Results 1  10
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11
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 ..."
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Cited by 704 (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
A multilinear singular value decomposition
 SIAM J. Matrix Anal. Appl
, 2000
"... Abstract. We discuss a multilinear generalization of the singular value decomposition. There is a strong analogy between several properties of the matrix and the higherorder tensor decomposition; uniqueness, link with the matrix eigenvalue decomposition, firstorder perturbation effects, etc., are ..."
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Cited by 467 (20 self)
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Abstract. We discuss a multilinear generalization of the singular value decomposition. There is a strong analogy between several properties of the matrix and the higherorder tensor decomposition; uniqueness, link with the matrix eigenvalue decomposition, firstorder perturbation effects, etc., are analyzed. We investigate how tensor symmetries affect the decomposition and propose a multilinear generalization of the symmetric eigenvalue decomposition for pairwise symmetric tensors.
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 448 (9 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...
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 252 (5 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.
Independent Component Analysis, A Survey Of Some Algebraic Methods
 IEEE INTERNATIONAL SYMPOSIUM ON CIRCUITS AND SYSTEMS
, 1996
"... The source separation problem has been addressed in many ways during the last decade, and one of its instances gave birth to Independent Component Analysis (ICA). Iterative methods can be opposed to algebraic ones for the computation of the ICA, and seem to reveal very interesting research tracks. T ..."
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Cited by 36 (0 self)
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The source separation problem has been addressed in many ways during the last decade, and one of its instances gave birth to Independent Component Analysis (ICA). Iterative methods can be opposed to algebraic ones for the computation of the ICA, and seem to reveal very interesting research tracks. This paper attempts to give an outline of some of the works that have been carried out in the latter area, without pretending to survey exhaustively or objectively the subject. Bibliographical pointers hopefully compensate for this drawback.
An Efficient Technique For The Blind Separation Of Complex Sources.
 in Proc. IEEE SP Workshop on HigherOrder Stat., Lake Tahoe
, 1993
"... Blind identification of spatial mixtures allows an array of sensors to implement source separation when the array manifold is unknown. A family of 4thorder cumulantbased criteria for blind source separation is introduced. These criteria involve a set of cumulant matrices, whose joint diagonalizati ..."
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Cited by 29 (8 self)
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Blind identification of spatial mixtures allows an array of sensors to implement source separation when the array manifold is unknown. A family of 4thorder cumulantbased 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 ...
Blind channel identification and extraction of more sources than sensors
, 1998
"... It is often admitted that a static system with more inputs (sources) than outputs (sensors, or channels) cannot be blindly identified, that is, identified only from the observation of its outputs, and without any a priori knowledge on the source statistics but their independence. By resorting to Hig ..."
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Cited by 21 (7 self)
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It is often admitted that a static system with more inputs (sources) than outputs (sensors, or channels) cannot be blindly identified, that is, identified only from the observation of its outputs, and without any a priori knowledge on the source statistics but their independence. By resorting to HighOrder Statistics, it turns out that static MIMO systems with fewer outputs than inputs can be identified, as demonstrated in the present paper. The principle, already described in a recent rather theoretical paper, had not yet been applied to a concrete blind identification problem. Here, in order to demonstrate its feasibility, the procedure is detailed in the case of a 2sensor 3source mixture; a numerical algorithm is devised, that blindly identifies a 3input 2output mixture. Computer results show its behavior as a function of the data length when sources are QPSKmodulated signals, widely used in digital communications. Then another algorithm is proposed to extract the 3 sources from the 2 observations, once the mixture has been identified. Contrary to the first algorithm, this one assumes that the sources have a known discrete distribution. Computer experiments are run in the case of three BPSK sources in presence of Gaussian noise.
Tensor diagonalization, a useful tool in signal processing
 IFAC SYMPOSIUM ON SYSTEM IDENTIFICATION
, 1994
"... Tensors appear more and more often in signal processing problems, and especially spatial processing, which typically involves multichannel modeling. Even if it is not always obvious that tensor algebra is the best framework to address a problem, there are cases where no choice is left. Blind identif ..."
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Cited by 17 (7 self)
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Tensors appear more and more often in signal processing problems, and especially spatial processing, which typically involves multichannel modeling. Even if it is not always obvious that tensor algebra is the best framework to address a problem, there are cases where no choice is left. Blind identification of multichannel non monic MA models is given as an illustrating example of this claim.
A Tetradic Decomposition of 4thOrder Tensors. Application to the Source Separation Problem
"... Two results re presented on SVDlike decomposition of 4thorder tensors. This is motiwted by n rry processing problem: consider n rry of m sensors listening t n independent nrrow bnd sources; the 4thorder cumulnts of the rry output form 4thorder rnkdeficient symmetric tensor which hs tetrdic str ..."
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Cited by 3 (0 self)
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Two results re presented on SVDlike decomposition of 4thorder tensors. This is motiwted by n rry processing problem: consider n rry of m sensors listening t n independent nrrow bnd sources; the 4thorder cumulnts of the rry output form 4thorder rnkdeficient symmetric tensor which hs tetrdic structure. Finding tetrdic decomposition of this tensor is equivalent to identify the spatial trnsfert function of the system which is mtrix whose knowledge llows to recover the source signals.
Performance And Implementation Of Invariant Source Separation Algorithms
 in ISCAS '96
, 1996
"... 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 equi ..."
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Cited by 3 (0 self)
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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...