Source Separation Of Convolutive Mixtures Research Articles

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.

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 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.

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.

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.

Blind Source Separation for Convolutive Mixtures with Neural Networks

Blind Source Separation for Convolutive Mixtures with Neural Networks

Extraction of Sources of Tremor in Hand Movements of Patients With Movement Disorders

This paper proposes an efficient method to acquire sources of tremor in patients with movement disorders based on blind source separation of convolutive mixtures. The extracted sources indicated neural activities that might be generated in the central nervous system. Four patients with essential tremor were tested in a set of movement tasks. Subjects wore a data glove that measured finger movements of the hand. The experimental data were then fed to a convolutive-mixture model, which revealed sources that imbibed in them the tremor frequency components of 2--8 Hz. Time--frequency analysis of these sources might be of potential help to clinicians to devise tasks that can manifest visible tremor from patients.

A weighted general discrete fourier transform for the frequency-domain Blind Source Separation of Convolutive Mixtures

This letter deals with the frequency domain Blind Source Separation of Convolutive Mixtures (CMBSS). From the frequency representation of the “overlap and save”, a Weighted General Discrete Fourier Transform (WGDFT) is derived to replace the traditional Discrete Fourier Transform (DFT). The mixing matrix on each frequency bin could be estimated more precisely from WGDFT coefficients than from DFT coefficients, which improves separation performance. Simulation results verify the validity of WGDFT for frequency domain blind source separation of convolutive mixtures.

A frequency domain-based approach for blind MIMO system identification using second-order cyclic statistics

This article introduces a new frequency domain approach for either MIMO system identification or source separation of convolutive mixtures of cyclostationary signals. We apply the joint diagonalization algorithm to a set of cyclic spectral density matrices of the measurements to identify the mixing system at each frequency bin up to permutation and phase ambiguity matrices. An efficient algorithm to overcome the frequency-dependent permutations and to recover the phase, even for non-minimum-phase channels, based on cyclostationarity is also presented. The new approach exploits the fact that each input signal has a different and specific cyclic frequency. Simulation examples are presented to illustrate the effectiveness of this approach.

Acoustic Source Separation of Convolutive Mixtures Based on Intensity Vector Statistics

Various techniques have previously been proposed for the separation of convolutive mixtures. These techniques can be classified as stochastic, adaptive, and deterministic. Stochastic methods are computationally expensive since they require an iterative process for the calculation of the demixing filters based on a separation criterion that usually assumes that the source signals are statistically independent. Adaptive methods, such as the adaptive beamformers, also exploit signal properties in order to optimize a multichannel filter structure. However, these algorithms need initialization and time to converge. Deterministic methods, on the other hand, provide a closed-form solution based on the deterministic aspects of the problem, such as the channel characteristics and the source directions. This paper presents a technique that exploits the intensity vector statistics to achieve a nearly closed-form solution for the separation of the convolutive mixtures as recorded with a coincident microphone array. No assumptions are made on the signals, but it is assumed that the source directions are known a priori. Directivity functions based on von Mises functions are designed for beamforming depending on the circular statistics of the calculated intensity vectors. Numerical evaluation results were presented for various speech and instrument sounds and source positions in two reverberant rooms.

Blind source separation for convolutive mixtures based on the joint diagonalization of power spectral density matrices

This paper studies the problem of blind separation of convolutively mixed source signals on the basis of the joint diagonalization (JD) of power spectral density matrices (PSDMs) observed at the output of the separation system. Firstly, a general framework of JD-based blind source separation (BSS) is reviewed and summarized. Special emphasis is put on the separability conditions of sources and mixing system. Secondly, the JD-based BSS is generalized to the separation of convolutive mixtures. The definition of a time and frequency dependent characteristic matrix of sources allows us to state the conditions under which the separation of convolutive mixtures is possible. Lastly, a frequency-domain approach is proposed for convolutive mixture separation. The proposed approach exploits objective functions based on a set of PSDMs. These objective functions are defined in the frequency domain, but are jointly optimized with respect to the time-domain coefficients of the unmixing system. The local permutation ambiguity problems, which are inherent to most frequency-domain approaches, are effectively avoided with the proposed algorithm. Simulation results show that the proposed algorithm is valid for the separation of both simulated and real-word recorded convolutive mixtures.

