Applying ICA in EEG: Choice of the Window Length and of the Decorrelation Method - Biomedical Engineering Systems and Technologies - page 246

structures and the resulting EEG is a linear mixture (with unknown or difficult to model
parameters) of brain sources and other electro-physiological disturbances, often with a
low signal to noise ratio (SNR) [2]. It is widely assumed that electrical brain potentials
recorded by the electrodes mainly arise from synchronous activity of neurons within
localized cortical patches . The far-field projection of such locally generated activity
can be suitably model by the projection of a single equivalent current dipole placed at
the center of the patch, resulting in a linear mixing of mostly dipolar sources on the
EEG [3].
The blind source separation (BSS) is a nowadays well established method to retrieve
original sources from the EEG mixing, as it can estimate both the mixing model and
original sources [4]. In particular, approaches based on High Order Statistics (HOS)
such as Independent Component Analysis (ICA) are common methods in this context
and have been very useful for denoising purpose or brain sources identification. Gen-
erally, ICA algorithms include a preliminary decorrelation step based on second order
statistics (estimated on a user chosen window length), which serves as an initialization
for the next optimization step (independence maximization). Still, there is an infinite
number of possible decorrelation matrices (as they are determined up to an arbitrary
rotation). The two most popular decorrelation techniques are whitening and sphering,
and it seems that they might influence the final separation results, especially in EEG
applications [5]. In this paper, two issues will then be evaluated: 1) the accuracy of the
decorrelation matrix estimation given the considered data length and 2) the sensitivity
to the initialization step using whitening or sphering in the specific context of dipolar
sources mixing. Four ICA algorithms based on HOS have been chosen: FastICA [6],
Extended InfoMax [7], AMICA [8] and JADER [9].
1) The use of BSS on EEG signals implicitly assumes that the estimated second order
statistics are meaningful. In order to ensure the reliability of these statistics, different
authors propose optimal sample sizes (i.e. EEG signal time points), generally equal to
k n 2 where n is number of channels and k is some empirical constant varying from 5

to 32 [10-12]. If these assumptions are correct, large amount of channels requires huge
sample sizes, processing and time resources. On the other hand, EEG signals are at most
short term stationary, so it would be interesting to find a sufficient inferior bound for
the number of necessary samples. The first question is then how to define a minimum
sample size that provides reliable estimation of sources and mixing model.
2) The second issue addressed in this paper concerns the sensitivity of the BSS/ICA
performance given the initial decorrelation step in the dipolar mixing context. In the
literature [13], some authors observed that using different initializations (different decor-
relation methods like classical whitening or sphering), the results are more or less bi-
ologically plausible, meaning that more or less dipolar sources are retrieved from the
data. A recent extensive study from the same authors [5] proposed an evaluation of
the ability of 18 source separation methods to result in maximally independent com-
ponent processes with nearly dipolar scalp projection. The results show that AMICA
and Extended InfoMax give better performances compared to FastICA and JADER.
Both AMICA and Extended InfoMax begin by sphering the data, while FastICA and
JADER begin with a classical whitening step. We would like to evaluate the impact of

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