Blind Separation Of Convolutive Mixtures Research Articles

Independent Vector Analysis for Blind Deconvolving of Digital Modulated Communication Signals

For the purpose of overcoming the random permutation ambiguity of the frequency-domain-independent component analysis (FDICA) for blind separation of convolutive mixtures, this paper proposes an independent vector analysis (IVA) detection receiver for blindly deconvolving the convolutive mixtures of digitally modulated signals for wireless communications. The foundation of IVA is through jointly carrying out separation work for different frequency bin data fusion, and the dependencies of frequency bins are exploited in solving the random permutation problem of separation signals. In addition, IVA uses multivariate prior distributions instead of the univariate distribution used in FDICA. Multivariate prior distribution is employed to preserve the interfrequency dependencies for individual sources, which can give rise to separation performance enhancement. Simulation results and analysis corroborate the effectiveness of the proposed detection method.

A RobustICA-based algorithmic system for blind separation of convolutive mixtures

In this paper, we propose a frequency-domain method employing robust independent component analysis (RICA) to address the multichannel Blind Source Separation (BSS) problem of convolutive speech mixtures in highly reverberant environments. We impose regularization processes to tackle the ill-conditioning problem of the covariance matrix and to mitigate the performance degradation. We evaluate the impact of several parameters on the performance of separation, e.g., windowing type and overlapping ratio of the frequency domain method. We then assess and compare different techniques to solve the frequency-domain permutation ambiguity. Furthermore, we develop an algorithm to separate the source signals in adverse conditions, i.e. high reverberation conditions when short observation signals are available. Finally, through extensive simulations and real-world experiments, we evaluate and demonstrate the superiority of the presented convolutive algorithmic system in comparison to other BSS algorithms, including recursive regularized ICA (RR-ICA) and independent vector analysis (IVA).

Fast spatio-temporal decorrelation using FIR filter network with decoupled adaptive step sizes

Blind separation of convolutive mixtures has many applications in the areas of acoustics, communications, biomedical signal processing. Spatio-temporal decorrelation is a useful preprocessing technique that can reduce the blind separation problem into a simpler orthogonal matrix estimation problem. However, it is computationally expensive for its large unknown parameter set. Realtime spatio-temporal decorrelation method remains an open issue for years. In this paper, we focus on accelerating the adaptation process in the FIR filter based decorrelation method. Firstly, the update equation is decoupled into spatial decorrelation and temporal decorrelation. Then, their respective convergence conditions are systematically analyzed using eigenvalue decomposing method. Based on it, a fast algorithm for FIR filter network with spatio-temporal decoupled adaptive step-sizes is proposed. Comprehensive simulations are performed on both synthetic data and real world captured sEMG data. We have compared the proposed algorithm with the fixed step size method, IIR filter with natural gradient, and the annealed step size method. The factors including number of iteration, number of channel, computational time, selection of filter order and window size are elaborately compared and discussed. The results verified the reliable performance of our method on accelerating the adaptation process for spatio-temporal decorrelation simultaneously compared to classical methods.

A Convex Approach to Blind MIMO Communications

This letter considers the blind separation of convolutive mixtures in a multi-in-multi-out (MIMO) communication system. Multiple source signals are transmitted simultaneously over a shared communication medium (modeled as linear convolutive channels) to multiple receivers. We recast the joint recovery of the source signals, and the channel impulse responses as a block-rank-one matrix recovery problem, which can be effectively solved using a convex program. Our numerical experiments show that the proposed convex program yields exact recovery of the source signals when they are members of known generic subspaces. Moreover, the numerics also show that the successful recovery is achieved in blind MIMO with the number of measurements that scale roughly optimally with the number of unknowns. We discuss our results in the context of an application in blind MIMO wireless communications, where coding the transmitted messages results in exact blind separation at the receiver array.

