the potential advantage of using the proposed technique for mixtures of correlated sparse sources is demonstrated. However, for more general sources that are not sparse, the proposed technique in its present form has, as expected, an inferior performance compared to the FastICA technique.     

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。     

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.     

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.     

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.      

Natural gradient-based recursive least-squares algorithm for adaptive blind source separation

This paper focuses on the problem of adaptive blind source separation (BSS). First, a recursive least-squares (RLS) whitening algorithm is proposed. By combining it with a natural gradient-based RLS algorithm for nonlinear principle component analysis (PCA), and using reasonable approximations, a novel RLS algorithm which can achieve BSS without additional pre-whitening of the observed mixtures is obtained. Analyses of the equilibrium points show that both of the RLS whitening algorithm and the natural gradient-based RLS algorithm for BSS have the desired convergence properties. It is also proved that the combined new RLS algorithm for BSS is equivariant and has the property of keeping the separating matrix from becoming singular. Finally, the effectiveness of the proposed algorithm is verified by extensive simulation results.     

A new concept for separability problems in blind source separation

The goal of blind source separation (BSS) lies in recovering the original independent sources of a mixed random vector without knowing the mixing structure. A key ingredient for performing BSS successfully is to know the indeterminacies of the problem-that is, to know how the separating model relates to the original mixing model (separability). For linear BSS, Comon (1994) showed using the Darmois-Skitovitch theorem that the linear mixing matrix can be found except for permutation and scaling. In this work, a much simpler, direct proof for linear separability is given. The idea is based on the fact that a random vector is independent if and only if the Hessian of its logarithmic density (resp. characteristic function) is diagonal everywhere. This property is then exploited to propose a new algorithm for performing BSS. Furthermore, first ideas of how to generalize separability results based on Hessian diagonalization to more complicated nonlinear models are studied in the setting of postnonlinear BSS.     

一种盲信号处理中的时域自适应滤波算法

滤波是信号处理中的重要环节,鉴于盲信号处理本身的特点,传统的滤波技术并不适合直接用于盲源分离之中。然而作为分离前的预处理,滤波技术在独立成分分离算法中是必要的。为此,本文结合稳健的数据非线性投影,首次提出盲信号中的自适应滤波方法,与此同时给出了具有自适应特性的阈值判决。在此基础上构造了盲信号中的自适应滤波算法,解决了利用低通和高通滤波处理盲信号所遇到的问题。仿真结果表明,在不破坏数据统计特性的前提下,该方法能有效滤除数据中的野值成分,避免了野值数据对独立成分分离算法性能的影响,为盲信号分离的预处理开辟了一种新的途径。     

基于广义相关系数的后非线性盲信号分离算法

基于互信息最小化的独立性测度对各分离信号间的非线性相关度度量没有归一化的问题,提出一种基于广义相关系数的肓信号分离(BSS)算法.首先选取后非线性混叠模型(PNL)分析基于广义相关系数的独立性测度;然后采用Gram-Charlier扩展形式估计输出参数并获取评价几率函数,结合最陡下降法求得分离矩阵和参数化可逆非线性映射的算法迭代公式.仿真结果表明,采用所提出的算法能够定量分析各分离信号间的非线性相关程度,有效分离后非线性混叠信号.