Bi-Smoothed Functional Independent Component Analysis for EEG Artifact Removal
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Functional dataFunctional kurtosisPenalized splinesSmoothed principal componentsAuditory–motor coupling taskEEGMotion artifacts
Vidal, M.; Rosso, M.; Aguilera, A.M. Bi-Smoothed Functional Independent Component Analysis for EEG Artifact Removal. Mathematics 2021, 9, 1243. https://doi.org/10.3390/math9111243
SponsorshipMethusalem funding from the Flemish Government; Project MTM2017-88708-P of the Spanish Ministry of Science, Innovation and Universities; Project FQM-307 of the Government of Andalusia (Spain)
Motivated by mapping adverse artifactual events caused by body movements in electroencephalographic (EEG) signals, we present a functional independent component analysis based on the spectral decomposition of the kurtosis operator of a smoothed principal component expansion. A discrete roughness penalty is introduced in the orthonormality constraint of the covariance eigenfunctions in order to obtain the smoothed basis for the proposed independent component model. To select the tuning parameters, a cross-validation method that incorporates shrinkage is used to enhance the performance on functional representations with a large basis dimension. This method provides an estimation strategy to determine the penalty parameter and the optimal number of components. Our independent component approach is applied to real EEG data to estimate genuine brain potentials from a contaminated signal. As a result, it is possible to control high-frequency remnants of neural origin overlapping artifactual sources to optimize their removal from the signal. An R package implementing our methods is available at CRAN.