Preconditioned optimization algorithms solving the problem of the non unitary joint block diagonalization: application to blind separation of convolutive mixtures

This article addresses the problem of the Non Unitary Joint Block Diagonalization ( $$\mathsf {NU-JBD}$$ ) of a given set of complex matrices for the blind separation of convolutive mixtures of sources. We propose new different iterative optimization schemes based on Conjugate Gradient, Preconditioned Conjugate Gradient, Levenberg–Marquardt and Quasi-Newton methods. We perform also a study to determine which of these algorithms offer the best compromise between efficiency and convergence speed in the studied context. To be able to derive all these algorithms, a preconditioner has to be computed which requires either the calculation of the complex Hessian matrices or the use of an approximation to these Hessian matrices. Furthermore, the optimal stepsize is also computed algebraically to speed up the convergence of these algorithms. Computer simulations are provided in order to illustrate the behavior of the different algorithms in various contexts: when exactly block-diagonal matrices are considered but also when these matrices are progressively perturbed by an additive Gaussian noise. Finally, it is shown that these algorithms enable solving the blind separation of the convolutive mixtures of sources problem.

An extended echo state network using Volterra filtering and principal component analysis

Echo state networks (ESNs) can be interpreted as promoting an encouraging compromise between two seemingly conflicting objectives: (i) simplicity of the resulting mathematical model and (ii) capability to express a wide range of nonlinear dynamics. By imposing fixed weights to the recurrent connections, the echo state approach avoids the well-known difficulties faced by recurrent neural network training strategies, but still preserves, to a certain extent, the potential of the underlying structure due to the existence of feedback loops within the dynamical reservoir. Moreover, the overall training process is relatively simple, as it amounts essentially to adapting the readout, which usually corresponds to a linear combiner. However, the linear nature of the output layer may limit the capability of exploring the available information, since higher-order statistics of the signals are not taken into account. In this work, we present a novel architecture for an ESN in which the linear combiner is replaced by a Volterra filter structure. Additionally, the principal component analysis technique is used to reduce the number of effective signals transmitted to the output layer. This idea not only improves the processing capability of the network, but also preserves the simplicity of the training process. The proposed architecture is then analyzed in the context of a set of representative information extraction problems, more specifically supervised and unsupervised channel equalization, and blind separation of convolutive mixtures. The obtained results, when compared to those produced by already proposed ESN versions, highlight the benefits brought by the novel network proposal and characterize it as a promising tool to deal with challenging signal processing tasks.

Independent Component Analysis Using Spherical Microphone Arrays

Spherical microphone arrays provide a new and promising tool for the spatial analysis of complex sound elds. Considerable previous work has investigated the use of spherical microphone arrays for phase-mode beamforming, which relies on the Bessel-weighted spherical harmonic transform of the sound eld. In this paper, we investigate the advantages that spherical microphone arrays provide for blind separation of convolutive mixtures using independent component analysis. We demonstrate that applying a standard, linear independent component analysis model in the phase-mode domain enables one to both localize the sources and resolve the permutation problem that plagues most implementations of independent component analysis. As well, we show that the standard linear independent component analysis model can be incorporated into beamforming approaches for source localization and source separation. Simulation results indicate that this approach works in realistic scenarios that include room reverberation.

Blind source separation of convolutive mixtures of non-circular linearly modulated signals with unknown baud rates

This paper addresses the problem of blind separation of convolutive mixtures of BPSK and circular linearly modulated signals with unknown (and possibly different) baud rates and carrier frequencies. In previous works, we established that the Constant Modulus Algorithm (CMA) is able to extract a source from a convolutive mixture of circular linearly modulated signals. We extend the analysis of the extraction capabilities of the CMA when the mixing also contains BPSK signals. We prove that if the various source signals do not share any non-zero cyclic frequency nor any non-conjugate cyclic frequencies, the local minima of the constant modulus cost function are separating filters. Unfortunately, the minimization of the Godard cost function generally fails when considering BPSK signals that have the same rates and the same carrier frequencies. This failure is due to the existence of non-separating local minima of the Godard cost function. In order to achieve the separation, we propose a simple modification of the Godard cost function which only requires knowledge of the BPSK sources frequency offsets at the receiver side. We provide various simulations of realistic digital communications scenarios that support our theoretical statements.

Indeterminacy Free Frequency-Domain Blind Separation of Reverberant Audio Sources

Blind separation of convolutive mixtures is a very complicated task that has applications in many fields of speech and audio processing, such as hearing aids and man-machine interfaces. One of the proposed solutions is the frequency-domain independent component analysis. The main disadvantage of this method is the presence of permutation ambiguities among consecutive frequency bins. Moreover, this problem is worst when reverberation time increases. Presented in this paper is a new frequency-domain method, that uses a simplified mixing model, where the impulse responses from one source to each microphone are expressed as scaled and delayed versions of one of these impulse responses. This assumption, based on the similitude among waveforms of the impulse responses, is valid for a small spacing of the microphones. Under this model, separation is performed without any permutation or amplitude ambiguity among consecutive frequency bins. This new method is aimed mainly to obtain separation, with a small reduction of reverberation. Nevertheless, as the reverberation is included in the model, the new method is capable of performing separation for a wide range of reverberant conditions, with very high speed. The separation quality is evaluated using a perceptually designed objective measure. Also, an automatic speech recognition system is used to test the advantages of the algorithm in a real application. Very good results are obtained for both, artificial and real mixtures. The results are significantly better than those by other standard blind source separation algorithms.

