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336
Algebraic Methods for Deterministic Blind Beamforming
, 1998
"... Deterministic blind beamforming algorithms try to separate superpositions of source signals impinging on a phased antenna array by using deterministic properties of the signals or the channels such as their constant modulus or directionsofarrival. Progress in this area has been abundant over the p ..."
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Cited by 38 (6 self)
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Deterministic blind beamforming algorithms try to separate superpositions of source signals impinging on a phased antenna array by using deterministic properties of the signals or the channels such as their constant modulus or directionsofarrival. Progress in this area has been abundant over the past ten years and has resulted in several powerful algorithms. Unlike optimal or adaptive methods, the algebraic methods discussed in this review act on a fixed block of data and give closedform expressions for beamformers by focusing on algebraic structures. This typically leads to subspace estimation and generalized eigenvalue problems. After introducing a simple and widely used multipath channel model, the paper provides an anthology of properties that are available, and generic algorithms that exploit them.
Nonnegative matrix factorization for rapid recovery of constituent spectra in magnetic resonance chemical shift imaging of the brain
 IEEE Trans on Med Imaging
, 2004
"... Abstract—We present an algorithm for blindly recovering constituent source spectra from magnetic resonance (MR) chemical shift imaging (CSI) of the human brain. The algorithm, which we call constrained nonnegative matrix factorization (cNMF), does not enforce independence or sparsity, instead only ..."
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Cited by 38 (1 self)
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Abstract—We present an algorithm for blindly recovering constituent source spectra from magnetic resonance (MR) chemical shift imaging (CSI) of the human brain. The algorithm, which we call constrained nonnegative matrix factorization (cNMF), does not enforce independence or sparsity, instead only requiring the source and mixing matrices to be nonnegative. It is based on the nonnegative matrix factorization (NMF) algorithm, extending it to include a constraint on the positivity of the amplitudes of the recovered spectra. This constraint enables recovery of physically meaningful spectra even in the presence of noise that causes a significant number of the observation amplitudes to be negative. We demonstrate and characterize the algorithm’s performance using P volumetric brain data, comparing the results with two different blind source separation methods: Bayesian spectral decomposition (BSD) and nonnegative sparse coding (NNSC). We then incorporate the cNMF algorithm into a hierarchical decomposition framework, showing that it can be used to recover tissuespecific spectra given a processing hierarchy that proceeds coarsetofine. We demonstrate the hierarchical procedure on H brain data and conclude that the computational efficiency of the algorithm makes it wellsuited for use in diagnostic workup. Index Terms—Blind source separation (BSS), chemical shift imaging (CSI), hierarchical decomposition, magnetic resonance (MR), magnetic resonance spectroscopy (MRS), nonnegative matrix factorization (NMF).
Joint Diagonalization via Subspace Fitting Techniques
 In Proc. ICASSP
, 2001
"... INTRODUCTION Suppose that we are given K complex Hermitian matrices Y k of the form where the k are diagonal and real, and E k represents additive noise. The joint diagonalization problem we consider is, given the Y k , to estimate the common factor A. We assume that all Y k are square d d matr ..."
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Cited by 33 (2 self)
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INTRODUCTION Suppose that we are given K complex Hermitian matrices Y k of the form where the k are diagonal and real, and E k represents additive noise. The joint diagonalization problem we consider is, given the Y k , to estimate the common factor A. We assume that all Y k are square d d matrices, and that A is square d d with full rank d. An extension of this problem is, for complex nonHermitian matrices, where A and B can be different, and the k are diagonal but not necessarily real. Joint diagonalization of either type turns up in several recently proposed blind source separation problems with data models X AS N, where X is the observation matrix, A is the mixing matrix, the rows of S contain the source signals, and N is additive noise. Depending on the assumptions on A and/or S, the following types of algebraic source separation techniques have been proposed:  Diagonalization of fourth order cumulant matrices, as in JADE [1] where K d and A is considered unitary.
separation of Gaussian sources via secondorder statistics with asymptotically optimal weighting
 IEEE Signal Processing Letters 7, 197–200 (2000). 418 Bull. Pol. Ac.: Tech. 60(3) 2012 Unauthenticated  89.67.242.59 Download Date  5/19/13 8:24 PM
"... Abstract—Blind separation of Gaussian sources with different spectra can be attained using secondorder statistics. The secondorder blind identification (SOBI) algorithm, proposed by Belouchrani et al., uses approximate joint diagonalization. We show that substantial improvement over SOBI can be a ..."
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Cited by 31 (5 self)
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Abstract—Blind separation of Gaussian sources with different spectra can be attained using secondorder statistics. The secondorder blind identification (SOBI) algorithm, proposed by Belouchrani et al., uses approximate joint diagonalization. We show that substantial improvement over SOBI can be attained when the joint diagonalization is transformed into a properly weighted nonlinear least squares problem. We provide an iterative solution and derive the optimal weights for our weightsadjusted SOBI (WASOBI) algorithm. The improvement is demonstrated by analysis and simulations. Index Terms—Blind source separation, joint diagonalization, weighted least squares. I.
