Multichannel blind deconvolution for source separation in convolutive mixtures of speech

This paper addresses the blind separation of convolutive and temporally correlated mixtures of speech, through the use of a multichannel blind deconvolution (MBD) method. In the proposed framework (LP-NGA), spatio-temporal separation is carried out by entropy maximization using the well-known natural gradient algorithm (NGA), while a temporal pre-whitening stage, based on linear prediction (LP), manages to fully preserve the original spectral characteristics of each source contribution. Confronted with synthetic convolutive mixtures, we show that the LP-NGA-an unconstrained natural extension to the multichannel BSS problem-benefits not only from fewer model constraints, but also from other factors, such as an overall increase in separation performance, spectral preservation efficiency and speed of convergence.     

Fast nonunitary joint block diagonalization with degenerate solution elimination for convolutive blind source separation

This paper addresses the problem of joint block diagonalization (JBD) of a set of given matrices. As is known that the nonunitary JBD algorithm has some advantages over the existing orthogonal one for convolutive blind source separation (CBSS). However, the nonunitary JBD algorithm is prone to converge to some unexpected degenerate solutions (singular or ill-conditioned solutions). Especially for the matrices of large dimension or the case that the number of the diagonal blocks is relatively large, the performances of the nonunitary JBD algorithm degrade more severely. To eliminate the degenerate solutions, we optimize a penalty term based weighted least-squares criterion and thus develop a fast efficient algorithm. The performance of the proposed algorithm is evaluated by computer simulations and compared with the existing state-of-the-art nonunitary JBD algorithm. The simulation results demonstrate the robustness and performance improvement of the proposed algorithm.     

基于频域卷积信号盲源分离的乐曲数据库构建*

将通过频域卷积信号盲源分离算法从MP3歌曲音频信号中分离出人声主唱信号,再从人声主唱信号中提取出能够表征歌曲的旋律特征构建哼唱检索系统的歌曲数据库。盲源分离要求观测信号数目不小于源信号数目,因此先用小波多分辨率分析构造一路观测信号,再用频域独立成分分析(FDICA)实现MP3歌曲音频信号的盲源分离(BSS)。实验证明,采用FDICA-based BSS从歌曲MP3中分离出的人声主唱信号的旋律特征与待检索的人声哼唱信号的旋律特征有较高的相似度,可以用歌曲MP3构建哼唱检索系统的歌曲数据库。     

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.     

Adaptive improved natural gradient algorithm for blind source separation

We propose an adaptive improved natural gradient algorithm for blind separation of independent sources. First, inspired by the well-known backpropagation algorithm, we incorporate a momentum term into the natural gradient learning process to accelerate the convergence rate and improve the stability. Then an estimation function for the adaptation of the separation model is obtained to adaptively control a step-size parameter and a momentum factor. The proposed natural gradient algorithm with variable step-size parameter and variable momentum factor is therefore particularly well suited to blind source separation in a time-varying environment, such as an abruptly changing mixing matrix or signal power. The expected improvement in the convergence speed, stability, and tracking ability of the proposed algorithm is demonstrated by extensive simulation results in both time-invariant and time-varying environments. The ability of the proposed algorithm to separate extremely weak or badly scaled sources is also verified. In addition, simulation results show that the proposed algorithm is suitable for separating mixtures of many sources (e.g., the number of sources is 10) in the complete case.     

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.     

