Harmonic retrieval by period blind source extraction method: Model and algorithm

A frequently encountered problem in signal processing field is harmonic retrieval in additive colored Gaussian or non-Gaussian noise, especially when the frequencies of the harmonic signals are closely spaced in frequency domain. The purpose of this paper is to develop novel harmonic retrieval algorithm based on blind source extraction (BSE) method from linear mixtures of harmonic signals using only one observed channel signal. First, we establish the blind source separation (BSS) based harmonic retrieval model in additive noise using the only one observed channel, at the same time, the fundamental principle of BSE based harmonics retrieval algorithm is analyzed in detail. Then, based on the established harmonic BSS model, we propose a BSE approach to the harmonic retrieval using the concept of period BSE method, as a result, the harmonic retrieval algorithm using only one channel mixed signals is derived. Simulation results show that the proposed algorithm is able to separate the harmonic source signals and yield ideal performance.     

基于最大信噪比的盲源分离算法

提出一种新的低计算复杂度的瞬时线性混叠信号的盲分离算法,该算法利用统计独立信号完全分离时信噪比量大作为分离准则。源信号用估计信号的滑动平均代替,把源信号和噪声信号协方差矩阵的函数表示成广义特征值问题,通过广义特征值问题求解分离矩阵不需要任何迭代运算。和典型的信息理论方法相比,该算法的优点是具有非常低的计算复杂度。计算机模拟实验证明,该算法能够分离线性混合的超高斯和亚高斯源信号,并且可以有效地分离语音信号。     

A robust approach to independent component analysis of signals with high-level noise measurements

We propose a robust approach for independent component analysis (ICA) of signals where observations are contaminated with high-level additive noise and/or outliers. The source signals may contain mixtures of both sub-Gaussian and super-Gaussian components, and the number of sources is unknown. Our robust approach includes two procedures. In the first procedure, a robust prewhitening technique is used to reduce the power of additive noise, the dimensionality and the correlation among sources. A cross-validation technique is introduced to estimate the number of sources in this first procedure. In the second procedure, a nonlinear function is derived using the parameterized t-distribution density model. This nonlinear function is robust against the undue influence of outliers fundamentally. Moreover, the stability of the proposed algorithm and the robust property of misestimating the parameters (kurtosis) have been studied. By combining the t-distribution model with a family of light-tailed distributions (sub-Gaussian) model, we can separate the mixture of sub-Gaussian and super-Gaussian source components. Through the analysis of artificially synthesized data and real-world magnetoencephalographic (MEG) data, we illustrate the efficacy of this robust approach.     

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 kurtosis-based dynamic approach to Gaussian mixture modeling

We address the problem of probability density function estimation using a Gaussian mixture model updated with the expectation-maximization (EM) algorithm. To deal with the case of an unknown number of mixing kernels, we define a new measure for Gaussian mixtures, called total kurtosis, which is based on the weighted sample kurtoses of the kernels. This measure provides an indication of how well the Gaussian mixture fits the data. Then we propose a new dynamic algorithm for Gaussian mixture density estimation which monitors the total kurtosis at each step of the EM algorithm in order to decide dynamically on the correct number of kernels and possibly escape from local maxima. We show the potential of our technique in approximating unknown densities through a series of examples with several density estimation problems     

超定条件下的盲信号提取算法

基于信号峭度理论,提出一种超定条件下的盲信号提取算法。该算法将混合矩阵辨识转化为一系列Givens矩阵辨识,从观察信号中一次提取出一个源信号。对于超定盲信号分离问题,待未知所有独立分量分离出后,余下分量可以看作是一个或多个独立分量的拷贝,是冗余信号。在算法运行结束后,所有源信号分离出,实现超定盲信号分离。该算法计算简单,收敛性好。计算机仿真试验验证了算法的有效性。     

