Convolutive Blind Source Separation Research Articles

Independent vector analysis for convolutive blind noncircular source separation

Independent vector analysis (IVA), an extension of independent component analysis (ICA) from univariate components to multivariate components, is a method to tackle blind source separation (BSS) in frequency domain. IVA utilizes both the statistical independence among multivariate signals and the statistical inner dependency of each multivariate signal. However, so far there is no research on IVA for convolutive mixtures of noncircular sources. In this study, we focus on this problem and propose noncircular independent vector analysis (nc-IVA) algorithm, by deriving a new fixed-point algorithm that uses the information of pseudo-covariance matrix in each frequency bin. This modification provides more widely application scenarios with noncircular sources. Simulations demonstrate the effectiveness of our proposed method.

Post-filtering algorithm for cross-talk cancellation in blind source separation outputs

In this study, cross-talk cancellation in convolutive blind source separation (BSS) is investigated using a new post-processing algorithm. In this algorithm, exclusive activity periods (EAPs) are used to model cross-talks in which only one BSS output signal is assumed to be active. Inactive intervals of each EAP are used to estimate the cross-talk leaked from each active signal. Then, the estimated cross-talk is subtracted from BSS outputs. Simulation results show that the proposed algorithm successfully suppresses the crosstalk by improving the signal-to-interference ratio (SIR) and signal-to-distortion ratio (SDR) of BSS outputs about 12 and 5 dB, respectively.

Use of bimodal coherence to resolve the permutation problem in convolutive BSS

Recent studies show that facial information contained in visual speech can be helpful for the performance enhancement of audio-only blind source separation (BSS) algorithms. Such information is exploited through the statistical characterization of the coherence between the audio and visual speech using, e.g., a Gaussian mixture model (GMM). In this paper, we present three contributions. With the synchronized features, we propose an adapted expectation maximization (AEM) algorithm to model the audio–visual coherence in the off-line training process. To improve the accuracy of this coherence model, we use a frame selection scheme to discard nonstationary features. Then with the coherence maximization technique, we develop a new sorting method to solve the permutation problem in the frequency domain. We test our algorithm on a multimodal speech database composed of different combinations of vowels and consonants. The experimental results show that our proposed algorithm outperforms traditional audio-only BSS, which confirms the benefit of using visual speech to assist in separation of the audio.

Evaluation of Blind Source Separation for different algorithms based on second order statistics and different spatial configurations of directional microphones

The present study is concerned with the convolutive Blind Source Separation (BSS) of sound sources that leads to a significant speech intelligibility enhancement. Two experiments were conducted. In the first experiment two different algorithms of convolutive BSS were compared. Both methods are based on second order statistics since such approach is simple and gives satisfactory performance. The data resulted from this experiment suggested that with different approaches, different speech intelligibility improvement could be obtained. In the second experiment the influence of the spatial configuration of the cardioid microphones on the BSS performance was measured. It was revealed that the best separation for a considered spatial configuration can be obtained when microphones are directed alternately.

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.

A Region-Growing Permutation Alignment Approach in Frequency-Domain Blind Source Separation of Speech Mixtures

The convolutive blind source separation (BSS) problem can be solved efficiently in the frequency domain, where instantaneous BSS is performed separately in each frequency bin. However, the permutation ambiguity in each frequency bin should be resolved so that the separated frequency components from the same source are grouped together. To solve the permutation problem, this paper presents a new alignment method based on an inter-frequency dependence measure: the powers of separated signals. Bin-wise permutation alignment is applied first across all frequency bins, using the correlation of separated signal powers; then the full frequency band is partitioned into small regions based on the bin-wise permutation alignment result. Finally, region-wise permutation alignment is performed in a region-growing manner. The region-wise permutation correction scheme minimizes the spreading of the misalignment at isolated frequency bins to others, hence to improve permutation alignment. Experiment results in simulated and real environments verify the effectiveness of the proposed method. Analysis demonstrates that the proposed frequency-domain BSS method is computationally efficient.