Convolutive Blind Source Separation Based on Disjointness Maximization of Subband Signals

The concept of disjoint component analysis (DCA) is based on the fact that different speech or audio signals are typically more disjoint than mixtures of them. This letter studies the problem of blind separation of convolutive mixtures through the subband-wise maximization of the disjointness of time-frequency representations of the signals. In our approach, we first define a frequency-dependent measure representing the closeness to disjointness of a group of subband signals. Then, this frequency-dependent measure is integrated to form an objective function that only depends on the time-domain parameters of the separation system. Lastly, an efficient natural-gradient-based learning rule is developed for the update of the separation-system coefficients.

Separating Convolutive Mixtures By Pairwise Mutual Information Minimization

Blind separation of convolutive mixtures by minimizing the mutual information between output sequences can avoid the side effect of temporally whitening the outputs, but it involves the score function difference, whose estimation may be problematic when the data dimension is greater than two. This greatly limits the application of this method. Fortunately, for separating convolutive mixtures, pairwise independence of outputs leads to their mutual independence. As an implementation of this idea, we propose a way to separate convolutive mixtures by enforcing pairwise independence. This approach can be applied to separate convolutive mixtures of a moderate number of sources.

A Nonunitary Joint Block Diagonalization Algorithm for Blind Separation of Convolutive Mixtures of Sources

This letter addresses the problem of the nonunitary joint block diagonalization of a given set of complex matrices whose potential applications stem from the blind separation of convolutive mixtures of sources and from the array processing. The proposed algorithm is based on the algebraic optimization of a least-mean-square criterion. One of its advantage is that a pre-whitening stage is no more compulsorily required when this algorithm is applied in the blind source separation context. Computer simulations are provided in order to illustrate its behavior in three cases: when exact block-diagonal matrices are built, then when they are progressively perturbed by an additive Gaussian noise and, finally, in the context of blind separation of convolutive mixtures of temporally correlated sources with estimated correlation matrices. A comparison with a classical orthogonal joint block diagonalization algorithm is also performed, and a new performance index is introduced to measure the performance of the separation.

Does mixing of speech signals comply with central limit theorem?

In this short communication compliance of central limit theorem (CLT) by the convolutive mixing of two speech signals has been investigated in the frequency domain keeping in view the blind separation of convolutive mixture of speech by the independent component analysis (ICA)-based algorithms exploiting properties of CLT. The convolutive mixing of speech is equivalent to superposition of spectral components of each signal. When two non-Gaussian signals are added, the resulting mixed signal gains Gaussianity over the addend signals under the light of CLT. This paper looks for the similar effect of CLT in the mixing process of speech signals with adequate doubts because speech signals from different speakers differ in spectral contents and are spectrally sparse. Interestingly, the results based on the measure of spectral kurtosis show that mixing process of speech signal does not gain Gaussianity in every frequency bin.

Spatio–Temporal FastICA Algorithms for the Blind Separation of Convolutive Mixtures

This paper derives two spatio-temporal extensions of the well-known FastICA algorithm of Hyvarinen and Oja that are applicable to the convolutive blind source separation task. Our time-domain algorithms combine multichannel spatio-temporal prewhitening via multistage least-squares linear prediction with novel adaptive procedures that impose paraunitary constraints on the multichannel separation filter. The techniques converge quickly to a separation solution without any step size selection or divergence difficulties, and unlike other methods, ours do not require special coefficient initialization procedures to obtain good separation performance. They also allow for the efficient reconstruction of individual signals as observed in the sensor measurements directly from the system parameters for single-input multiple-output blind source separation tasks. An analysis of one of the adaptive constraint procedures shows its fast convergence to a paraunitary filter bank solution. Numerical evaluations of the proposed algorithms and comparisons with several existing convolutive blind source separation techniques indicate the excellent relative performance of the proposed methods.

