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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.
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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Cited by 1 (1 self)
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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.
Inverse problems optimization Signal classification
"... Abstract Epilepsy is a neurological disorder caused by intense electrical activity in the brain. The electrical activity, which can be modelled through the superposition of several electrical dipoles, can be determined in a noninvasive way by analysing the electroencephalogram. This source localiza ..."
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Abstract Epilepsy is a neurological disorder caused by intense electrical activity in the brain. The electrical activity, which can be modelled through the superposition of several electrical dipoles, can be determined in a noninvasive way by analysing the electroencephalogram. This source localization requires the solution of an inverse problem. Locally convergent optimization algorithms may be trapped in local solutions and when using global optimization techniques, the computational effort can become expensive. Fast recovery of the electrical sources becomes difficult that way. Therefore, there is a need to solve the inverse problem in an accurate and fast way. This paper performs the localization of multiple dipoles using a global–local hybrid algorithm. Global convergence is guaranteed by using space mapping techniques and independent component analysis in a computationally efficient way. The accuracy is locally obtained by using the Recursively Applied and ProjectedMUltiple Signal Classification (RAPMUSIC) algorithm. When using this hybrid algorithm, a four times faster solution is obtained.
Stable Focal Inverse Source Localization Using Combinatorial Optimization Techniques Combined With Regularization Methods
, 1998
"... The inverse problem arising from EEG and MEG is largely underdetermined. One strategy to alleviate this problem is the restriction to a limited number of pointlike sources, the focal source model. Although the singular value decomposition of the spatiotemporal data gives an estimate of the minimal ..."
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The inverse problem arising from EEG and MEG is largely underdetermined. One strategy to alleviate this problem is the restriction to a limited number of pointlike sources, the focal source model. Although the singular value decomposition of the spatiotemporal data gives an estimate of the minimal number of dipoles contributing to the measurement, the exact number is unknown in advance and noise complicates the reconstruction. Classical nonlinear dipole fit algorithms do not give an estimate for the correct number because they are not stable with regard to an overestimation of this parameter. Too many sources may only describe noise, but can still attain a large magnitude during the inverse procedure and may be indiscernible from the true sources. This paper describes a nonlinear dipole fit reconstruction algorithm with a new regularization approach for the embedded linear problem, automatically controlled by the noise in the data and the condition of the occuring least square problem...