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257
Multichannel Blind Deconvolution: Fir Matrix Algebra And Separation Of Multipath Mixtures
, 1996
"... A general tool for multichannel and multipath problems is given in FIR matrix algebra. With Finite Impulse Response (FIR) filters (or polynomials) assuming the role played by complex scalars in traditional matrix algebra, we adapt standard eigenvalue routines, factorizations, decompositions, and mat ..."
Abstract

Cited by 75 (0 self)
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A general tool for multichannel and multipath problems is given in FIR matrix algebra. With Finite Impulse Response (FIR) filters (or polynomials) assuming the role played by complex scalars in traditional matrix algebra, we adapt standard eigenvalue routines, factorizations, decompositions, and matrix algorithms for use in multichannel /multipath problems. Using abstract algebra/group theoretic concepts, information theoretic principles, and the Bussgang property, methods of single channel filtering and source separation of multipath mixtures are merged into a general FIR matrix framework. Techniques developed for equalization may be applied to source separation and vice versa. Potential applications of these results lie in neural networks with feedforward memory connections, wideband array processing, and in problems with a multiinput, multioutput network having channels between each source and sensor, such as source separation. Particular applications of FIR polynomial matrix alg...
Mapping directed influence over the brain using Granger causality and fMRI
 NEUROIMAGE. 25:230242
, 2005
"... We propose Granger causality mapping (GCM) as an approach to explore directed influences between neuronal populations (effective connectivity) in fMRI data. The method does not rely on a priori specification of a model that contains preselected regions and connections between them. This distinguish ..."
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Cited by 52 (1 self)
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We propose Granger causality mapping (GCM) as an approach to explore directed influences between neuronal populations (effective connectivity) in fMRI data. The method does not rely on a priori specification of a model that contains preselected regions and connections between them. This distinguishes it from other fMRI effective connectivity approaches that aim at testing or contrasting specific hypotheses about neuronal interactions. Instead, GCM relies on the concept of Granger causality to define the existence and direction of influence from information in the data. Temporal precedence information is exploited to compute Granger causality maps that identify voxels that are sources or targets of directed influence for any selected regionofinterest. We investigated the method by simulations and by application to fMRI data of a complex visuomotor task. The presented exploratory approach of mapping influences between a region of interest and the rest of the brain can form a useful complement to existing models of effective connectivity.
Multivariate Autoregressive Models for Classification of Spontaneous Electroencephalogram During Mental Tasks
 IEEE Transactions on Biomedical Engineering
, 1998
"... This article explores the use of scalar and multivariate autoregressive (AR) models to extract features from the human electroencephalogram (EEG) with which mental tasks can be discriminated. This is part of a larger project to investigate the feasibility of using EEG to allow paralyzed persons to c ..."
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Cited by 49 (2 self)
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This article explores the use of scalar and multivariate autoregressive (AR) models to extract features from the human electroencephalogram (EEG) with which mental tasks can be discriminated. This is part of a larger project to investigate the feasibility of using EEG to allow paralyzed persons to control a device like a wheelchair. EEG signals from four subjects were recorded while they performed two mental tasks. Quartersecond windows of 6channel EEG were transformed into four different representations: scalar AR model coefficients, multivariate AR coefficients, eigenvalues of a correlation matrix, and the KarhunenLoeve transform of the multivariate AR coefficients. Feature vectors defined by these representations were classified with a standard, feedforward neural network trained via the error backpropagation algorithm. The four representations produced similar results, with the multivariate AR coefficients performing slightly better and more consistently with an average classifi...
Exploring estimator biasvariance tradeoffs using the uniform CR bound
 IEEE Trans. on Sig. Proc
, 1996
"... We introduce a plane, which we call the deltasigma plane, that is indexed by the norm of the estimator bias gradient and the variance of the estimator. The norm of the bias gradient is related to the maximum variation in the estimator bias function over a neighborhood of parameter space. Using a un ..."
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Cited by 38 (14 self)
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We introduce a plane, which we call the deltasigma plane, that is indexed by the norm of the estimator bias gradient and the variance of the estimator. The norm of the bias gradient is related to the maximum variation in the estimator bias function over a neighborhood of parameter space. Using a uniform CramerRao (CR) bound on estimator variance a deltasigma tradeoff curve is specied which denes an "unachievable region" of the deltasigma plane for a specified statistical model. In order to place an estimator on this plane for comparison to the deltasigma tradeoff curve, the estimator variance, bias gradient, and bias gradient norm must be evaluated. We present a simple and accurate method for experimentally determining the bias gradient norm based on applying a bootstrap estimator to a sample mean constructed from the gradient of the loglikelihood. We demonstrate the methods developed in this paper for linear Gaussian and nonlinear Poisson inverse problems.
