Biomedical Engineering Reference
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main problem in transform-based time-frequency decompositions. In applications
to event-related EEG responses, the time-frequency decomposition is usually per-
formed for each trial separately and then averaged and subjected to statistical com-
parison with a “baseline” period.
Since the matching pursuits approach chooses functions from a nonorthogonal
dictionary, it avoids biases resulting from identical tiling of the time-frequency
plane, as in other methods. Furthermore, the choice of Gabor functions ensures the
best possible time resolution allowed by the uncertainty principle. The original
Mallat-Zhang algorithm uses a dyadic dictionary in which the scale variable
s
[as
defined in (14.1)] is restricted to be a power of two [i.e.,
s
2
j
for 0
j
< log
2
(
N
)].
This restriction results in a bias toward frequencies that are of the form
Fs
/2
j
and
their multiples, where
Fs
is the sampling frequency. To reduce the bias in determin-
ing the location of component functions in the decomposition, an additional step of
searching on a finer grid is performed. Typically, this finer grid includes smaller
intervals in time between functions with small scale and smaller intervals in fre-
quency for functions with large scale. Durka et al. [36] introduced an alternative
method using a stochastic dictionary where the dictionary functions are evenly dis-
tributed in time-frequency space. However, this method is computationally more
expensive. In ERD/ERS applications where the results are computed by averaging
the Wigner-Ville distributions from multiple trials, the results obtained using sto-
chastic and dyadic dictionaries are not significantly different [37]. Typically, for
ERD/ERS analyses we use the original Mallat-Zhang algorithm with a dyadic dic-
tionary with subsampling in time and frequency for the two smallest and two largest
scale octaves, respectively.
=
<
14.3.3.2 Statistical Analysis of Nonphase-Locked Responses
To study event-related EEG responses in the context of functional brain activation,
time-frequency decomposition of the EEG signal must be followed by statistical
analysis of the time-frequency signal representations in order to determine whether
there are energy changes during activation that are statistically different from
changes that might otherwise occur without activation. For this purpose a reference
or baseline interval may be chosen from a variety of possible sources. In reality there
is no such time interval when one can be sure that the EEG signal contains no energy
related to brain activation or cortical computation. This problem is analogous to
the search for an “inactive” reference in EEG recordings, though the search here is
in time instead of space. The best reference interval would be one under which all
conditions are equal to the experiment except the functional task under study. The
most frequently chosen reference interval is a time immediately preceding the stimu-
lus or behavior that marks the onset of each trial or repetition of a functional task.
The main potential pitfall of this approach is contamination of the baseline interval
by brain activation or deactivation due to stimuli or responses from the previous
trial, extraneous stimuli (e.g., people talking or moving nearby), or anticipation of
regularly occurring stimuli (thus the need for jittered intertrial intervals).
An alternative approach is to take random samples of epochs throughout the
recorded experiment to generate a surrogate distribution of energy estimates that is
independent of the timing of the task. One can also record a long segment of EEG
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