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 signal separation (BSS) and independent component analysis (ICA) are emerging techniques of array processing and data analysis, aiming at recovering unobserved signals or `sources' from observed mixtures (typically, the output of an array of sensors), exploiting only the assumption of mutual independence between the signals. The weakness of the assumptions makes it a powerful approach but requires to venture beyond familiar second order statistics. The objective of this paper is to review some of the approaches that have been recently developed to address this exciting problem, to show how they stem from basic principles and how they relate to each other.

Separation of sources consists in recovering a set of signals of which only instantaneous linear mixtures are observed. In many situations, no a priori information on the mixing matrix is available: the linear mixture should be `blindly' processed. This typically occurs in narrow-band array processing applications when the array manifold is unknown or distorted. This paper introduces a new source separation technique exploiting the time coherence of the source signals. In contrast to other previously reported techniques, the proposed approach relies only on stationary second-order statistics, being based on a joint diagonalization of a set of covariance matrices. Asymptotic performance analysis of this method is carried out; some numerical simulations are provided to illustrate the effectiveness of the proposed method. I. Introduction I N many situations of practical interest, one has to process multidimensional observations of the form: x(t) = y(t) + n(t) = As(t) + n(t); (1) i.e. x...

In this paper we propose two methods for separating mixtures of independent sources without any precise knowledge of their probability distribution. They are obtained by considering a maximum likelihood solution corresponding to some given distributions of the sources and relaxing this assumption afterward. The first method is specially adapted to temporally independent non Gaussian sources and is based on the use of nonlinear separating functions. The second method is specially adapted to correlated sources with distinct spectra and is based on the use of linear separating filters. A theoretical analysis of the performance of the methods has been made. A simple procedure for choosing optimally the separating functions from a given linear space of functions is proposed. Further, in the second method, a simple implementation based on the simultaneous diagonalization of two symmetric matrices is provided. Finally, some numerical and simulation results are given illustrating the performan...

This paper focuses on the equivariant nature of source separation : the unknown parameter of source separation is an invertible matrix i.e. it belongs to a multiplicative group. In this instance, inference theory calls for `equivariant' estimation. This paper discusses some consequences of equivariance with respect to implementation and performance of source separation algorithms. 1. SOURCE SEPARATION Source separation is receiving increasing attention in both signal processing and neural network literature since the seminal work of Jutten and H'erault [1]. The model of source separation is that of n statistically independent signals whose m (possibly noisy) linear combinations are observed; the problem consists in recovering the original signals from their mixture. The `blind' qualification refers to the coefficients of the mixture: no a priori information is assumed to be available about them. This feature makes the blind approach extremely versatile because it does not rely on mod...

In this paper, we present a geometrical method for solving the problem of blind separation of sources. The method assumes that sources have bounded probability density functions pdf. It is based on estimation of edges of a parallelepiped. We propose an algorithm for two mixtures of two sources, performance of which are discussed. Currently,we address the generalization of the method for more than two mixtures and two sources.