Application to biomedical signals - Practical Biomedical Signal Analysis Using MATLAB - page 147

R i x

that all parameters, except the amplitude weight a i , are kept identical

across all trials, yet not set a priori to any particular values. This approach guarantees
that only these features, which consistently occurred across all trials, emerge from
the multi-trial decomposition. Relaxing the constraint of a constant phase allows for
accounting for the jitter and some limited shape variability of s i :

= , g γ i

x i ( t )= a i s i ( t )+ n i ( t ) (4.16)

Both approaches were successfully validated in the task of analysis of habituation
influence on amplitude and in the latter case also on the latency of auditory M100
evoked magnetic field. At first glance, the relaxation of the phase constraint may be
seen as a favorable reduction of the bias of the estimation; however, the algorithm be-
comes more prone to individual noise patterns in each trial [Sieluzycki et al., 2009b].
Therefore, neither of the two approaches is superior to the other one in an absolute
sense. They should be used according to the particular conditions of the paradigm,
taking into account the inherent assumptions and limitations of the two methods.
Recently, [Benar et al., 2009] introduced a so-called consensus matching pursuit
algorithm, with which the authors tried to explain the trial-to-trial variability in the
parameter space by means of a certain restricted variation of the Gabor functions ap-
proximating each trial independently within a certain neighborhood of the so-called
consensus atom. This consensus atom is selected by means of a specific voting pro-
cedure, and is the most representative atom for all trials.This approach constitutes a
further step in releasing constraints on the parameters of the Gabor functions, since it
allows amplitude, scale, frequency, and phase variations, at least to a certain degree,
which is controlled by a Gaussian kernel.

4.1.7.2.4 ERP topography So far we discussed the evaluation of the time course
of the ERP. Much valuable information is obtained by considering ERP topography
since the distribution of the current sources in the brain is reflected in the spatial
pattern of evoked potential, which can be visualized in the form of an ERP map.
The first problem one has to face when analyzing multichannel EEG data, is the
problem of reference. EEG can only be measured as a difference of potentials, and
as such the measured waveform differs when the reference electrode changes.This
may influence the interpretation of the results [Murray et al., 2008].
One popular solution to this problem is the use of global field power (GFP) intro-
duced by Lehmann and Skrandies [Lehmann and Skrandies, 1980]. GFP is computed
at any moment in time as the standard deviation of voltage across the set of channels.
The GFP tells how steep on average are gradients of potentials across the electrode
montage. In this sense the GFP is a measure of the strength of activation at a given
time point. It can be evaluated with the standard ERP parameters like: latencies, area,
peak amplitude, etc. 3 The GFP extrema can be used in order to identify brain activity
components in a reference invariant way.

3 It is important to note that because GFP is a non-linear transformation, the GFP of the group-average
ERP is not equivalent to the mean GFP of the single-subject ERPs.