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Spatiotemporal EEG/MEG source analysis based on a parametric noise covariance model
 IEEE Transactions on Biomedical Engineering
, 2002
"... c○2000 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other w ..."
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Cited by 22 (4 self)
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c○2000 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
The spatiotemporal MEG covariance matrix modeled as a sum of Kronecker products
 NeuroImage
, 2005
"... The single Kronecker product (KP) model for the spatiotemporal covariance of MEG residuals is extended to a sum of Kronecker products. This sum of KP is estimated such that it approximates the spatiotemporal sample covariance best in matrix norm. Contrary to the single KP, this extension allows for ..."
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Cited by 7 (0 self)
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The single Kronecker product (KP) model for the spatiotemporal covariance of MEG residuals is extended to a sum of Kronecker products. This sum of KP is estimated such that it approximates the spatiotemporal sample covariance best in matrix norm. Contrary to the single KP, this extension allows for describing multiple, independent phenomena in the ongoing background activity. Whereas the single KP model can be interpreted by assuming that background activity is generated by randomly distributed dipoles with certain spatial and temporal characteristics, the sum model can be physiologically interpreted by assuming a composite of such processes. Taking enough terms into account, the spatiotemporal sample covariance matrix can be described exactly by this extended model. In the estimation of the sum of KP model, it appears that the sum of the first 2 KP describes between 67 % and 93%. Moreover, these first two terms describe two physiological processes in the background activity: focal, frequencyspecific alpha activity, and more widespread nonfrequencyspecific activity. Furthermore, temporal nonstationarities due to trialtotrial variations are not clearly visible in the first two terms, and, hence, play only a minor role in the sample covariance matrix in terms of matrix power. Considering the dipole localization, the single KP model appears to describe around 80 % of the noise and seems therefore adequate. The emphasis of further improvement of localization accuracy should be on improving the source model rather than the covariance model.
Model selection in electromagnetic source analysis with an application to VEF’s
 IEEE Transactions on Biomedical Engineering
, 2002
"... Abstract — In electromagnetic source analysis it is necessary to determine how many sources are required to describe the EEG or MEG adequately. Model selection procedures (MSP’s, or goodness of fit procedures) give an estimate of the required number of sources. Existing and new MSP’s are evaluated i ..."
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Abstract — In electromagnetic source analysis it is necessary to determine how many sources are required to describe the EEG or MEG adequately. Model selection procedures (MSP’s, or goodness of fit procedures) give an estimate of the required number of sources. Existing and new MSP’s are evaluated in different source and noise settings: two sources which are close or distant, and noise which is uncorrelated or correlated. The commonly used MSP residual variance is seen to be ineffective, that is it often selects too many sources. Alternatives like the adjusted Hotelling’s test, Bayes information criterion, and the Wald test on source amplitudes are seen to be effective. The adjusted Hotelling’s test is recommended if a conservative approach is taken, and MSP’s such as Bayes information criterion or the Wald test on source amplitudes are recommended if a more liberal approach is desirable. The MSP’s are applied to empirical data (visual evoked fields). I.
Efficient dipole parameter estimation in EEG systems with nearML performance
 IEEE Trans. Biomed. Eng
"... Abstract—Source signals that have strong temporal correlation can pose a challenge for highresolution EEG source localization algorithms. In this paper, we present two methods that are able to accurately locate highly correlated sources in situations where other highresolution methods such as mult ..."
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Abstract—Source signals that have strong temporal correlation can pose a challenge for highresolution EEG source localization algorithms. In this paper, we present two methods that are able to accurately locate highly correlated sources in situations where other highresolution methods such as multiple signal classification and linearly constrained minimum variance beamforming fail. These methods are based on approximations to the optimal maximum likelihood (ML) approach, but offer significant computational advantages over ML when estimates of the equivalent EEG dipole orientation and moment are required in addition to the source location. The first method uses a twostage approach in which localization is performed assuming an unstructured dipole moment model, and then the dipole orientation is obtained by using these estimates in a second step. The second method is based on the use of the noise subspace fitting concept, and has been shown to provide performance that is asymptotically equivalent to the direct ML method. Both techniques lead to a considerably simpler optimization than ML since the estimation of the source locations and dipole moments is decoupled. Examples using data from simulations and auditory experiments are presented to illustrate the performance of the algorithms. Index Terms—Electroencephalography (EEG), magnetoencephalography (MEG), sensor array processing, source localization.
Frequency domain simultaneous source and source coherence estimation with an application to MEG
 IEEE Trans. on Biomedical Engineering
, 2004
"... c○2000 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other w ..."
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Cited by 3 (2 self)
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c○2000 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained
On Toeplitz and Kronecker Structured Covariance Matrix Estimation (Invited Paper)
"... Abstract—A number of signal processing applications require the estimation of covariance matrices. Sometimes, the particular scenario or system imparts a certain theoretical structure on the matrices that are to be estimated. Using this knowledge allows the design of algorithms exploiting such struc ..."
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Abstract—A number of signal processing applications require the estimation of covariance matrices. Sometimes, the particular scenario or system imparts a certain theoretical structure on the matrices that are to be estimated. Using this knowledge allows the design of algorithms exploiting such structure, resulting in more robust and accurate estimators, especially for small samples. We study a scenario with a measured covariance matrix known to be the Kronecker product of two other, possibly structured, covariance matrices that are to be estimated. Examples of scenarios in which such a problem occurs are MIMOcommunications and EEG measurements. When the matrices that are to be estimated are Toeplitz structured, we show our algorithms to be able to achieve the CramérRao Lower Bound already at very small sample sizes. I.
