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51
Blind Beamforming for Non Gaussian Signals
 IEE ProceedingsF
, 1993
"... This paper considers an application of blind identification to beamforming. The key point is to use estimates of directional vectors rather than resorting to their hypothesized value. By using estimates of the directional vectors obtained via blind identification i.e. without knowing the arrray mani ..."
Abstract

Cited by 494 (31 self)
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This paper considers an application of blind identification to beamforming. The key point is to use estimates of directional vectors rather than resorting to their hypothesized value. By using estimates of the directional vectors obtained via blind identification i.e. without knowing the arrray manifold, beamforming is made robust with respect to array deformations, distortion of the wave front, pointing errors, etc ... so that neither array calibration nor physical modeling are necessary. Rather surprisingly, `blind beamformers' may outperform `informed beamformers' in a plausible range of parameters, even when the array is perfectly known to the informed beamformer. The key assumption blind identification relies on is the statistical independence of the sources, which we exploit using fourthorder cumulants. A computationally efficient technique is presented for the blind estimation of directional vectors, based on joint diagonalization of 4thorder cumulant matrices
Blind Signal Separation: Statistical Principles
, 2003
"... 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 i ..."
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Cited by 390 (4 self)
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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.
Equivariant Adaptive Source Separation
 IEEE Trans. on Signal Processing
, 1996
"... 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 (Eq ..."
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Cited by 381 (10 self)
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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...
A Blind Source Separation Technique Using Second Order Statistics
, 1997
"... 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 narrowband array processi ..."
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Cited by 201 (6 self)
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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 narrowband 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 secondorder 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...
HighOrder Contrasts for Independent Component Analysis
"... This article considers highorder measures of independence for the independent component analysis problem and discusses the class of Jacobi algorithms for their optimization. Several implementations are discussed. We compare the proposed approaches with gradientbased techniques from the algorithmic ..."
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Cited by 187 (4 self)
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This article considers highorder measures of independence for the independent component analysis problem and discusses the class of Jacobi algorithms for their optimization. Several implementations are discussed. We compare the proposed approaches with gradientbased techniques from the algorithmic point of view and also on a set of biomedical data.
Blind Separation of Mixture of Independent Sources Through a Maximum Likelihood Approach
 In Proc. EUSIPCO
, 1997
"... 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 af ..."
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Cited by 101 (8 self)
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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...
A Unifying Informationtheoretic Framework for Independent Component Analysis
, 1999
"... We show that different theories recently proposed for Independent Component Analysis (ICA) lead to the same iterative learning algorithm for blind separation of mixed independent sources. We review those theories and suggest that information theory can be used to unify several lines of research. Pea ..."
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Cited by 82 (8 self)
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We show that different theories recently proposed for Independent Component Analysis (ICA) lead to the same iterative learning algorithm for blind separation of mixed independent sources. We review those theories and suggest that information theory can be used to unify several lines of research. Pearlmutter and Parra (1996) and Cardoso (1997) showed that the infomax approach of Bell and Sejnowski (1995) and the maximum likelihood estimation approach are equivalent. We show that negentropy maximization also has equivalent properties and therefore all three approaches yield the same learning rule for a fixed nonlinearity. Girolami and Fyfe (1997a) have shown that the nonlinear Principal Component Analysis (PCA) algorithm of Karhunen and Joutsensalo (1994) and Oja (1997) can also be viewed from informationtheoretic principles since it minimizes the sum of squares of the fourthorder marginal cumulants and therefore approximately minimizes the mutual information (Comon, 1994). Lambert (19...
Blind Separation of Instantaneous Mixture of Sources based on order statistics
 IEEE Trans. Signal Processing
, 1996
"... In this paper we introduce a novel procedure for separating an instantaneous mixture of source based on the order statistics. The method is derived in a general context of independence component analysis, using a contrast function defined in term of the KullbackLeibner divergence or of the mutual i ..."
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Cited by 62 (11 self)
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In this paper we introduce a novel procedure for separating an instantaneous mixture of source based on the order statistics. The method is derived in a general context of independence component analysis, using a contrast function defined in term of the KullbackLeibner divergence or of the mutual information. We introduce a discretized form of this contrast permitting its easy estimation through the order statistics. We show that the local contrast property is preserved and also derive a global contrast exploiting only the information of the support of the distribution (in the case this support is finite). Some simulations are given illustrating the good performance of the method. 1 Introduction The problem of separation of sources has been the subject of rapid development in the signal processing literature recently (see for example [2]  [5], [7]  [12], [14], [15] : : : ). We consider here the simplest case where one observes K sequences X 1 (t), : : : , XK (t), each being a li...
SuperSymmetric Decomposition Of The FourthOrder Cumulant Tensor. Blind Identification Of More Sources Than Sensors
, 1991
"... New ideas for HigherOrder Array Processing are introduced. The paper focuses on fourthorder cumulant statistics. They are expressed in an indexfree formalism (that is believed to be of general interest) allowing the exploitation of all their symmetry properties. We show that, when dealing with 4 ..."
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Cited by 54 (12 self)
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New ideas for HigherOrder Array Processing are introduced. The paper focuses on fourthorder cumulant statistics. They are expressed in an indexfree formalism (that is believed to be of general interest) allowing the exploitation of all their symmetry properties. We show that, when dealing with 4index quantities, symmetries are related to rank properties. The rich symmetry structure yields a whole class of new identification algorithms. Main features are : . Use of fourthorder cumulant statistics only : yielding asymptotically unbiased estimates in presence of Gaussian noise regardless of its spatial structure.
Separating Reflections from Images Using Independent Components Analysis
 Journal of the Optical Society of America
, 1998
"... this paper describes a method for photographing objects behind glass and digitally removing the reflections off the glass leaving the image of the objects behind the glass intact. We describe the details of this method which employssimple optical techniques and independent components analysis (ICA) ..."
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Cited by 50 (3 self)
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this paper describes a method for photographing objects behind glass and digitally removing the reflections off the glass leaving the image of the objects behind the glass intact. We describe the details of this method which employssimple optical techniques and independent components analysis (ICA) and show its efficacy with several examples. 1 Introduction