A Robust Whitening Procedure in Blind Source Separation Context
 Electronics Letters
, 2000
"... The main objective of this letter is to present an efficient algorithm for robust whitening in the presence of temporally uncorrelated additive noise that may be spatially correlated. This whitening is introduced as a preprocessing step in the blind source separation process. The robust whitenin ..."
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Cited by 28 (6 self)
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The main objective of this letter is to present an efficient algorithm for robust whitening in the presence of temporally uncorrelated additive noise that may be spatially correlated. This whitening is introduced as a preprocessing step in the blind source separation process. The robust whitening consists in the eigenvalue decomposition of a positive definite linear combination of a set a correlation matrices taken at nonzero lags. The coefficients of the linear combination are computed byafinite step global convergence algorithm. Some numerical simulations are provided to illustrate the effectiveness of the solution. Indexing terms: Blind separation of noisy signals, correlation matrices, robust whitening for noisy data. 1 1 Introduction Blind source separation consists of recovering independent signals from their instantaneous mixtures without any a priori knowledge on these mixtures. Some approaches estimate the source signals by prewhitening the sensor data followed by ...
Joint blind source separation by multiset canonical correlation analysis
 IEEE Trans. Signal Processing
, 2009
"... Abstract—In this paper, we introduce a simple and effective scheme to achieve joint blind source separation (BSS) of multiple datasets using multiset canonical correlation analysis (MCCA) [J. R. Kettenring, “Canonical analysis of several sets of variables,” Biometrika, vol. 58, pp. 433–451, 1971]. ..."
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Cited by 27 (7 self)
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Abstract—In this paper, we introduce a simple and effective scheme to achieve joint blind source separation (BSS) of multiple datasets using multiset canonical correlation analysis (MCCA) [J. R. Kettenring, “Canonical analysis of several sets of variables,” Biometrika, vol. 58, pp. 433–451, 1971]. We first propose a generative model of joint BSS based on the correlation of latent sources within and between datasets. We specify source separability conditions, and show that, when the conditions are satisfied, the group of corresponding sources from each dataset can be jointly extracted by MCCA through maximization of correlation among the extracted sources. We compare source separation performance of the MCCA scheme with other joint BSS methods and demonstrate the superior performance of the MCCA scheme in achieving joint BSS for a large number of datasets, group of corresponding sources with heterogeneous correlation values, and complexvalued sources with circular and noncircular distributions. We apply MCCA to analysis of functional magnetic resonance imaging (fMRI) data from multiple subjects and show its utility in estimating meaningful brain activations from a visuomotor task. Index Terms—Canonical correlation analysis, group analysis, independent component analysis, joint blind source separation. I.
Contrasts, independent component analysis, and blind deconvolution
 J. ADAPTIVE CONTR. SIGNAL PROCESS. (SPECIAL ISSUE ONBLIND SIGNAL SEPARATION
, 2004
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a potential tool for BCI systems
 IEEE Signal Processing Magazine, special issue on BrainComputer Interfaces
, 2008
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Multiclass Common Spatial Patterns and Information Theoretic Feature Extraction
, 2008
"... We address two shortcomings of the Common Spatial Patterns (CSP) algorithm for spatial filtering in the context of BrainComputer Interfaces (BCIs) based on EEG/MEG: First, the question of optimality of CSP in terms of the minimal achievable classification error remains unsolved. Second, CSP has bee ..."
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Cited by 25 (1 self)
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We address two shortcomings of the Common Spatial Patterns (CSP) algorithm for spatial filtering in the context of BrainComputer Interfaces (BCIs) based on EEG/MEG: First, the question of optimality of CSP in terms of the minimal achievable classification error remains unsolved. Second, CSP has been initially proposed for twoclass paradigms. Extensions to multiclass paradigms have been suggested, but are based on heuristics. We address these shortcomings in the framework of Information Theoretic Feature Extraction (ITFE). We show that for twoclass paradigms CSP maximizes an approximation of mutual information of extracted EEG/MEG components and class labels. This establishes a link between CSP and the minimal classification error. For multiclass paradigms, we point out that CSP by joint approximate diagonalization (JAD) is equivalent to Independent Component Analysis (ICA), and provide a method to choose those independent components (ICs) that approximately maximize mutual information of ICs and class labels. This eliminates the need for heuristics in multiclass CSP, and allows incorporating prior class probabilities. The proposed method is applied to the dataset IIIa of the third BCI competition, and is shown to increase the mean classification accuracy by 23.4 % in comparison to multiclass CSP.