Separation Of Convolutive Mixtures Research Articles

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.

An ICA Algorithm for Separation of Convolutive Mixture of Speech Signals

An ICA Algorithm for Separation of Convolutive Mixture of Speech Signals

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.

Enhancement of speech signals separated from their convolutive mixture by FDICA algorithm

This paper presents a novel method for the enhancement of independent components of mixed speech signal segregated by the frequency domain independent component analysis (FDICA) algorithm. The enhancement algorithm proposed here is based on maximum a posteriori (MAP) estimation of the speech spectral components using generalized Gaussian distribution (GGD) function as the statistical model for the time-frequency series of speech (TFSS) signal. The proposed MAP estimator has been used and evaluated as the post-processing stage for the separation of convolutive mixture of speech signals by the fixed-point FDICA algorithm. It has been found that the combination of separation algorithm with the proposed enhancement algorithm provides better separation performance under both the reverberant and non-reverberant conditions.

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.

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.

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.

Independent component analysis applied to the removal of motion artifacts from electrocardiographic signals

Electrocardiographic (ECG) signals are affected by several kinds of artifacts that may hide vital signs of interest. In this study we apply independent component analysis (ICA) to isolate motion artifacts. Standard or instantaneous ICA, which is currently the most addressed ICA model within the context of artifact removal, is compared to two other ICA techniques. The first technique is a frequency domain approach to convolutive mixture separation. The second is based on temporally constrained ICA, which enables the estimation of only one component close to a particular reference signal. Performance indexes evaluate ECG complex enhancement and relevant heart rate errors. Our results show that both convolutive and constrained ICA implementations perform better than standard ICA, thus opening up a new field of application for these two methods. Moreover, statistical analysis reveals that constrained ICA and convolutive ICA do not significantly differ concerning heart rate estimation, even though the latter overcomes the former in ECG morphology recovery.

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.

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.

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.

Separation of convolved mixtures in frequency domain ICA

In this paper, a novel approach to solve the permutation indeterminacy in the separation of convolved mixtures in frequency domain is proposed. A fixed-point algorithm in complex domain is used to separate the signals in each frequency bin. These are obtained applying a Short Time Fourier Transform on a set of fixed frames. To solve the ambiguity of the amplitude dilation, a simple method is proposed. The permutation indeterminacy is solved using an approach based on the Hungarian algorithm that solves an Assignment Problem and an algorithm of Dynamic Programming. To obtain the distances in the Assignment Problem, a Kullback-Leibler divergence is adopted. The results of the experiments, performed using both synthetic and benchmark data, allows us to conclude that the approach presents a good performance and permits to obtain a clear separation of the signals also when they are more than two.