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...

In this paper, we analyze and extend a class of adaptive networks for secondorder blind decorrelation of instantaneous signal mixtures. Firstly, we compare the performance of the decorrelation neural network employing global knowledge of the adaptive coefficients with a similar structure whose coefficients are adapted via local output connections. Through statistical analyses, the convergence behaviors and stability bounds for the algorithms' step sizes are studied and derived. Secondly, we analyze the behaviors of locally-adaptive multilayer decorrelation networks and quantify their performances for poorly-conditioned signal mixtures. Thirdly, we derive a robust locally-adaptive network structure based on a posteriori output signals that remains stable for any step size value. Finally, we present an extension of the locally-adaptive network for linear-phase temporal and spatial whitening of multichannel signals. Simulations verify the analyses and indicate the usefulness of the locall...

Independent component analysis (ICA) is a statistical method for transforming an observed multidimensional random vector into components that are statistically as independent from each other as possible. In this paper, the linear version of the ICA problem is approached from an information-theoretic viewpoint, using Comon's framework of minimizing mutual information of the components. Using maximum entropy approximations of dioeerential entropy, we introduce a family of new contrast (objective) functions for ICA, which can also be considered 1-D projection pursuit indexes. The statistical properties of the estimators based on such contrast functions are analyzed under the assumption of the linear mixture model. It is shown how to choose optimal contrast functions according to dioeerent criteria. Novel algorithms for maximizing the contrast functions are then introduced. Hebbian-like learning rules are shown to result from gradient descent methods. Finally, in order to speed up the conv...

In this paper, we analyze and extend a class of adaptive networks for second-order blind decorrelation of instantaneous signal mixtures. Firstly, we compare the performance of the decorrelation neural network employing global knowledge of the adaptive coefficients in [27] with a similar structure whose coefficients are adapted via local output connections in [8]. Through statistical analyses, the convergence behaviors and stability bounds for the algorithms' step sizes are studied and derived. Secondly, we analyze the behaviors of locally-adaptive multilayer decorrelation networks and quantify their performances for poorly-conditioned signal mixtures. Thirdly, we derive a robust locally-adaptive network structure based on a posteriori output signals that remains stable for any step size value. Finally, we present an extension of the locally-adaptive network for linear-phase temporal and spatial whitening of multichannel signals. Simulations verify the analyses and indicate the usefulne...

Abstract { In this paper, we analyze and extend a class of adaptive networks for secondorder blind decorrelation of instantaneous signal mixtures. Firstly, we compare the performance of the decorrelation neural network employing global knowledge of the adaptive coe cients with a similar structure whose coe cients are adapted via local output connections. Through statistical analyses, the convergence behaviors and stability bounds for the algorithms ' step sizes are studied and derived. Secondly, we analyze the behaviors of locally-adaptive multilayer decorrelation networks and quantify their performances for poorly-conditioned signal mixtures. Thirdly, wederive a robust locally-adaptive network structure based on aposteriori output signals that remains stable for any step size value. Finally, we present an extension of the locally-adaptive network for linear-phase temporal and spatial whitening of multichannel signals. Simulations verify the analyses and indicate the usefulness of the locally-adaptive networks for decorrelating signals in space and time. accepted for publication in