Projection versus prewhitening for EEG interference suppression
 IEEE Trans. Biomed. Eng
"... Abstract—Suppression of strong, spatially correlated background interference is a challenge associated with electroencephalography (EEG) source localization problems. The most common way of dealing with such interference is through the use of a prewhitening transformation based on an estimate of ..."
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Abstract—Suppression of strong, spatially correlated background interference is a challenge associated with electroencephalography (EEG) source localization problems. The most common way of dealing with such interference is through the use of a prewhitening transformation based on an estimate of the covariance of the interference plus noise. This approach is based on strong assumptions regarding temporal stationarity of the data, which do not commonly hold in EEG applications. In addition, prewhitening cannot typically be implemented directly due to ill conditioning of the covariance matrix, and ad hoc regularization is often necessary. Using both simulation examples and experiments involving real EEG data with auditory evoked responses, we demonstrate that a straightforward interference projection method is significantly more robust than prewhitening for EEG source localization. Index Terms—Electroencephalography (EEG), interference suppression, magnetoencephalography (MEG), sensor array processing, source localization. I.
Bilinear Probabilistic Principal Component Analysis
"... Abstract — Probabilistic principal component analysis (PPCA) is a popular linear latent variable model for multilayer performing dimension reduction on 1D data in a probabilistic manner. However, when used on 2D data such as images, PPCA suffers from the curse of dimensionality due to the subsequ ..."
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Abstract — Probabilistic principal component analysis (PPCA) is a popular linear latent variable model for multilayer performing dimension reduction on 1D data in a probabilistic manner. However, when used on 2D data such as images, PPCA suffers from the curse of dimensionality due to the subsequently large number of model parameters. To overcome this problem, we propose in this paper a novel probabilistic model on 2D data called bilinear PPCA (BPPCA). This allows the establishment of a closer tie between BPPCA and its nonprobabilistic counterpart. Moreover, two efficient parameter estimation algorithms for fitting BPPCA are also developed. Experiments on a number of 2D synthetic and realworld data sets show that BPPCA is more accurate than existing probabilistic and nonprobabilistic dimension reduction methods. Index Terms — 2D data, dimension reduction, expectation maximization, principal component analysis, probabilistic model. I.
A maximumlikelihood estimator for trialtotrial variations in noisy MEG/EEG data sets
 IEEE Trans Biomed Eng
"... Abstract—The standard procedure to determine the brain response from a multitrial evoked magnetoencephalography (MEG) or electroencephalography (EEG) data set is to average the individual trials of these data, time locked to the stimulus onset. When the brain responses vary from trialtotrial thi ..."
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Abstract—The standard procedure to determine the brain response from a multitrial evoked magnetoencephalography (MEG) or electroencephalography (EEG) data set is to average the individual trials of these data, time locked to the stimulus onset. When the brain responses vary from trialtotrial this approach is false. In this paper, a maximumlikelihood estimator is derived for the case that the recorded data contain amplitude variations. The estimator accounts for spatially and temporally correlated background noise that is superimposed on the brain response. The model is applied to a series of 17 MEG data sets of normal subjects, obtained during median nerve stimulation. It appears that the amplitude of late component (30–120 ms) shows a systematic negative trend indicating a weakening response during stimulation time. For the early components (20–35 ms) no such a systematic effect was found. The model is furthermore applied on a MEG data set consisting of epileptic spikes of constant spatial distribution but varying polarity. For these data, the advantage of applying the model is that positive and negative spikes can be processed with a single model, thereby reducing the number of degrees of freedom and increasing the signaltonoise ratio. Index Terms—Covariance, habituation, maximumlikelihood, MEG noise.
A Statistical Framework to Infer Functional Gene Associations from Multiple Biologically Interrelated Microarray Experiments
, 2007
"... A major task in understanding biological processes is to elucidate relationships between genes involved in the underlying biological pathways. Microarray data from an increasing number of biologically interrelated experiments now allows for more complete portrayals of functional gene relationships i ..."
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A major task in understanding biological processes is to elucidate relationships between genes involved in the underlying biological pathways. Microarray data from an increasing number of biologically interrelated experiments now allows for more complete portrayals of functional gene relationships in the pathways. In current studies of gene relationships, the existence of expression dependencies attributable to the biologically interrelated experiments, however, has been widely ignored. When not accounted for, these (experimental) dependencies can result in inaccurate inferences of functional gene relationships, and hence incorrect biological conclusions. This article contributes a framework to provide a model and an estimation procedure for inferring gene relationships when there are twoway dependencies in the gene expression matrix (the genewise and experimentwise dependencies). The main aspect of the framework is the use of the Kronecker product covariance matrix to model the geneexperiment interactions. The resulting novel gene coexpression measure, named Knorm correlation, can be understood as a natural extension of the widely used Pearson coefficient. Compared to Pearson approach, the Knorm correlation has a much smaller estimation variance and is asymptotically consistent with the Pearson coefficient. We demonstrated the advantages of the Knorm correlation in both simulation studies and real datasets applications. The Knorm correlation estimation procedure is implemented in the R package Knorm that is freely available from the Bioconductor website.