一种基于独立分量分析的模糊图像盲分离算法

利用独立分量分析（ICA）的不完整自然梯度算法对因混合而引起的多幅模糊灰度图像进行盲分离,并针对算法中的非线性函数与源信号概率分布密切相关,而源信号的分布却是未知的先验信息的问题,利用算法输出信号的峰度对非线性激活函数进行自适应选择,提出了一种改进的自适应不完整自然梯度算法,并将其应用于模糊图像的盲分离,分析了不同混合矩阵对本文算法恢复原始灰度图像的影响及算法性能。仿真结果证明了本文算法与经典的FastICA算法相比,计算耗时更少、性能指标明显优越。     

一种新的用于语音分离的盲源分离算法

提出了一种基于自然梯度的语音盲分离改进算法。该算法首先使用奇异值分解（SVD）的方法对观测信号进行预白化处理,而后使用自然梯度算法对预白化处理后的观测信号进行分离。通过计算机模拟试验,结果显示该算法能够有效地分离随机混合的自然语音信号。     

A hybrid technique for blind separation of non-gaussian and time-correlated sources using a multicomponent approach.

Blind inversion of a linear and instantaneous mixture of source signals is a problem often encountered in many signal processing applications. Efficient fastICA (EFICA) offers an asymptotically optimal solution to this problem when all of the sources obey a generalized Gaussian distribution, at most one of them is Gaussian, and each is independent and identically distributed (i.i.d.) in time. Likewise, weights-adjusted second-order blind identification (WASOBI) is asymptotically optimal when all the sources are Gaussian and can be modeled as autoregressive (AR) processes with distinct spectra. Nevertheless, real-life mixtures are likely to contain both Gaussian AR and non-Gaussian i.i.d. sources, rendering WASOBI and EFICA severely suboptimal. In this paper, we propose a novel scheme for combining the strengths of EFICA and WASOBI in order to deal with such hybrid mixtures. Simulations show that our approach outperforms competing algorithms designed for separating similar mixtures.     

A robust extraction algorithm for biomedical signals from noisy mixtures

Blind source extraction (BSE) is widely used to solve signal mixture problems where there are only a few desired signals. To improve signal extraction performance and expand its application, we develop an adaptive BSE algorithm with an additive noise model. We first present an improved normalized kurtosis as an objective function, which caters for the effect of noise. By combining the objective function and Lagrange multiplier method, we further propose a robust algorithm that can extract the desired signal as the first output signal. Simulations on both synthetic and real biomedical signals demonstrate that such combination improves the extraction performance and has better robustness to the estimation error of normalized kurtosis value in the presence of noise.     

Stochastic analysis of the LMS algorithm for cyclostationary colored Gaussian and non-Gaussian inputs

This paper studies the stochastic behavior of the LMS algorithm in a system identification framework for a cyclostationary colored input without assuming a Gaussian distribution for the input. The input cyclostationary signal is modeled by a colored random process with periodically time-varying power. The generation of the colored non-Gaussian random process is parametrized in novel manner by passing a Gaussian random process through a coloring filter followed by a zero memory nonlinearity. The unknown system parameters are fixed in most of the cases studied here. Mathematical models are derived for the behavior of the mean and mean-square-deviation (MSD) and the excess mean-square error (EMSE) of the adaptive weights as a function of the input cyclostationarity. The models display the dependence of the algorithm upon the input nonlinearity and coloration. Three nonlinearities that are studied in detail with Monte Carlo simulations provide strong support for the theory.     

基于峭度图像的超分辨率重建算法

针对在强噪声环境下,传统的超分辨率重建算法重建图像效果不佳的问题,提出一种基于峭度图像的超分辨率重建算法。定义峭度图像,从统计学角度分析得到峭度图像的2个重要性质,即具有高斯不变性,并且图像越模糊,峭度绝对值越小。在满足高分辨率图像与低分辨率图像之间反卷积的剩余误差有界的前提下,通过最大化峭度绝对值求解未知的高分辨率图像,采用Lagrange乘子法则求解此约束优化问题。分析高斯噪声和非高斯噪声环境下算法性能。仿真结果表明,该算法在主观视觉和客观评价上都明显优于传统算法。     

