Single-Trial Analysis of Bioelectromagnetic Signals: The Quest for Hidden Information - Modeling in Computational Biology and Biomedicine - page 243

Fig. 7.8 Comparison of the atoms recovered by three variants of matching pursuit: EMP, IMP and
CMP. Atoms are shown a time-frequency map, the parameter ξ being illustrated by a small wavelet
in the plot. The indices above the wavelets correspond to the iteration at which the atom has been
extracted by matching pursuit

power representations of all the individual trials. It was originally proposed by
Gribonval et al. for multichannel data [ 11 ]. Figure 7.8 compares the atoms obtained
on a real dataset with the three variants of matching pursuit: CMP (the variant
described in this article), EMP and IMP.
The real dataset was measured during a visual task which is a variation of
the protocol introduced in [ 21 ]. The original protocol consisted in observing
a succession of illusory triangles (curved and non-curved), real triangles and
no-triangle stimuli. This results in a mixture of event-related potentials and high-
frequency oscillatory activity. The variation consists in presenting the triangles
pointing either up or down. The subject is instructed to press a button as a response
to the curved illusory triangles. Intracerebral EEG was acquired (sampled at 1 kHz)
from an epileptic patient implanted in the occipital region (stereotaxic EEG, SEEG)
for the sole clinical purpose of presurgical evaluation. The studied channel is located
in the occipital cortex, for which a standard time-frequency has shown there is high-
frequency activity. For evoked potential (frequencies < 10

Hz), the three methods
identified rather similar atoms. Both IMP and CMP identify an oscillation around
30 Hz, which was not visible with EMP. Furthermore, CMP detects one oscillation
at 400 ms and 20 Hz. IMP missed this 20 Hz component because it required more
atoms to represent the averaged signal under 20 Hz. For EMP and IMP, these
missed components appear only if the number of extracted components is increased.
This shows that CMP provides a sparser description of the analyzed signal (or
equivalently a more accurate description for a limited of extracted components).

7.4 Success Stories

This section presents examples where single-trial analysis has allowed the extraction
of unique information that was not available on the averaged data.