## Spatiotemporal EEG/MEG source analysis based on a parametric noise covariance model (2002)

Venue: | IEEE Transactions on Biomedical Engineering |

Citations: | 8 - 3 self |

### BibTeX

@ARTICLE{Huizenga02spatiotemporaleeg/meg,

author = {Hilde M. Huizenga and Jan C. De Munck and Lourens J. Waldorp and Raoul P. P. P. Grasman and Student Member and Student Member},

title = {Spatiotemporal EEG/MEG source analysis based on a parametric noise covariance model},

journal = {IEEE Transactions on Biomedical Engineering},

year = {2002},

volume = {49},

pages = {200--2}

}

### OpenURL

### Abstract

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Citation Context ...x models the temporal covariances as lag dependent. In the second part, sources are estimated given this Kronecker noise model. This can be done very efficiently due to the Kronecker formulation [1], =-=[19]-=-. The method is described in more detail in Section II. In Section III, the method is compared to the standard OLS approach. II. METHODS A. Observed Noise Covariance EEG and/or MEG is measured in tria... |

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Citation Context ...source analysis. The essential feature is that the estimation problem is split into two parts. First, a model is fitted to the observed noise covariance matrix. This model is a Kronecker product [1], =-=[14]-=-–[18] of a spatial matrix and a temporal matrix. The spatial matrix models the spatial covariances by a function dependent on sensor distance. The temporal matrix models the temporal covariances as la... |

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Citation Context ...permuted version of [24], [19]. This is especially useful if one of the matrices is Toeplitz, as in (8). ML noise covariance estimates can also be obtained by minimizing (13) for and separately [15], =-=[16]-=-, [18]. That is, an estimate for is first obtained given a starting value for , for example the unit matrix. Then, an estimate for is obtained given the previous estimate of . This process is then rep... |

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Citation Context ...re obtained by minimizing (13). There exist, however, alternative approaches. OLS noise covariance estimates can also be obtained by performing a singular value decomposition on a permuted version of =-=[24]-=-, [19]. This is especially useful if one of the matrices is Toeplitz, as in (8). ML noise covariance estimates can also be obtained by minimizing (13) for and separately [15], [16], [18]. That is, an ... |

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Citation Context ...e covariance matrix of the source parameter estimates is corrected for the constraints as outlined in [25], [28]. Note that setting both in (19) equal to the unit matrix yields the OLS Hessian matrix =-=[29]-=-, [30]. III. RESULTS First, the noise covariance model is fitted to empirical EEG data. Then, OLS and PEGLS source estimates are compared in a simulation study. Finally, the covariance matrix of the s... |

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Citation Context ...The Netherlands. Publisher Item Identifier S 0018-9294(02)04842-5. 0018-9294/02$17.00 © 2002 IEEE published in which the spatial covariance is incorporated, both in an instantaneous analysis [3], [6]–=-=[9]-=-, as well as in a spatiotemporal analysis [10]–[12]. But the temporal covariance has received less attention (see, however, [13]). Therefore, a method has been developed to incorporate the spatiotempo... |

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Citation Context ...0018-9294(02)04842-5. 0018-9294/02$17.00 © 2002 IEEE published in which the spatial covariance is incorporated, both in an instantaneous analysis [3], [6]–[9], as well as in a spatiotemporal analysis =-=[10]-=-–[12]. But the temporal covariance has received less attention (see, however, [13]). Therefore, a method has been developed to incorporate the spatiotemporal noise covariance into a source analysis. T... |

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Citation Context ...9294(02)04842-5. 0018-9294/02$17.00 © 2002 IEEE published in which the spatial covariance is incorporated, both in an instantaneous analysis [3], [6]–[9], as well as in a spatiotemporal analysis [10]–=-=[12]-=-. But the temporal covariance has received less attention (see, however, [13]). Therefore, a method has been developed to incorporate the spatiotemporal noise covariance into a source analysis. The es... |