基于盲信号分离的混合气体分析

结合盲信号分离算法和热催化传感器特性,对混合气体进行分析,讨论了混合气体分析的盲可分离性,并使用基于峭度的盲信号分离算法对CH4和CO的混合气体进行分析和验证。实验结果表明,此方法无须预先假设源信号的概率密度函数(PDF),可在学习过程中直接判断信号的PDF并进行分离,提高了混合气体分析的可行性,实验结果为CH4的测量误差为4.27%,CO的测量误差为3.51%。     

Blind Source Extraction for Noisy Mixtures by Combining Gaussian Moments and Generalized Autocorrelations

In the blind source extraction problem, the concept of generalized autocorrelations has been successfully used when the desired signal has special temporal structures. However, their applications are only limited to noise-free mixtures, which is not realistic. Therefore, this paper addresses the extraction of the noisy model based on these temporal characteristics of sources. An objective function, which combines Gaussian moments and generalized autocorrelations, is proposed. Maximizing this objective function, we present a blind source extraction algorithm for noisy mixtures. Simulations on synthesized signals, images, artificial electrocardiogram (ECG) data and the real-world ECG data show the better performance of the proposed algorithm. Moreover, comparisons with the existing algorithms further indicate its validity and also show its robustness to the estimated error of time delay.     

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.     

基于自适应滤波的多模噪声抑制研究

多数研究都是将噪声当作高斯噪声处理,但实际上在多模噪声(整体上属于非高斯噪声)背景下,信号受损严重。用传统的LMS自适应算法不能很好的抑制噪声,格里菲斯LMS算法收敛速度较慢。提出一种将格里菲斯LMS算法(GLMS)与LMS-Newton算法相结合的GLMS-Newton算法,并给予了改进。在改进中,不仅采用了基于互相关变步长因子,而且引入了基于输入信号与期望信号的互相关的梯度算子。仿真表明,在收敛速度、稳态误差等方面都有了较大改善,能够很好的抑制多模噪声,提取出有用信号。     

Mean-square error and stability analysis of a subband structure for the rapid identification of sparse impulse responses

In a context of supervised adaptive filtering, the sparsity of the impulse response to be identified can be employed to accelerate the convergence rate of the algorithm. This idea was first explored by the so-called proportionate NLMS (PNLMS) algorithm, where the adaptation step-sizes are made larger for the coefficients with larger magnitudes. Whereas fast initial adaptation convergence rate is obtained with the PNLMS algorithm for white-noise input, slow convergence is observed for colored input signals. The combination of the PNLMS approach and a subband structure results in an algorithm with better convergence rate for sparse systems and colored input signals. In this paper, the steady-state mean-square error (MSE) and the maximum value of the step-size β that allows convergence of the subband PNLMS-type algorithm are analyzed. Theoretical results are confirmed by simulations.     

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。     

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.     

Two-microphone separation of speech mixtures.

Separation of speech mixtures, often referred to as the cocktail party problem, has been studied for decades. In many source separation tasks, the separation method is limited by the assumption of at least as many sensors as sources. Further, many methods require that the number of signals within the recorded mixtures be known in advance. In many real-world applications, these limitations are too restrictive. We propose a novel method for underdetermined blind source separation using an instantaneous mixing model which assumes closely spaced microphones. Two source separation techniques have been combined, independent component analysis (ICA) and binary time - frequency (T-F) masking. By estimating binary masks from the outputs of an ICA algorithm, it is possible in an iterative way to extract basis speech signals from a convolutive mixture. The basis signals are afterwards improved by grouping similar signals. Using two microphones, we can separate, in principle, an arbitrary number of mixed speech signals. We show separation results for mixtures with as many as seven speech signals under instantaneous conditions. We also show that the proposed method is applicable to segregate speech signals under reverberant conditions, and we compare our proposed method to another state-of-the-art algorithm. The number of source signals is not assumed to be known in advance and it is possible to maintain the extracted signals as stereo signals.