Underdetermined Convolutive Blind Source Separation via Frequency Bin-Wise Clustering and Permutation Alignment

This paper presents a blind source separation method for convolutive mixtures of speech/audio sources. The method can even be applied to an underdetermined case where there are fewer microphones than sources. The separation operation is performed in the frequency domain and consists of two stages. In the first stage, frequency-domain mixture samples are clustered into each source by an expectation-maximization (EM) algorithm. Since the clustering is performed in a frequency bin-wise manner, the permutation ambiguities of the bin-wise clustered samples should be aligned. This is solved in the second stage by using the probability on how likely each sample belongs to the assigned class. This two-stage structure makes it possible to attain a good separation even under reverberant conditions. Experimental results for separating four speech signals with three microphones under reverberant conditions show the superiority of the new method over existing methods. We also report separation results for a benchmark data set and live recordings of speech mixtures.

Convolutive BSS of Short Mixtures by ICA Recursively Regularized Across Frequencies

This paper proposes a new method of frequency-domain blind source separation (FD-BSS), able to separate acoustic sources in challenging conditions. In frequency-domain BSS, the time-domain signals are transformed into time-frequency series and the separation is generally performed by applying independent component analysis (ICA) at each frequency envelope. When short signals are observed and long demixing filters are required, the number of time observations for each frequency is limited and the variance of the ICA estimator increases due to the intrinsic statistical bias. Furthermore, common methods used to solve the permutation problem fail, especially with sources recorded under highly reverberant conditions. We propose a recursively regularized implementation of the ICA (RR-ICA) that overcomes the mentioned problem by exploiting two types of deterministic knowledge: 1) continuity of the demixing matrix across frequencies; 2) continuity of the time-activity of the sources. The recursive regularization propagates the statistics of the sources across frequencies reducing the effect of statistical bias and the occurrence of permutations. Experimental results on real-data show that the algorithm can successfully perform a fast separation of short signals (e.g., 0.5-1s), by estimating long demixing filters to deal with highly reverberant environments (e.g., ms).

Blind adaptive wideband beamforming for circular arrays based on phase mode transformation

To recover the desired signals without the knowledge of its direction of arrival for a wideband array system is a difficult problem and a direct application of the convolutive blind source separation (BSS) algorithms will not work even for a small number of sensors. In this paper, a novel approach is proposed to solve this blind adaptive wideband beamforming problem based on a uniform circular array. The received array signals are first transformed into different phase modes and each phase mode output is then processed by a filter to achieve a frequency independent response. As a result, a set of instantaneous mixtures of the original source signals is obtained and the original wideband beamforming problem can be readily solved using the standard instantaneous BSS algorithms.

Glimpsing IVA: A Framework for Overcomplete/Complete/Undercomplete Convolutive Source Separation

Independent vector analysis (IVA) is a method for separating convolutedly mixed signals that significantly reduces the occurrence of the well-known permutation problem in frequency domain blind source separation (BSS). In this paper, we develop a novel IVA-based unifying framework for overcomplete/complete/undercomplete convolutive noisy BSS. We show that in order for the sources to be separable in the frequency domain, they must have a temporal dynamic structure. We exploit a common form of dynamics, especially present in speech, wherein the signals have silence periods intermittently, hence varying the set of active sources with time. This feature is extremely useful in dealing with overcomplete situations. An approach using hidden Markov models (HMMs) is proposed that takes advantage of different combinations of silence gaps of the source signals at each time period. This enables the algorithm to “glimpse” or listen in the gaps, hence compensating for the global degeneracy by allowing it to learn the mixing matrices at periods where it is locally less degenerate. The same glimpsing strategy can be employed to the complete/undercomplete case as well. Moreover, additive noise is considered in our model. Real and simulated experiments were carried out for overcomplete convoluted mixtures of speech signals yielding improved separation results compared to a sparsity-based robust time-frequency masking method. Signal-to-disturbance ratio (SDR) and machine intelligibility of a speech recognizer was used to evaluate their performances. Experiments were also conducted for the classical complete setting using the proposed algorithm and compared with standard IVA showing that the results compare favorably.

