  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 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.
