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Estimating Evoked Dipole Responses in Unknown Spatially Correlated Noise with EEG/MEG Arrays
, 2000
"... We present maximum likelihood (ML) methods for estimating evoked dipole responses using electroencephalography (EEG) and magnetoencephalography (MEG) arrays, which allow for spatially correlated noise between sensors with unknown covariance. The electric source is modeled as a collection of current ..."
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Cited by 9 (1 self)
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We present maximum likelihood (ML) methods for estimating evoked dipole responses using electroencephalography (EEG) and magnetoencephalography (MEG) arrays, which allow for spatially correlated noise between sensors with unknown covariance. The electric source is modeled as a collection of current dipoles at fixed locations and the head as a spherical conductor. We permit the dipoles' moments to vary with time by modeling them as linear combinations of parametric or nonparametric basis functions. We estimate the dipoles' locations and moments and derive the CramrRao bound for the unknown parameters. We also propose an MLbased method for scanning the brain response data, which can be used to initialize the multidimensional search required to obtain the true dipole location estimates. Numerical simulations demonstrate the performance of the proposed methods. Index TermsCramrRao bound, dipole source, EEG, evoked responses, maximum likelihood parameter estimation, MEG, sensor arr...
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 8 (3 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.
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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Cited by 7 (4 self)
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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.
Maximum likelihood spatiotemporal EEG/MEG source analysis
"... Introduction EEG/MEG noise has an unequal variance and is correlated, both in space and in time. Noise variance may differ greatly between samples or sensors, and correlations between samples or sensors can be very high [14]. If these noise characteristics are neglected, then an EEG/MEG source an ..."
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Cited by 1 (1 self)
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Introduction EEG/MEG noise has an unequal variance and is correlated, both in space and in time. Noise variance may differ greatly between samples or sensors, and correlations between samples or sensors can be very high [14]. If these noise characteristics are neglected, then an EEG/MEG source analysis will yield unreliable results [e.g. 5, 6]. First, source parameter estimates will be inefficient. That is, their standard errors will be too high. Second, the estimated covariance matrix of the parameter estimates will be inaccurate. In general it will give a too optimistic impression of precision. Third, goodness of fit measures will be unreliable, which may result in over or undermodeling of the data. For these reasons, it is very beneficial to incorporate the spatiotemporal noise covariance in the analysis. Although the spatial covariance is incorporated quite often [611], the temporal covariance is disregarded up to now. Therefore, we are developing a method to incorporate the
The Wald Test and Cramér–Rao Bound for Misspecified Models in Electromagnetic Source Analysis
"... Abstract—By using signal processing techniques, an estimate of activity in the brain from the electro or magnetoencephalogram (EEG or MEG) can be obtained. For a proper analysis, a test is required to indicate whether the model for brain activity fits. A problem in using such tests is that often, ..."
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Abstract—By using signal processing techniques, an estimate of activity in the brain from the electro or magnetoencephalogram (EEG or MEG) can be obtained. For a proper analysis, a test is required to indicate whether the model for brain activity fits. A problem in using such tests is that often, not all assumptions are satisfied, like the assumption of the number of shells in an EEG. In such a case, a test on the number of sources (model order) might still be of interest. A detailed analysis is presented of the Wald test for these cases. One of the advantages of the Wald test is that it can be used when not all assumptions are satisfied. Two different, previously suggested, Wald tests in electromagnetic source analysis (EMSA) are examined: a test on source amplitudes and a test on the closeness of source pairs. The Wald test is analytically studied in terms of alternative hypotheses that are close to the null hypothesis (local alternatives). It is shown that the Wald test is asymptotically unbiased, that it has the correct level and power, which makes it appropriate to use in EMSA. An accurate estimate of the Cramér–Rao bound (CRB) is required for the use of the Wald test when not all assumptions are satisfied. The sandwich CRB is used for this purpose. It is defined for nonseparable least squares with constraints required for the Wald test on amplitudes. Simulations with EEG show that when the sensor positions are incorrect, or the number of shells is incorrect, or the conductivity parameter is incorrect, then the CRB and Wald test are still good, with a moderate number of trials. Additionally, the CRB and Wald test appear robust against an incorrect assumption on the noise covariance. A combination of incorrect sensor positions and noise covariance affects the possibility of detecting a source with small amplitude. Index Terms—Approximate model, constrained optimization, Fisher information with constraints, model checking, parameter covariance, separable least squares, source localization. I.