Applying ICA in EEG: Choice of the Window Length and of the Decorrelation Method - Biomedical Engineering Systems and Technologies - page 251

(a) (b) (c) (d)
Fig. 3. Histograms of real SEEG samples ((a) background and (b) ictal activities) and histograms
of generalized Gaussian simulated data ((c) super-Gaussian and (d) sub-Gaussian data)

4 Simulated Data Set

The algorithms performances are assessed on two types of data. Following our BIOSIG-
NALS paper [16], the first data set consists in simulated generalized Gaussian sources
mixed by randomly simulated matrices. The second one is obtained by mixing sources
given by macroscopic neural populations models [17] with mixing matrices computed
from a realistic three layers lead field model.

4.1 Random Data Set

We have chosen to simulate stationary white source signals, as the retrieval of time
structures is not the purpose of this work (in fact, in all the tested algorithms, as in
most of the HOS type methods, the time structure is ignored). In order to simulate
sources with realistic probability distributions, we analysed depth intra-cerebral mea-
sures (SEEG). According to our observations (see also [11, 10]), the probability distri-
bution of the electrical brain activity signals can be suitably modelled by Generalized
zero-mean Gaussians, as shown in fig. 3(a) and fig. 3(b)). For this reason we used ran-
domly generated both supergaussian (Laplace - Figure 3(c)) and subgaussian (close to
uniform (Figure 3(d))) distributions.
Several simulations were made, using 8 , 16 , 24 , 32 and 48 source signals. Half of
the sources were generated as supergaussian and half as subgaussian. The sources were
afterwards mixed using a randomly generated mixing matrix A (uniform distribution
in [ − 1 , 1] ). We then consider here the performance of each of the four ICA algorithms
facing simulated stationary non-artefacted data. Such evaluation is likely to give us a
rule of a minimum amount of data needed for a reliable source separation in favourable
conditions (after an artefact elimination step for example).

4.2 Plausible Data Set

More realistic contexts is to be simulated in order to evaluate the behaviour of the
algorithm confronted to the real EEG BSS problem. We then propose a second data
set where the sources are simulated by a macroscopic model [17] able to reproduce
normal background activity as well as pre-ictal and ictal (epileptic) electromagnetic ac-
tivity. The mixing matrices are designed using a fast accurate three layers head model