Blind source separation with convolutive noise cancellation

On-line adaptive learning algorithms for cancellation of additive, convolutive noise from linear mixtures of sources with a simultaneous blind source separation are developed. Associated neural network architectures are proposed. A simple convolutive noise model is assumed, i.e. the unknown additive noise in each channel is a (FIR) filtering version of environmental noise, where some convolutive reference noise is measurable. Two approaches are considered: in the first, the noise is cancelled from the linear mixture of source signals as pre-processing, after that the source signals are separated; in the second, both source separation and additive noise cancellation are performed simultaneously. Both steps consist of adaptive learning processes. By computer simulation experiments, it was found that the first approach is applicable for a large amount of noise, whereas in the second approach, a considerable increase of the convergence speed of the separation process can be achieved. Performance and validity of the proposed approaches are demonstrated by extensive computer simulations.Nomenclature Symbol Meaning - ₄ normalised kurtosis of a signal - (t), t learning rates - m number of sources - n number of sensors - N,M order of the FIR filters - s(t) m-dimensional vector of (unknown) source signals - x(t) n-dimensional vector of mixed signals (sensors) - y(t) n-dimensional vector of separated output signals (estimated sources) - v _R(t) (unknown) primary environment noise signal - n _R(t) secondary reference noise signal - n(t) n-dimensional vector of additive noise signals - f(·),g(·) activation functions in separation rule - f _R(·) activation function in noise cancellation rule - A=[a _ij]_m×n (unknown) mixing matrix - B=[b _ij]_n×N additive noise generation matrix - H(t)=[h _ij]_n×M noise cancellation matrix - W(t)=[w _ij]_n×n global de-mixing matrix     

一种新的联合块对角化卷积盲分离时域算法

提出一种基于高阶累积量联合块对角化的时域算法求解卷积混合盲信号分离问题。引入白化处理,将混叠矩阵转变成酉矩阵,混合信号转变为互不相关的,进而计算出其对应的一系列高阶累积量矩阵,通过最小化代价函数来实现高阶累积量矩阵联合块对角化的目的,在时域中解决超定卷积盲分离问题。实验表明,相比于经典的自然梯度算法,所提方法的分离精度更高,且运算速度也更快。     

基于回溯搜索优化的卷积混合语音盲分离

针对独立矢量分析（IVA）算法初始分离矩阵取值对分离性能影响较大的局限性,提出了基于回溯搜索优化的卷积混合语音盲分离算法。采用频域各频率点IVA分离信号的复数峭度和作为目标函数,利用回溯搜索优化算法（BSA）对初始分离矩阵进行优化调整,更好地实现了语音信号的盲分离。在分离过程中,采用复Givens旋转变换原理将对分离矩阵的求解转化为对旋转角度的求解,有效减少了BSA的参数编码维数,降低了优化求解难度。针对语音信号的卷积混合分离实验表明,该算法具有良好的分离效果,其分离性能较之基本IVA算法显著提升。     

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。     

Grading learning for blind source separation

By generalizing the learning rate parameter to a learning rate matrix, this paper proposes a grading learning algorithm for blind source separation. The whole learning process is divided into three stages: initial stage, capturing stage and tracking stage. In different stages, different learning rates are used for each output component, which is determined by its dependency on other output components. It is shown that the grading learning algorithm is equivariant and can keep the separating matrix from becoming singular. Simulations show that the proposed algorithm can achieve faster convergence, better steady-state performance and higher numerical robustness, as compared with the existing algorithms using fixed, time-descending and adaptive learning rates.     

MISEP method for postnonlinear blind source separation

In this letter, a standard postnonlinear blind source separation algorithm is proposed, based on the MISEP method, which is widely used in linear and nonlinear independent component analysis. To best suit a wide class of postnonlinear mixtures, we adapt the MISEP method to incorporate a priori information of the mixtures. In particular, a group of three-layered perceptrons and a linear network are used as the unmixing system to separate sources in the postnonlinear mixtures, and another group of three-layered perceptron is used as the auxiliary network. The learning algorithm for the unmixing system is then obtained by maximizing the output entropy of the auxiliary network. The proposed method is applied to postnonlinear blind source separation of both simulation signals and real speech signals, and the experimental results demonstrate its effectiveness and efficiency in comparison with existing methods.     

