Quantitative analysis of EEG signals: Time-frequency methods and ...

the ones having wide peaks (being the limit case a wide band spectrum corresponding
to noise or to a chaotic system). Then, the concept of entropy isvery interesting due to
the fact that it can be associated to frequency tuning of the neuronal groups.
Although in principle the entropy of the signal can be visualized from the Fourier
spectrum (i.e. just by looking how narrow or wide are the peaks), the WS allows the
following of its time evolution and furthermore, gives a reliable way of quantication.
Moreover, the advantage of dening the measure of entropy from the wavelet coecients
and not from other alternative time-frequency distribution as the Gabor Transform is
that the resolution of the Wavelet Transform is crucial for analyzing the evolution of
fast varying signals as in the case of event-related potentials.
7.2.6 Wavelet-Entropy vs. Chaos analysis
As stated in several parts of this thesis, ERPs can be considered as a selective enhancement,
synchronization or in another words, an ordering of the spontaneous EEG
oscillations. In this context, Wavelet Entropy appears as a natural and optimal method
for measuring this evoked ordering of the EEG signals.
Although using a completely dierent approach, and applied to dierenttypeofEEG
signals, Chaos analysis was in principle used for answering similar type of questions. Parameters
such asD 2 or 1 give a measure of the complexity, chaoticity, and by extension
give an idea of the order of the signal. In this context, converging low values of D 2 for
example, were used as a proof of a low dimensional, deterministic, ordered dynamic of
the EEG signals in several situations. However as I already mentioned, chaos methods
are very dicult to apply to EEG signals and furthermore, in many cases lead to pitfalls
and wrong results.
As discussed in section x7.1.3, it is very dicult to resolve disputes about the
nature of EEG signals by using these methods and it is more reasonable to consider
other physiological evidence as for example the response of the EEG to stimulation
(ERP). However, Chaos methods are limited to the analysis of long and stationary EEG
recordings, being impossible to implement them to the analysis of fast varying nonstationary
signals as ERPs. On the other hand, WS is applicable to ERPs and appears
as an ideal parameter for obtaining quantitative answers to these type of questions. In
particular, I showed in section x6.3.2 that decreases of entropy after stimulation were
correlated with an ordering of the brain rhythms involved in a cognitive process.
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