Source separation consists in recovering a set of independent signals when only mixtures with unknown coefficients are observed. This paper introduces a class of adaptive algorithms for source separation which implements an adaptive version of equivariant estimation and is henceforth called EASI (Equivariant Adaptive Separation via Independence) . The EASI algorithms are based on the idea of serial updating: this specific form of matrix updates systematically yields algorithms with a simple, parallelizable structure, for both real and complex mixtures. Most importantly, the performance of an EASI algorithm does not depend on the mixing matrix. In particular, convergence rates, stability conditions and interference rejection levels depend only on the (normalized) distributions of the source signals. Close form expressions of these quantities are given via an asymptotic performance analysis. This is completed by some numerical experiments illustrating the effectiveness of the proposed ap...

Blind identification of spatial mixtures allows an array of sensors to implement source separation when the array manifold is unknown. A family of 4th-order cumulant-based criteria for blind source separation is introduced. These criteria involve a set of cumulant matrices, whose joint diagonalization is equivalent to criterion optimization. An efficient algorithm is described to this effect. Simulations on both real and synthetic signals show that source separation is achieved even at small sample size. 1 Introduction The problem of blind separation of sources is a typical HOS issue, since it amounts to identifying a linear system whose only output is observed. While much attention has been paid to the identification of convolutional mixtures, blind source separation concerns itself only with `spatial' mixtures. It is naturally targeted to narrow band array processing. Consider an array of m sensors receiving signals from n narrow band sources. The array output denoted x(t) is a m ...

. This communication deals with the source separation problem which consists in the separation of a noisy mixture of independent sources without a priori knowledge of the mixture coefficients. In this paper, we consider the maximum likelihood (ML) approach for discrete source signals with known probability distributions. An important feature of the ML approach in Gaussian noise is that the covariance matrix of the additive noise can be treated as a parameter. Hence, it is not necessary to know or to model the spatial structure of the noise. Another striking feature offered in the case of discrete sources is that, under mild assumptions, it is possible to separate more sources than sensors. In this paper, we consider maximization of the likelihood via the Expectation-Maximization (EM) algorithm. 1. Introduction When an array of m sensors samples the fields radiated by n narrow band sources its output is classically modeled as an instantaneous spatial mixture of a random vector made of ...

A measure of temporal predictability is defined and used to separate linear mixtures of signals. Given any set of statistically independent source signals, it is conjectured here that a linear mixture of those signals has the following property: the temporal predictability of any signal mixture is less than (or equal to) that of any of its component source signals. It is shown that this property can be used to recover source signals from a set of linear mixtures of those signals by finding an un-mixing matrix that maximizes a measure of temporal predictability for each recovered signal. This matrix is obtained as the solution to a generalized eigenvalue problem; such problems have scaling characteristics of O(N 3), where N is the number of signal mixtures. In contrast to independent component analysis, the temporal predictability method requires minimal assumptions regarding the probability density functions of source signals. It is demonstrated that the method can separate signal mixtures in which each mixture is a linear combination of source signals with supergaussian, subgaussian, and gaussian probability density functions and on mixtures of voices and music.

this article, we propose a simple batch algorithm that guarantees blind extraction of any source signal s i that satisfies for the specific time delay # i the following relations: E[s i (k)s i (k E[s i (k)s j (k i j. (2.1) Because we want to extract only a desired source signal, we can use a simple processing unit described as y(k) x(k), where y(k) is the output signal (which estimates the specific source signal s i ), k is the sampling number, andw is the weight vector. For the purpose of developing the algorithm, let us first define the following error, #(k) y(k) by(k p), (2.2) where b is a coefficient of a simple FIR filter with single delay z -pT s , where T s is the sampling period (assumed to be one)

In blind array processing, the array manifold is unknown but, under the signal independence assumption, the signal parameters can be estimated by resorting to higher-order information. We consider the 4th-order cumulant tensor and show that sample cumulant enhancement based on rank and symmetry properties yields cumulant estimates with the exact theoretical structure. Any identification procedure based on enhanced cumulants is then equivalent to cumulant matching, bypassing the need for initialization and optimization. 1. INTRODUCTION This paper deals with a linear data model where a m- dimensional complex vector x(t) is assumed to be the superposition of n linear components, possibly corrupted by additive noise. An observation can then be written as: x(t) = X p=1;n sp(t) ap +N(t) (1) where each sp(t) is a complex stationary scalar process, each ap is a deterministic m21 vector, and the m21 vector N(t) represents additive noise. This is the standard model in narrow band array p...

Blind separation of sources consists in recovering a set of statistically independent signals whose only instantaneous mixtures are observed. Such mixtures occur in narrow band array data which can then be processed without knowing the array manifold (blindness). This paper introduces a new source separation technique exploiting the possible time coherence of the source signals. In contrast to other previously reported techniques, the proposed approach relies only on second-order statistics, being based on a `joint diagonalization' of correlation matrices. The effectiveness of the method in difficult contexts is illustrated by numerical simulations. 1 Introduction L'approche dite de s'eparation aveugle de sources consiste `a estimer les signaux sources sans information a priori sur la forme du front d'onde ou la g'eom'etrie de l'antenne. Ce probl`eme a d'ej`a fait l'objet de nombreux travaux qui n'exploitent que la structure spatiale instantan'ee du processus en utilisant les statisti...

This communication deals with the problem of blind separation of an instantaneous linear mixture of mutually uncorrelated sources. A second order source separation technique exploiting the time coherence of the source signals is considered. Asymptotic performance analysis of the proposed method is performed. Several numerical simulations are presented to demonstrate the effectiveness of the proposed method and to validate the theoretical expression of the asymptotic performance index. 1. INTRODUCTION When an array of n sensors samples the fields radiated by m narrow band sources its output is classically modeled as a n-dimensional multivariate process, whose components consist in an (unknown) instantaneous linear mixture of the m source signals, corrupted by an additive noise. Source separation may be obtained by first identifying the directional vectors associated to each source, and then by projecting the array signal onto the estimated vectors. This is a standard program in arra...

this paper are two: rst an ecient (linear) method for estimating the score function of a source. This can be readily plugged in the already available maximum likelihood algorithms that use the relative or natural gradient. Second, a practical method for ICA and projection pursuit that has linear complexity (fast), is robust to outliers, needs no additional user-dependent parameters or safeguards for convergence, and exhibits good global convergence characteristics. We show the validity of our method through synthetic and real experiments on ICA and projection pursuit. 2 The maximum likelihood setting

Independent component analysis (ICA) and projection pursuit (PP) are two related techniques for separating mixtures of source signals into their individual components. These rapidly evolving techniques are currently finding applications in speech separation, ERP, EEG, fMRI, and low-level vision. Their power resides in the simple and realistic assumption that different physical processes tend to generate statistically independent signals. We provide an account that is intended as an informal introduction, as well as a mathematical and geometric description of the methods. 1 Introduction Independent component analysis (ICA) [Jutten and Herault, 1988] and projection pursuit (PP) [Friedman, 1987] are methods for recovering underlying source signals from linear mixtures of these signals. This rather terse description does not capture the deep connection between ICA/PP and the fundamental nature of the physical world. In the following pages, we hope to establish, not only that ICA/PP are po...