Blind Separation Of Instantaneous Mixtures Research Articles

Blind Separation of Instantaneous Mixtures of Independent/Dependent Sources

Blind Source Separation (BSS) has always been an active research field within the signal processing community; it is used to reconstruct primary source signals from their observed mixtures. Independent Component Analysis has been and is still used to solve the BSS problem; however, it is based on the mutual independence of the original source signals. In this paper, we propose to use Copulas to model the dependency structure between these signals, enabling the separation of dependent source components; we also deploy $$\alpha $$ -divergence as our cost function to minimize, considering its superiority to handle noisy data as well as its ability to converge faster. We test our approach for various values of alpha and give a comparative study between the proposed methodology and other existing methods; this approach exhibited a higher quality performance and accuracy, especially when the value of $$\alpha $$ is equal to $$\frac{1}{2}$$ , which is equivalent to the Hellinger divergence.

A novel blind deconvolution algorithm using single frequency bin

Former frequency-domain blind devolution algorithms need to consider a large number of frequency bins and recover the sources in different orders and with different amplitudes in each frequency bin, so they suffer from permutation and amplitude indeterminacy troubles. Based on sliding discrete Fourier transform, the presented deconvolution algorithm can directly recover time-domain sources from frequency-domain convolutive model using single frequency bin. It only needs to execute blind separation of instantaneous mixture once there are no permutation and amplitude indeterminacy troubles. Compared with former algorithms, the algorithm greatly reduces the computation cost as only one frequency bin is considered. Its good and robust performance is demonstrated by simulations when the signal-to-noise-ratio is high.

Nonorthogonal Joint Diagonalization/Zero Diagonalization for Source Separation Based on Time-Frequency Distributions

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> This paper deals with the blind separation of instantaneous mixtures of source signals using time-frequency distributions (TFDs). We propose iterative algorithms to perform the nonorthogonal zero diagonalization and/or joint diagonalization of given sets of matrices. As an application, we show that the source separation can be realized by applying one of these algorithms to a set of spatial quadratic TFD matrices corresponding only to the so-called cross-source terms and/or to the so-called autosource terms. The determination of the above matrices to be jointly decomposed requires first an automatic selection procedure of useful time-frequency points. Regarding this last point, we also propose a new selection procedure and a modification of an existing one and provide a comparison with other existing ones. The nonorthogonal joint diagonalization and/or zero diagonalization algorithm's main advantage is to not require (in the blind source separation context) a prewhitening stage, which allows them to work even with a class of correlated signals and provides generally improved separation performance. Finally, an analytical example and computer simulations are provided in order to illustrate the effectiveness of the proposed approach and to compare it with classical ones. </para>

Simultaneous Blind Separation of Instantaneous Mixtures With Arbitrary Rank

This paper presents a gradient-based method for simultaneous blind separation of arbitrarily linearly mixed source signals. We consider the regular case (i.e., the mixing matrix has full column rank) as well as the ill-conditioned case (i.e., the mixing matrix does not have full column rank). We provide one necessary and sufficient condition for the identifiability of simultaneous blind separation. According to our identifiability condition and the existing general identifiability condition, all source signals are separated into two categories: separable single sources and inseparable mixtures of several single sources. A sufficient condition is also derived for the existence of optimal partition of the mixing matrix which leads to a unique maximum set of separations. One sufficient condition is proved to show that each maximum partition of the mixing matrix corresponds to a unique class of separated signals and as a result we can determine the number of maximum partitions from the classes of outputs under different separation matrices. For sub-Gaussian or super-Gaussian source signals, a cost function based on fourth-order cumulants is introduced to simultaneously separate all separable single sources and all inseparable mixtures. By minimizing the cost function, a gradient-based method is developed. Finally, simulation results show the effectiveness of the present method

A Generalized Contrast Function and Stability Analysis for Overdetermined Blind Separation of Instantaneous Mixtures

In this letter, the problem of blind separation of n independent sources from their m linear instantaneous mixtures is considered. First, a generalized contrast function is defined as a valuable extension of the existing classical and nonsymmetrical contrast functions. It is applicable to the overdetermined blind separation (m &gt; n) with an unknown number of sources, because not only independent components but also redundant ones are allowed in the outputs of a separation system. Second, a natural gradient learning algorithm developed primarily for the complete case (m = n) is shown to work as well with an n × m or m × m separating matrix, for each optimizes a certain mutual information contrast function. Finally, we present stability analysis for a newly proposed generalized orthogonal natural gradient algorithm (which can perform the overdetermined blind separation when n is unknown), obtaining an expectable result that its local stability conditions are slightly stricter than those of the conventional natural gradient algorithm using an invertible mixing matrix (m = n).