Blind Source Separation Based on Time-Domain Optimization of a Frequency-Domain Independence Criterion

A new technique for the blind separation of convolutive mixtures is proposed in this paper. Inspired by the works of Amari, Sabala , and Rahbar, we firstly start from the application of Kullback-Leibler divergence in frequency domain, and then we integrate Kullback-Leibler divergence over the whole frequency range of interest to yield a new objective function which turns out to be time-domain variable dependent. In other words, the objective function is derived in frequency domain which can be optimized with respect to time domain variables. The proposed technique has the advantages of frequency domain approaches and is suitable for very long mixing channels, but does not suffer from the local permutation problem as the separation is achieved in time-domain

Subspace-Based Channel Shortening for the Blind Separation of Convolutive Mixtures

A novel subspace-based channel shortening procedure is proposed based on the structure of the delayed autocorrelation matrices of the observation process. This purely second-order approach applies to overdetermined multiple-input multiple-output (MIMO) channels with independent, white sources. The channel may be sparse, and its length is assumed to be unknown. Through successive deflations, the problem can be transformed into an instantaneous blind source separation (BSS) problem which is simpler to solve using, for example, independent component analysis (ICA) techniques. The algorithm is computationally fast although it requires large input datasets. Such data can be acquired either through large numbers of sensors or by using increased data sampling rate. When not enough data are available, the method can still be used for reducing the channel length thus simplifying the problem for subsequent treatment

A Nonlinear Prediction Approach to the Blind Separation of Convolutive Mixtures

We propose a method for source separation of convolutive mixture based on nonlinear prediction-error filters. This approach converts the original problem into an instantaneous mixture problem, which can be solved by any of the several existing methods in the literature. We employ fuzzy filters to implement the prediction-error filter, and the ecacy of the proposed method is illustrated by some examples.

Permutation Correction in the Frequency Domain in Blind Separation of Speech Mixtures

This paper presents a method for blind separation of convolutive mixtures of speech signals, based on the joint diagonalization of the time varying spectral matrices of the observation records. The main and still largely open problem in a frequency domain approach is permutation ambiguity. In an earlier paper of the authors, the continuity of the frequency response of the unmixing filters is exploited, but it leaves some frequency permutation jumps. This paper therefore proposes a new method based on two assumptions. The frequency continuity of the unmixing filters is still used in the initialization of the diagonalization algorithm. Then, the paper introduces a new method based on the time-frequency representations of the sources. They are assumed to vary smoothly with frequency. This hypothesis of the continuity of the time variation of the source energy is exploited on a sliding frequency bandwidth. It allows us to detect the remaining frequency permutation jumps. The method is compared with other approaches and results on real world recordings demonstrate superior performances of the proposed algorithm.

Blind Separation of rotating machine signals using Penalized Mutual Information criterion and Minimal Distortion Principle

The Blind Separation problem of convolutive mixtures is addressed in this paper. We have developed a new algorithm based on a penalized mutual information criterion recently introduced in [El Rhabi et al., A penalized mutual information criterion for blind separation of convolutive mixtures, Signal Processing 84 (2004) 1979–1984] and which also allows to choose an optimal separator among an infinite number of valid separators that can extract the source signals in a certain sense according to the Minimal Distortion Principle. So, the minimisation of this criterion is easily done using a direct gradient approach without constraint on the displacements. Thus, our approach allows to restore directly the contribution of the sources to the sensor signals without post-processing as it is usually done. Finally, we illustrate the performances of our algorithm through simulations and on real rotating machine vibration signals.

A blind source separation framework for detecting CPM sources mixed by a convolutive MIMO filter

This paper deals with blind separation of convolutive mixtures of continuous phase modulated (CPM) sources. The main difficulty lies in the fact that CPM sources are non-linear (and hence non i.i.d.) sources. The problem is addressed through the general formulation of blind source separation (BSS). The separation method consists in iterative constrained optimizations of criteria depending on the fourth-order statistics. We prove the validity of the considered contrast functions for the extraction of one source. A local study then allows us to show that the optimization is free of spurious local maxima at each step and that it is possible to alleviate the error accumulation problem by using an unconstrained post-optimization technique. After separation is achieved, the emitted symbols are estimated, based on recent results concerning CPM equalization. Finally, simulations illustrate the validity of the method.