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Citation Context ...oth EEG and MEG covariances quite well [1], [3]. Let be the noise standard deviation at sensor , let be the distance between sensors and , and let the spatial (co)variance between sensors and be (cf. =-=[22]-=-) where and determine the spatial correlations. Since EEG is measured with respect to a reference, the spatial covariances also depend on the reference. Therefore, (9) should be transformed to the ref... |

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Citation Context ...all source parameters with the square root of . IV. DISCUSSION PEGLS source estimates are more reliable than OLS estimates, these effects will even be more pronounced for lower signal to noise ratios =-=[31]-=-. In addition, the PEGLS covariance matrix of the source parameter estimates yields a far more reliable impression of precision than the OLS matrix. However, PEGLS requires extra computational effort.... |

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Citation Context ...riance matrix of the source parameter estimates is corrected for the constraints as outlined in [25], [28]. Note that setting both in (19) equal to the unit matrix yields the OLS Hessian matrix [29], =-=[30]-=-. III. RESULTS First, the noise covariance model is fitted to empirical EEG data. Then, OLS and PEGLS source estimates are compared in a simulation study. Finally, the covariance matrix of the source ... |

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Citation Context ...tion vectors have unit norm. In addition, in case of MEG and a spherical head model, it is required to impose the constraints that sources are tangential [25]. The augmented Lagrangian algorithm [25]–=-=[28]-=- takes these constraints into account by minimizing a weighted combination of (17) and the constraint functions. After this minimization of (17), the estimated source amplitudes are derived from (16).... |

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Citation Context ...sterdam, The Netherlands. Publisher Item Identifier S 0018-9294(02)04842-5. 0018-9294/02$17.00 © 2002 IEEE published in which the spatial covariance is incorporated, both in an instantaneous analysis =-=[3]-=-, [6]–[9], as well as in a spatiotemporal analysis [10]–[12]. But the temporal covariance has received less attention (see, however, [13]). Therefore, a method has been developed to incorporate the sp... |

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Citation Context ...SPATIOTEMPORAL EEG/MEG SOURCE ANALYSIS BASED ON A PARAMETRIC NOISE COVARIANCE MODEL 535 C. Estimation of Noise Parameters Noise covariance parameters can be estimated by iteratively minimizing (e.g., =-=[23]-=-) (10) where denotes the trace. Different choices of the weighting matrix yield different types of noise parameter estimates [23]. yields GLS estimates, which are asymptotically efficient. However, th... |

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Citation Context ...ividing (4) by a factor (e.g., [20]); cf. [3], [6], [9] Inserting this estimate , in (3) yields the unparametrisized estimated generalized least squares (UEGLS) function [9]. This UEGLS approach (cf. =-=[21]-=-) generates more accurate results than the standard OLS approach in which is set to , the unit matrix with ones on the diagonal and zero off-diagonal elements. However, there are also disadvantages. F... |

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Citation Context ...ephalogram (MEG) noise has an unequal variance and is correlated, both in space and in time. Noise variance may differ greatly between sensors, and correlations between samples or sensors can be high =-=[1]-=-–[4]. In a standard, that is Ordinary Least Squares (OLS), source analysis these noise characteristics are neglected, which has two disadvantages [5, p. 272], [6]. First, source parameter estimates ar... |

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Citation Context ...l covariance is incorporated, both in an instantaneous analysis [3], [6]–[9], as well as in a spatiotemporal analysis [10]–[12]. But the temporal covariance has received less attention (see, however, =-=[13]-=-). Therefore, a method has been developed to incorporate the spatiotemporal noise covariance into a source analysis. The essential feature is that the estimation problem is split into two parts. First... |

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Citation Context ...ot contain signal, for example from baseline measurements. Presently, we are working on the following extensions. First, various goodness of fit measures have been proposed for the instantaneous case =-=[32]-=-. Generalization to the spatiotemporal case is quite straightforward. Second, the availability of an accurates538 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 49, NO. 6, JUNE 2002 covariance matr... |

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