Biomedical Engineering Reference
In-Depth Information
As it is equivalent, in the remainder of this article, an atom of the dictionary is
parameterized by
(
t 0 ,f,ξ
)
instead of
(
t 0 ,f,σ
)
. This is because ξ directly qualifies
the transient ( ξ<
) nature of the activity. Both types of
parameterizations provide for a convenient interpretation of events as they account
for the variability in the duration ( ξ or σ ), latency ( t 0 ) and frequency ( f )of
activities.
2
) vs. oscillatory ( ξ
2
7.3.3
Consensus Matching Pursuit
Consensus Matching Pursuit (CMP) is an evolution of the standard matching pursuit
algorithm presented in Sect. 7.3.1 . It is designed to take advantage of the multitrial
nature of MEG and EEG measurements. Indeed, as events of interest are supposed
to be evoked by the experimental protocol, such events should repeat in every trial
of the experiment. Traditionally, in multitrial data analysis, trials are just averaged,
which is simple and easy. Unfortunately, as explained in Sect. 7.1.3 , working with
averaged data has two major drawbacks:
1. Average activities do not give access to the variability of the events of interest
across trials;
2. The events detected in the averaged signals are often deformed both in their
amplitudes and durations, as illustrated in Fig. 7.2 b-d.
To overcome these difficulties, CMP completely avoids the use of averaging and
instead uses a voting scheme. Each individual signal is first represented into a time-
frequency- ξ map (an extension of the more classical time-frequency map). Such
maps provide for each atom (i.e. each possible value of
(
t 0 ,f,ξ
)
) its associated
amplitude obtained by convolving s k (
t
)
with the atom. As atoms vary smoothly,
with
the map is also smooth, and its peaks (local maxima of the map
with respect to the variables
(
t 0 ,f,ξ
)
(
t 0 ,f,ξ
)
) indicate atoms that locally best represent
the signal.
In practise, the dictionary is discretized: the time step is given by the sampling
of the signal, and the ranges of the parameters in the frequency and ξ dimensions
derive from a priori information on the range of interest. Hereafter, discretization of
ξ is set to
.Foragiven ξ and a particular window length,
only a certain range of frequencies are acceptable, as the time-support of the atom
(given by σ ) must be smaller than the signal time window. Moreover, we choose not
to analyze high frequencies ( f>
0
.
8;1
.
5;3;5;7;9;13;25
):
this stems from the assumption that high-frequency activity must be oscillatory. In
the maps, frequencies that were not computed were set to zero.
To extract the most sensible atoms that repeat across trials, the peaks of the
time-frequency- ξ map are extracted for each trial. Each peak then votes in a voting
map common to all trials with a weight given by the amplitude associated with the
peak (a vote is a smooth function around the peak position). Once the votes of all
the peaks of all the trials have been accumulated, the highest peak of the voting
15
Hz ) for small oscillation parameters ( ξ<
2
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