On Blind MIMO System Identification Based on Second-Order Cyclic Statistics

This letter introduces a new frequency domain approach for either MIMO System Identification or Source Separation of convolutive mixtures in cyclostationary context. We apply the joint diagonalization algorithm to a set of cyclic spectral density matrices of the measurements to identify the mixing system at each frequency up to permutation and phase ambiguity matrices. An efficient algorithm to overcome the frequency dependent permutations and to recover the phase, even for non-minimum-phase channels, based on cyclostationarity is also presented. The new approach exploits the fact that each input has a different and specific cyclic frequency. A comparison with an existing MIMO method is proposed.

MAP-Based Underdetermined Blind Source Separation of Convolutive Mixtures by Hierarchical Clustering and -Norm Minimization

We address the problem of underdetermined BSS. While most previous approaches are designed for instantaneous mixtures, we propose a time-frequency-domain algorithm for convolutive mixtures. We adopt a two-step method based on a general maximum a posteriori (MAP) approach. In the first step, we estimate the mixing matrix based on hierarchical clustering, assuming that the source signals are suciently sparse. The algorithm works directly on the complex-valued data in the time-frequency domain and shows better convergence than algorithms based on self-organizing maps. The assumption of Laplacian priors for the source signals in the second step leads to an algorithm for estimating the source signals. It involves the l1-norm minimization of complex numbers because of the use of the time-frequency-domain approach. We compare a combinatorial approach initially designed for real numbers with a second-order cone programming (SOCP) approach designed for complex numbers. We found that although the former approach is not theoretically justified for complex numbers, its results are comparable to, or even better than, the SOCP solution. The advantage is a lower computational cost for problems with low input/output dimensions.

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.

Blind Source Separation of Convolutive Mixtures of Speech in Frequency Domain

This paper overviews a total solution for frequency-domain blind source separation (BSS) of convolutive mixtures of audio signals, especially speech. Frequency-domain BSS performs independent component analysis (ICA) in each frequency bin, and this is more efficient than time-domain BSS. We describe a sophisticated total solution for frequency-domain BSS, including permutation, scaling, circularity, and complex activation function solutions. Experimental results of 2 × 2, 3 × 3, 4 × 4, 6 × 8, and 2 × 2 (moving sources), (#sources × #microphones) in a room are promising.

Audio source separation of convolutive mixtures

The problem of separation of audio sources recorded in a real world situation is well established in modern literature. A method to solve this problem is blind source separation (BSS) using independent component analysis (ICA). The recording environment is usually modeled as convolutive. Previous research on ICA of instantaneous mixtures provided solid background for the separation of convolved mixtures. The authors revise current approaches on the subject and propose a fast frequency domain ICA framework, providing a solution for the apparent permutation problem encountered in these methods.

The fundamental limitation of frequency domain blind source separation for convolutive mixtures of speech

Despite several recent proposals to achieve blind source separation (BSS) for realistic acoustic signals, the separation performance is still not good enough. In particular, when the impulse responses are long, performance is highly limited. In this paper, we consider a two-input, two-output convolutive BSS problem. First, we show that it is not good to be constrained by the condition T>P, where T is the frame length of the DFT and P is the length of the room impulse responses. We show that there is an optimum frame size that is determined by the trade-off between maintaining the number of samples in each frequency bin to estimate statistics and covering the whole reverberation. We also clarify the reason for the poor performance of BSS in long reverberant environments, highlighting that the framework of BSS works as two sets of frequency-domain adaptive beamformers. Although BSS can reduce reverberant sounds to some extent like adaptive beamformers, they mainly remove the sounds from the jammer direction. This is the reason for the difficulty of BSS in reverberant environments.

Stability analysis of adaptive algorithms for blind source separation of convolutive mixtures

In this paper we present a stability analysis of two adaptive algorithms proposed in (Nguyen-Thi and Jutten, 1995) for blind source separation of convolutive mixtures. We demonstrate that for temporally white sources and causal mixing filters the first algorithm is not stable whereas the second is always stable provided that the step-size parameters are adequately chosen. Moreover, we show that the second algorithm exhibits isotropic convergence.