一种欠定盲源分离新算法

提出了一种基于两步法的欠定盲源分离新算法。在混合矩阵估计阶段,采用基于势函数的聚类方法,在源信号恢复阶段,提出一种快速的稀疏信号重构算法,通过定义一个连续可微函数来近似[?0]范数,使得[?0]范数可解。该算法的特点是实现简单、速度快。仿真实验表明,与现有的采用快速[?1]范数最小化和OMP算法的欠定盲源分离方法相比,提出的算法在保证分离性能的前提下大幅度提高了算法的运行速度。     

一种基于NPCA的自适应变步长盲源分离算法

收敛速度和稳定误差是在线盲源分离算法的两个重要的性能指标。为了加快算法的收敛速度,提高算法的跟踪性能,提出一种基于NPCA的自适应变步长盲源分离算法。该算法的迭代步长随着输入信号和混合矩阵的变化而变化,因而具有更好的跟踪性能。仿真结果表明,该算法提高了NPCA算法的收敛速度和跟踪性能。     

基于邻域风险最小化概率密度估计的自适应盲分离算法*

为实现由不同统计特性和概率分布平滑特性信号得到混合信号的盲分离,对基于支持向量机的邻域风险最小化概率密度估计算法进行研究,提出一种邻域函数的构造方法,将其与自然梯度批处理算法相结合,形成一种新的自适应盲分离算法;利用广义高斯模型分析了分离算法的精确度。通过仿真实验,验证了该算法能分离统计特性不同的混合信号,相比于基于经验风险最小化的方法,该方法在收敛速度和精度方面的性能有很大提高。     

基于非线性主成分分析的自适应变步长盲源分离算法

算法的迭代步长对于算法的收敛性能有着重要影响。针对固定步长的非线性主成分分析(NPCA)算法不能兼顾收敛速度和估计精度的情形,提出基于梯度的自适应变步长NPCA算法和最优变步长NPCA算法两种自适应变步长算法来改善其收敛性能。特别地,最优变步长NPCA算法通过对代价函数进行一阶线性近似表示,从而计算出当前的最优迭代步长。该算法的迭代步长随估计误差的变化而变化,估计误差大,迭代步长相应大,反之亦然;且不需要人工设置任何参数。仿真结果表明,当算法的估计精度相同时,与固定步长NPCA算法相比,两种自适应变步长NPCA算法相对固定步长NPCA算法都具有更好的收敛速度或跟踪性能,且最优变步长NPCA算法的性能优于基于梯度的自适应变步长NPCA算法。     

Nonholonomic orthogonal learning algorithms for blind source separation

Independent component analysis or blind source separation extracts independent signals from their linear mixtures without assuming prior knowledge of their mixing coefficients. It is known that the independent signals in the observed mixtures can be successfully extracted except for their order and scales. In order to resolve the indeterminacy of scales, most learning algorithms impose some constraints on the magnitudes of the recovered signals. However, when the source signals are nonstationary and their average magnitudes change rapidly, the constraints force a rapid change in the magnitude of the separating matrix. This is the case with most applications (e.g., speech sounds, electroencephalogram signals). It is known that this causes numerical instability in some cases. In order to resolve this difficulty, this article introduces new nonholonomic constraints in the learning algorithm. This is motivated by the geometrical consideration that the directions of change in the separating matrix should be orthogonal to the equivalence class of separating matrices due to the scaling indeterminacy. These constraints are proved to be nonholonomic, so that the proposed algorithm is able to adapt to rapid or intermittent changes in the magnitudes of the source signals. The proposed algorithm works well even when the number of the sources is overestimated, whereas the existent algorithms do not (assuming the sensor noise is negligibly small), because they amplify the null components not included in the sources. Computer simulations confirm this desirable property.     

Fuzzy-based learning rate determination for blind source separation

Many independent component analysis (ICA) algorithms have been proposed for blind source separation. These algorithms belong to the LMS-type algorithm in natural. Hence, the choice of the step-size reflects a tradeoff between misadjustment and the speed of convergence. Based on the separation state of outputs of the neural network for ICA, the paper develops a fuzzy inference-based step-size selection algorithm. The fuzzy inference system consists of two inputs (the second- and higher order correlation coefficients of output components) and one output (the fuzzy learning rate). In this way, the ICA algorithms become more efficient, which is verified by simulation results.     

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.