Convolutive blind source separation by efficient blind deconvolution and minimal filter distortion

Convolutive blind source separation (BSS) usually encounters two difficulties—the filter indeterminacy in the recovered sources and the relatively high computational load. In this paper we propose an efficient method to convolutive BSS, by dealing with these two issues. It consists of two stages, namely, multichannel blind deconvolution (MBD) and learning the post-filters with the minimum filter distortion (MFD) principle. We present a computationally efficient approach to MBD in the first stage: a vector autoregression (VAR) model is first fitted to the data, admitting a closed-form solution and giving temporally independent errors; traditional independent component analysis (ICA) is then applied to these errors to produce the MBD results. In the second stage, the least linear reconstruction error (LLRE) constraint of the separation system, which was previously used to regularize the solutions to nonlinear ICA, enforces a MFD principle of the estimated mixing system for convolutive BSS. One can then easily learn the post-filters to preserve the temporal structure of the sources. We show that with this principle, each recovered source is approximately the principal component of the contributions of this source to all observations. Experimental results on both synthetic data and real room recordings show the good performance of this method.

Two-channel speech denoising through minimum tracking

A blind two-channel interference reduction algorithm to suppress localised interferers in reverberant environments is presented. The algorithm requires neither knowledge of source positions nor a speech-free noise reference. The goal is to estimate the speech signal as observed at one of the microphones, without any additional filtering effects that are typical in convolutive blind source separation.

An Improved Method of Permutation Correction in Convolutive Blind Source Separation

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Underdetermined Convolutive Blind Source Separation via Time–Frequency Masking

In this paper, we consider the problem of separation of unknown number of sources from their underdetermined convolutive mixtures via time-frequency (TF) masking. We propose two algorithms, one for the estimation of the masks which are to be applied to the mixture in the TF domain for the separation of signals in the frequency domain, and the other for solving the permutation problem. The algorithm for mask estimation is based on the concept of angles in complex vector space. Unlike the previously reported methods, the algorithm does not require any estimation of the mixing matrix or the source positions for mask estimation. The algorithm clusters the mixture samples in the TF domain based on the Hermitian angle between the sample vector and a reference vector using the well known <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> -means or fuzzy <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</i> -means clustering algorithms. The membership functions so obtained from the clustering algorithms are directly used as the masks. The algorithm for solving the permutation problem clusters the estimated masks by using <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> -means clustering of small groups of nearby masks with overlap. The effectiveness of the algorithm in separating the sources, including collinear sources, from their underdetermined convolutive mixtures obtained in a real room environment, is demonstrated.

Visual voice activity detection with optical flow

Current voice activity detection methods generally utilise only acoustic information. Therefore they are susceptible to false classification because of the presence of other acoustic sources such as another speaker or non-stationary noise. To address this issue, the authors propose a new method of voice activity detection using solely visual information in the form of a speaker&apos;s mouth region. Such video information is not affected by the acoustic environment. Simulations show that a high percentage correct silence detection (CSD) can be obtained with a low percentage false silence detection (FSD). Comparisons with two other visual voice activity detectors show the proposed method to be consistently more accurate, and on average yields a 4% improvement in CSD. The usefulness of the method is confirmed by applying it to a previously published audio–visual convolutive blind source separation algorithm, to increase the intelligibility of a speaker.

Under-Determined Reverberant Audio Source Separation Using a Full-Rank Spatial Covariance Model

This paper addresses the modeling of reverberant recording environments in the context of under-determined convolutive blind source separation. We model the contribution of each source to all mixture channels in the time-frequency domain as a zero-mean Gaussian random variable whose covariance encodes the spatial characteristics of the source. We then consider four specific covariance models, including a full-rank unconstrained model. We derive a family of iterative expectation-maximization (EM) algorithms to estimate the parameters of each model and propose suitable procedures adapted from the state-of-the-art to initialize the parameters and to align the order of the estimated sources across all frequency bins. Experimental results over reverberant synthetic mixtures and live recordings of speech data show the effectiveness of the proposed approach.

