Separation Of Convolutive Mixtures Research Articles

Independent vector analysis: Model, applications, challenges

This paper overviews an appealing unsupervised learning method named independent vector analysis (IVA) for its promising applications, such as in audio/speech signal separation, medical signal processing, remote sensing, video/image processing, wireless communication processing, and so on. As a useful data-driven technique in blind source separation (BSS) field, IVA has played an increasingly vital role in dealing with the problems of convolutive mixture separation, multivariate latent variable analysis and multivariate data fusion. IVA extends the conventional independent component analysis (ICA) to multidimensional components, which can result in more available information utilization. Compared with ICA mechanism, IVA is not only to utilize the statistical independence of multivariate signals but also the statistical inner dependency of each multivariate signal. With this generalization, IVA can manipulate some prominent ill-pose issues faced in sensor receiving models and has the advantage to overcome the inherent random permutation ambiguity problem in joint BSS. Motivated by the flexible and versatile technology superiorities of IVA, this paper concentrates on reviewing the IVA model in details, associated methods briefly, and its potential applications as well as prospects. Moreover, some significant open problems about IVA challenges are also discussed in this paper.

A Unifying View on Blind Source Separation of Convolutive Mixtures Based on Independent Component Analysis

In many daily-life scenarios, acoustic sources recorded in an enclosure can only be observed with other interfering sources. Hence, convolutive Blind Source Separation (BSS) is a central problem in audio signal processing. Methods based on Independent Component Analysis (ICA) are especially important in this field as they require only few and weak assumptions and allow for blindness regarding the original source signals and the acoustic propagation path. Most of the currently used algorithms belong to one of the following three families: Frequency Domain ICA (FD-ICA), Independent Vector Analysis (IVA), and TRIple- N Independent component analysis for CONvolutive mixtures (TRINICON). While the relation between ICA, FD-ICA and IVA becomes apparent due to their construction, the relation to TRINICON is not well established yet. This paper fills this gap by providing an in-depth treatment of the common building blocks of these algorithms and their differences, and thus provides a common framework for all considered algorithms.

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.

Energy Correlation Permutation Algorithm of Frequency-Domain Blind Source Separation Based on Frequency Bins Correction

Although blind source separation of convolutive mixtures can be efficiently solved in the frequency domain, the problem of permutation ambiguity must be solved. Thus, this paper proposes an improved permutation algorithm. Firstly, the improved algorithm uses energy correlation of the separated signal to sort the signals of each frequency bin. Then, the reliability of the sorting of the signals on the frequency bin will be judged according to the threshold. The unreliable frequency bins will be corrected in time so that we can obtain the separated signal accurately, eventually. This algorithm effectively reduces sorting errors and error propagation, thereby improving the separation effect. BSS experiments are performed on the voice signals and radar signals under different convolutive mixing models. The simulation results show that the improved algorithm has better separation performance and higher robustness than the traditional permutation algorithms, which is reflected by the increasing signal to interference ratio of separated signals.

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).

A Permutation Algorithm of Frequency-Domain Blind Source Separation Based on Influence Weights

In the frequency domain, convolutive mixes with blind source separation can be successfully resolved. But the permutation issue in frequency-domain blind source separation needs to be resolved. We investigated the impact of frequency space and separation performance at each frequency bin on the amplitude correlation permutation algorithm with the goal of addressing the permutation ambiguity problem in frequency-domain blind source separation of convolutive mixtures, and we proposed an enhanced permutation algorithm. The improved algorithm uses spacing influence weight and performance influence weight to control the influence of the frequency bins sorted in the neighborhood on the frequency bins unsorted. Experiments have shown that the two influence weights are effective. Finally, blind source separation experiments are performed on the speech signals under the two convolutive mixing models and the simulated room mixing model. According to experiments, the increased signal to interference plus noise ratio of separated signals demonstrates that the improved algorithm outperforms the amplitude correlation permutation algorithm in terms of separation performance and robustness.

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.

Accelerated 3D blind separation of convolved mixtures based on the fast iterative shrinkage thresholding algorithm for adaptive multiple subtraction

After multiple prediction, adaptive multiple subtraction is essential for the success of multiple removal. The 3D blind separation of convolved mixtures (3D BSCM) method, which is effective in conducting adaptive multiple subtraction, needs to solve an optimization problem containing L1-norm minimization constraints on primaries by the iterative reweighted least-squares (IRLS) algorithm. The 3D BSCM method can better separate primaries and multiples than the 1D/2D BSCM method and the method with energy minimization constraints on primaries. However, the 3D BSCM method has high computational cost because the IRLS algorithm achieves nonquadratic optimization with an LS optimization problem solved in each iteration. In general, it is good to have a faster 3D BSCM method. To improve the adaptability of field data processing, the fast iterative shrinkage thresholding algorithm (FISTA) is introduced into the 3D BSCM method. The proximity operator of FISTA can solve the L1-norm minimization problem efficiently. We demonstrate that our FISTA-based 3D BSCM method achieves similar accuracy of estimating primaries as that of the reference IRLS-based 3D BSCM method. Furthermore, our FISTA-based 3D BSCM method reduces computation time by approximately 60% compared with the reference IRLS-based 3D BSCM method in the synthetic and field data examples.

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.

