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Shrinkage approach for spatiotemporal EEG covariance matrix estimation

Beltrachini, Leandro, von Ellenrieder, Nicolas and Muravchik, Carlos 2013. Shrinkage approach for spatiotemporal EEG covariance matrix estimation. IEEE Transactions on Signal Processing 61 (7) , pp. 1797-1808. 10.1109/TSP.2013.2238532

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Abstract

The characterization of the background activity in electroencephalography (EEG) is of interest in many problems, such as in the study of the brain rhythms and in the solution of the inverse problem for source localization. In most cases the background activity is modeled as a random process, and a basic characterization is done via the second order moments of the process, i.e., the spatiotemporal covariance. The general spatiotemporal covariance matrix of the background activity in EEG is extremely large. To reduce its dimensionality it is generally decomposed as a Kronecker product of a spatial and a temporal covariance matrices. They are generally estimated from the data using sample estimators, which have numerical and statistical problems when the number of trials is small. We present a shrinkage estimator for both EEG spatial and temporal covariance matrices of the background activity. We show that this estimator outperforms the commonly used ones when the quantity of available data is low. We find sufficient conditions for the consistency of the shrinkage estimator and present some results concerning its numerical stability. We compare several shrinkage approaches and show how to improve the estimator by incorporating known structure in the covariance matrix based on background activity models. Results using simulated and real EEG data support our approach.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Physics and Astronomy
Cardiff University Brain Research Imaging Centre (CUBRIC)
Psychology
Subjects: Q Science > QC Physics
Uncontrolled Keywords: Background activity; Covariance matrix estimation; EEG; Shrinkage estimator
Publisher: Institute of Electrical and Electronics Engineers
ISSN: 1053-587X
Date of Acceptance: 14 December 2012
Last Modified: 08 May 2019 13:48
URI: http://orca.cf.ac.uk/id/eprint/101084

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