Classification of EEG signals from four subjects during five mental tasks
 Proceedings of the Conference on Engineering Applications in Neural Networks (EANN’96
, 1996
"... anderson,sijercic¡ ..."
Using Signal Processing to Analyze Wireless Data Traffic
 Proc. ACM workshop on Wireless Security
, 2002
"... Experts have long recognized that theoretically it was possible to perform traffic analysis on encrypted packet streams by analyzing the timing of packet arrivals (or transmissions). We report on experiments to realize this possiblity using basic signal processing techniques taken from acoustics to ..."
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Cited by 29 (4 self)
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Experts have long recognized that theoretically it was possible to perform traffic analysis on encrypted packet streams by analyzing the timing of packet arrivals (or transmissions). We report on experiments to realize this possiblity using basic signal processing techniques taken from acoustics to perform traffic analysis on encrypted transmissions over wireless networks. While the work discussed here is preliminary, we are able to demonstrate two very interesting results. First, we can extract timing information, such as roundtrip times of TCP connections, from traces of aggregated data traffic. Second, we can determine how data is routed through a network using coherence analysis. These results show that signal processing techniques may prove to be valuable network analysis tools in the future.
Frequency Domain Blind MIMO System Identification Based on Second and Higher Order Statistics
 IEEE TRANS. SIGNAL PROCESSING
, 2001
"... We present a novel frequencydomain framework for the identification of a multipleinput multipleoutput (MIMO) system driven by white, mutually independent, unobservable inputs. The system frequency response is obtained based on singular value decomposition (SVD) of a matrix constructed based on th ..."
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Cited by 21 (8 self)
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We present a novel frequencydomain framework for the identification of a multipleinput multipleoutput (MIMO) system driven by white, mutually independent, unobservable inputs. The system frequency response is obtained based on singular value decomposition (SVD) of a matrix constructed based on the powerspectrum and slices of polyspectra of the system output. By appropriately selecting the polyspectra slices, we can create a set of such matrices, each of which could independently yield the solution, or they could all be combined in a joint diagonalization scheme to yield a solution with improved statistical performance. The freedom to select the polyspectra slices allows us to bypass the frequencydependent permutation ambiguity that is usually associated with frequency domain SVD, while at the same time allows us compute and cancel the phase ambiguity. An asymptotic consistency analysis of the system magnitude response estimate is performed.
Sound Texture Modelling with Linear Prediction in Both Time and Frequency Domains
 in Proc. ICASSP
, 2003
"... Sound textures—for instance, a crackling fire, running water, or applause—constitute a large and largely neglected class of audio signals. Whereas tonal sounds have been effectively and flexibly modelled with sinusoids, aperiodic energy is usually modelled as white noise filtered to match the approx ..."
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Cited by 19 (3 self)
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Sound textures—for instance, a crackling fire, running water, or applause—constitute a large and largely neglected class of audio signals. Whereas tonal sounds have been effectively and flexibly modelled with sinusoids, aperiodic energy is usually modelled as white noise filtered to match the approximate spectrum of the original over 1030 ms windows, which fails to provide a perceptually satisfying reproduction of many realworld noisy sound textures. We attribute this failure to the loss of shortterm temporal structure, and we introduce a second modelling stage in which the time envelope of the residual from conventional linear predictive modelling is itself modelled with linear prediction in the spectral domain. This cascade time and frequencydomain linear prediction (CTFLP) leads to noiseexcited resyntheses that have high perceptual fidelity. We perform a novel quantitative error analysis by measuring the proportional error within timefrequency cells across a range of timescales. 1.
Imaging Below the Diffraction Limit: A Statistical Analysis
 IEEE TRANSACTIONS ON IMAGE PROCESSING
, 2004
"... The present paper is concerned with the statistical analysis of the resolution limit in a socalled "diffractionlimited" imaging system. The canonical case study is that of incoherent imaging of two closelyspaced sources of possibly unequal brightness. The objective is to study how far b ..."
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Cited by 18 (4 self)
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The present paper is concerned with the statistical analysis of the resolution limit in a socalled "diffractionlimited" imaging system. The canonical case study is that of incoherent imaging of two closelyspaced sources of possibly unequal brightness. The objective is to study how far beyond the classical Rayleigh limit of resolution one can reach at a given signal to noise ratio. The analysis uses tools from statistical detection and estimation theory. Specifically, we will derive explicit relationships between the minimum detectable distance between two closelyspaced point sources imaged incoherently at a given SNR. For completeness, asymptotic performance analysis for the estimation of the unknown parameters is carried out using the CramrRao bound. To gain maximum intuition, the analysis is carried out in one dimension, but can be well extended to the twodimensional case and to more practical models.