A Contrast Function Based on Generalized Divergences for Solving the Permutation Problem in Convolved Speech Mixtures

In this paper, we propose a method for solving the permutation problem that is inherent in the separation of convolved mixtures of speech signals in the time-frequency domain. The proposed method obtains the solution through maximization of a contrast function that exploits the similarity of the temporal envelope of the speech spectrum. For this purpose, the contrast calculation uses a global measure of similarity based on the recently developed family of generalized Alpha-Beta divergences, which depend on two tuning parameters, alpha and beta. This parameterization is exploited to best measure the similarity of the speech spectrum and to obtain solutions that are robust against noise and outliers. The ability of this contrast function to solve the permutation problem is supported by a theoretical study that shows that for a simple time-frequency speech model, the contrast value reaches its maximum when the estimated components are properly aligned. Several performance studies demonstrate that the proposed method maintains a high level of permutation correction accuracy in a wide variety of acoustic environments. Moreover, it produces better results than other state-of-the-art methods for solving permutations in highly reverberant environments.

A Convolutive Bounded Component Analysis Framework for Potentially Nonstationary Independent and/or Dependent Sources

Bounded Component Analysis (BCA) is a recent framework which enables development of methods for the separation of dependent as well as independent sources from their mixtures. This paper extends a recent geometric BCA approach introduced for the instantaneous mixing problem to the convolutive mixing problem. The paper proposes novel deterministic convolutive BCA frameworks for the blind source extraction and blind source separation of convolutive mixtures of sources which allows the sources to be potentially nonstationary. The global maximizers of the proposed deterministic BCA optimization settings are proved to be perfect separators. The paper also illustrates that the iterative algorithms corresponding to these frameworks are capable of extracting/separating convolutive mixtures of not only independent sources but also dependent (even correlated) sources in both component (space) and sample (time) dimensions through simulations based on a Copula distributed source system. In addition, even when the sources are independent, it is shown that the proposed BCA approach have the potential to provide improvement in separation performance especially for short data records based on the setups involving convolutive mixtures of digital communication sources.

Adaptive multiple subtraction based on 3D blind separation of convolved mixtures

Multiple removal is one of the important preprocessing steps in a seismic data processing sequence. For an accurate multiple prediction, a full 3D method is required. However, the application of such methods is often limited by practical and economic constraints. Therefore, in practical situations, 2D prediction methods are used, such as 2D surface-related multiple elimination. However, the resulting predicted multiples may have significant temporal shift, spatial mismatch, and amplitude inconsistency, compared with true 3D multiples. Adaptive multiple subtraction based on 2D blind separation of convolved mixtures (BSCM) has been proposed to estimate the 2D matching filter in a single gather. To improve the flexibility of the adaptive multiple subtraction for the inconsistencies between the 2D predicted multiples and true 3D multiples, we evaluated the adaptive multiple subtraction as a problem of 3D BSCM. In the proposed method, the predicted multiples were modeled as the convolution of the true multiples with a 3D kernel, whose third dimension is in the gather direction. By maximizing the non-Gaussianity of the estimated primaries, the iterative reweighted least-squares algorithm was exploited to obtain the 3D matching filter, which is the inverse of the 3D kernel. To avoid the possible overfitting problem introduced by the 3D matching filter, the proposed method fit several seismic gathers using one 3D matching filter. In addition, by using the non-Gaussian maximization criterion, the proposed method alleviated the orthogonality assumption used by the least-squares subtraction method. Furthermore, the proposed method can eliminate the temporal and spatial mismatches between the 2D predicted multiples and true 3D multiples better than the 2D BSCM subtraction method. Tests on synthetic and field data sets demonstrated the effectiveness of the 3D BSCM subtraction method.

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 Speech Separation in the Frequency Domain Using Assignment Problem Approach

In this paper, we propose a method for blind speech separation of convolutive mixtures in the frequency domain. The main difficulty in a frequency approach is the so-called permutation problem. In the proposed method, we use the Assignment Problem (AP) approach to solve permuation ambiguity in the frequency domain. In our work, we apply three different algorithms including Hugarian, Jonker-Volgenant and Bertsekas’s Auction to solve the AP to find the optimal solution. Computer simulation experiments are presented to illustrate the proposed method.

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.

Automatic detection of long-period events at Campi Flegrei Caldera (Italy)

[1] We propose a novel approach to analyze continuous seismic signal and separate the sources from background noise. A specific application to the seismicity recorded at Campi Flegrei Caldera during the 2006 ground uplift is presented. The fundamental objective is to improve the standard procedures of picking the emergent onset arrivals of the seismic signals, often buried in the high-level ambient noise, in order to obtain an appropriate catalogue for monitoring the activity of this densely populated volcanic area. This is particularly useful in order to estimate the release of the seismic energy and to put constraints on the source dynamics. An Independent Component Analysis based approach for the Blind Source Separation of convolutive mixtures is adopted to obtain a clear separation of Long Period events from the ambient noise. The approach presents good performance and it is suitable for real time implementation in seismic monitoring. Its application to the continuous seismic signal recorded at Campi Flegrei has allowed the extraction of high-quality waveforms, considerably improving the detection of low-energy events.

Blind Source Separation of Convolutive Mixtures by Using Time-Delayed Statistics and Exact Diagonalization

The convolutive blind source separation (BSS) problem has been received much more attentions in recent years. This paper investigates a convolutive BSS algorithm via employing the time-delayed second-order statistics information and exact diagonalization without any a priori knowledge on the mixtures. This decorrelated second-order statistics and its multi-sample delayed copies, which form two positive-definite symmetry matrices, are obtained from whitened mixtures. By using a set of transforms such as Cholesky decomposition and singular value decomposition (SVD) to these two matrices, a unitary matrix is obtained and utilized to diagonalize them exactly. It attributes the estimates of source signals to this matrix. The similarity between the estimated and original signals is quantified by calculating their correlation coefficients (CC). For the mixtures of speech and noise, ItakuraSaito distance (ISD) is applied to measure the intelligibility of estimated speech signals. Better performance of the investigated algorithm is demonstrated in experimental results compared with the previous algorithm.

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.