Convolutive blind source separation based on joint block Toeplitzation and block-inner diagonalization

This paper takes a close look at the block Toeplitz structure and block-inner diagonal structure of auto correlation matrices of source signals in convolutive blind source separation (BSS) problems. The aim is to propose a one-stage time-domain algorithm for convolutive BSS by explicitly exploiting the structure in autocorrelation matrices of source signals at different time delays and inherent relations among these matrices. The main idea behind the proposed algorithm is to implement the joint block Toeplitzation and block-inner diagonalization (JBTBID) of a set of correlation matrices of the observed vector sequence such that the mixture matrix can be extracted. For this purpose, a novel tri-quadratic cost function is introduced. The important feature of this tri-quadratic contrast function enables the development of an efficient algebraic method based on triple iterations for searching the minimum point of the cost function, which is called the triply iterative algorithm (TIA). Through the cyclic minimization process in the proposed TIA, it is expected that the JBTBID is achieved. The source signals can be retrieved. Moreover, the asymptotic convergence of the proposed TIA is analyzed. Convergence performance of the TIA and the separation results are also demonstrated by simulations in comparison with some other prominent two-stage time-domain methods.

MIMO-AR System Identification and Blind Source Separation for GMM-Distributed Sources

The problem of blind source separation (BSS) and system identification for multiple-input multiple-output (MIMO) auto-regressive (AR) mixtures is addressed in this paper. Two new time-domain algorithms for system identification and BSS are proposed based on the Gaussian mixture model (GMM) for sources distribution. Both algorithms are based on the generalized expectation-maximization (GEM) method for joint estimation of the MIMO-AR model parameters and the GMM parameters of the sources. The first algorithm is derived under the assumption of unstructured input signal statistics, while the second algorithm incorporates the prior knowledge about the structure of the input signal statistics due to the statistically independent source assumption. These methods are tested via simulations using synthetic and audio signals. The system identification performances are tested by comparison between the state transition matrix estimation using the proposed algorithms and the well-known multidimensional Yule-Walker solution followed by an instantaneous BSS method. The results show that the proposed algorithms outperform the Yule-Walker based approach. The BSS performances were compared to other convolutive BSS methods. The results show that the proposed algorithms achieve higher signal-to-interference ratio (SIR) compared to the other tested methods.

An Approach for Solving the Permutation Problem of Convolutive Blind Source Separation Based on Statistical Signal Models

In this paper, we present a new algorithm for solving the permutation ambiguity in convolutive blind source separation. Transformed to the frequency domain, existing algorithms can efficiently solve the reduction of the source separation problem into independent instantaneous separation in each frequency bin. However, this independency leads to the problem of correctly aligning these single bins. The new algorithm models the frequency-domain separated signals by means of the generalized Gaussian distribution and employs the small deviation of the parameters between neighboring bins for the detection of correct permutations. The performance of the algorithm will be demonstrated on synthetic and real-world data.

Independent vector analysis using densities represented by chain-like overlapped cliques in graphical models for separation of convolutedly mixed signals

Independent vector analysis (IVA), a multivariate extension of independent component analysis, tackles the convolutedly mixed blind source separation (BSS) problem in a way to avoid the permutation problem by employing a multivariate source prior of the short-time Fourier transform (STFT) components. As the source prior in IVA, overall hyperspherical joint densities have been used, which imply that the dependence between the STFT components is invariant over bin difference. As a more effective source prior in the IVA framework, a dependence model is proposed that can be represented by chain-like overlaps of local cliques in graphical models. For convolutive BSS, the proposed method demonstrates consistently improved performance over using the overall hyperspherical joint density representation.