Biomedical Engineering Reference
In-Depth Information
b
a
Vote map, iteration 3
Vote map, iteration 1
ξ
=0.8
ξ
=1.5
ξ
=3
ξ
=0.8
ξ
=1.5
ξ
=3
41
31
21
11
1
-
41
31
21
11
1
-
41
41
31
21
11
1
-
0.2
41
31
21
11
1
-
0.2
41
31
21
11
1
-
0.2
31
21
11
1
-
0.2
0
0.2
0.4
0.2
0
0.2
0.4
0.2
0
0.2
0.4
0
0.2
0.4
0
0.2
0.4
0
0.2
0.4
ξ
=5
ξ
=7
ξ
=9
ξ
=5
ξ
=7
ξ
=9
41
31
21
11
1
-
41
31
21
11
1
-
41
31
21
11
1
-
41
31
21
11
1
-
41
31
21
11
1
-
41
31
21
11
1
-
0.2
0
0.2
0.4
0.2
0
0.2
0.4
0.2
0
0.2
0.4
0.2
0
0.2
0.4
0.2
0
0.2
0.4
0.2
0
0.2
0.4
ξ
=13
ξ
=25
ξ
=13
ξ
=25
41
31
21
11
1
-
0.2
41
31
21
11
1
-
0.2
41
31
21
11
1
-
0.2
41
31
21
11
1
-
0.2
0
0.2
0.4
0
0.2
0.4
0
0.2
0.4
0
0.2
0.4
time (s)
time (s)
time (s)
time (s)
Fig. 7.7
The voting map at two iterations of the algorithm for a given (synthetic) trial.
Deep blue
areas correspond to disallowed parameter values (Sect.
7.3.3
). The
black dot
in each map indicates
the highest peak of the map, i.e., the best “common atom” extracted at that iteration: (
a
)Result
after one iteration; (
b
) Result after three iterations. Please note that each iteration is normalized
independently
map is extracted as the next most significant “consensus atom” to extract for the
matching pursuit algorithm. As this “consensus atom” is not necessarily a peak in
the individual trial maps, the peak closest to this “consensus atom” is computed
and the corresponding atom is recorded for each individual map. Its contribution is
subtracted from the signal to finish the iteration of the matching pursuit algorithm.
Figure
7.7
illustrates two iterations of the algorithm for one trial of a synthetic
dataset.
After
P
iterations of CMP, the signals have been decomposed as:
P
s
k
(
t
)=
a
ik
ψ
p
i
(
k
)
(
t
)+
n
k
(
t
)
.
(7.10)
i
=1
Because of the voting map, the CMP decomposition guarantees a cross-trial
coherence between atom parameters
p
i
(
k
)
.
7.3.4
Experiments with Real Data
Other adaptations of the matching pursuit algorithm have been devised to deal with
EEG data. Evoked Matching Pursuit (EMP) is a standard matching pursuit algorithm
applied on a signal obtained by averaging all the individual trials. Closer to the
Consensus Matching Pursuit, Induced Matching Pursuit (IMP) is a matching pursuit
algorithm applied on a multi-trial dataset obtained by averaging the time-frequency
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