A Generalized Contrast Function and Stability Analysis for Overdetermined Blind Separation of Instantaneous Mixtures

In this letter, the problem of blind separation of n independent sources from their m linear instantaneous mixtures is considered. First, a generalized contrast function is defined as a valuable extension of the existing classical and nonsymmetrical contrast functions. It is applicable to the overdetermined blind separation (m > n) with an unknown number of sources, because not only independent components but also redundant ones are allowed in the outputs of a separation system. Second, a natural gradient learning algorithm developed primarily for the complete case (m = n) is shown to work as well with an n × m or m × m separating matrix, for each optimizes a certain mutual information contrast function. Finally, we present stability analysis for a newly proposed generalized orthogonal natural gradient algorithm (which can perform the overdetermined blind separation when n is unknown), obtaining an expectable result that its local stability conditions are slightly stricter than those of the conventional natural gradient algorithm using an invertible mixing matrix (m = n).

Blind separation of instantaneous mixture of sources via the Gaussian mutual information criterion

A method for blind separation of an instantaneous mixture of colored sources is proposed. It is based on the minimization of the Gaussian mutual information criterion, leading to a second-order procedure, which amounts to jointly approximately diagonalizing a set of estimated spectral density matrices. An efficient algorithm for this purpose is described. It is shown that separation is achievable (up to a scaling and a permutation) if there is no pair of sources with proportional spectral densities. Results on the asymptotic performance of the procedure are derived and some simulation are performed for finite samples, showing good agreement with the theoretical findings. It is seen that nearly optimal performance can be attained by jointly approximately diagonalizing only a few spectral matrices.

Blind separation of instantaneous mixtures of nonstationary sources

Most source separation algorithms are based on a model of stationary sources. However, it is a simple matter to take advantage of possible nonstationarities of the sources to achieve separation. This paper develops novel approaches in this direction based on the principles of maximum likelihood and minimum mutual information. These principles are exploited by efficient algorithms in both the off-line case (via a new joint diagonalization procedure) and in the on-line case (via a Newton-like procedure). Some experiments showing the good performance of our algorithms and evidencing an interesting feature of our methods are presented: their ability to achieve a kind of super-efficiency. The paper concludes with a discussion contrasting separating methods for non-Gaussian and nonstationary models and emphasizing that, as a matter of fact, "what makes the algorithms work" is-strictly speaking-not the nonstationarity itself but rather the property that each realization of the source signals has a time-varying envelope.

Blind separation of instantaneous mixture of sources based on order statistics

In this paper, we introduce a novel procedure for separating an instantaneous mixture of sources based on order statistics. The method is derived in a general context of independence component analysis, using a contrast function defined in term of the Kullback-Leibler divergence or of the mutual information. We introduce a discretized form of this contrast permitting its easy estimation through order statistics. We show that the local contrast property is preserved and derive a global contrast, exploiting only the information of the support of the distribution (in case this support is finite). Some simulations are given, illustrating the good performance of the method.

Blind separation of BPSK sources with residual carriers

Blind separation of instantaneous mixtures of binary sources with equal carrier frequencies has been studied before. For independent sources, it may be reasonable to assume that their carrier frequencies are not exactly identical, so that a residual carrier is present after demodulation to baseband. We show how this can be used to separate the sources. If the receiving antenna array is centro-symmetric and there is no multipath, then the performance of the algorithm can be significantly improved.

Blind separation of instantaneous mixture of sources via an independent component analysis

In this paper, we introduce a procedure for separating a multivariate distribution into nearly independent components based on minimizing a criterion defined in terms of the Kullback-Leibner distance. By replacing the unknown density with a kernel estimate, we derive useful forms of this criterion when only a sample from that distribution is available. We also compute the gradient and Hessian of our criteria for use in an iterative minimization. Setting this gradient to zero yields a set of separating functions similar to the ones considered in the source separation problem, except that here, these functions are adapted to the observed data. Finally, some simulations are given, illustrating the good performance of the method.