Biomedical Engineering Reference
In-Depth Information
estimate and
k
is a multiplier. As reported in the EEGLAB tutorial
5
,thevalueof
k
increases as the number of channels increases. In general, it is important to give ICA
as much data as possible for successful estimation. ICA works best when a large
amount of basically similar and mostly clean data are available.
3.6.2.4
Possible applications
The most often reported applications of ICA in the field of biomedical signal anal-
ysis are related to EEG and MEG artifact reduction (Sect. 4.1.5) and feature extrac-
tion in studies of event-related brain dynamics [Onton and Makeig, 2006] and as
a preprocessing step in the search of sources of EEG and MEG activity localiza-
tion [Grau et al., 2007]. ICA is applied as well in analysis of heart (Sect. 4.2) and
muscle signals (Sect. 4.3).
3.6.3 Multivariate matching pursuit (MMP)
In Sect. 2.4.2.2.7 a single channel version of matching pursuit algorithm was
described. The MP algorithm decomposes the signal into waveforms
g
γ
(time-
frequency atoms). Each atom is characterized by a set of parameters γ. In the case
of Gabor functions (equation 2.114) these are γ
where
u
-time trans-
lation,
f
-frequency, σ - time width, φ - phase. The MP algorithm can be extended
into multivariate cases by introducing multichannel time-frequency atoms. A multi-
channel time-frequency atom is a set of functions
g
γ
=
{
u
,
f
,
σ
,
φ
}
g
1
γ
,
g
2
γ
,...,
g
n
γ
}
=
{
. Each of the
g
i
γ
functions is a univariate time-frequency atom. Let
x
x
1
x
2
x
n
=
{
,
,...,
}
be the
n
channel signal. The multivariate matching pursuit acts in the following iterative way:
1. The null residue is the signal
R
0
x
R
0
x
1
R
0
x
2
R
0
x
n
=
{
,
,...,
}
=
x
.
2. In the
k
-th iteration of the algorithm a multichannel atom
g
γ
k
is selected that
satisfies the optimality criterion.
3. The next residuum is computed as the difference of the current residuum and
the projection of the selected atom on each channel. For channel
i
it can be
expressed as:
R
k
+
1
x
i
R
k
x
i
R
k
x
i
g
i
γ
k
g
i
γ
k
.
=
−
,
An interesting possibility in the MMP framework is that the optimality criterion can
be model driven, i.e., it can correspond to the assumed model of signal generation. As
an example we can presume that each given component of the measured multichan-
nel signal results from the activity of an individual source, and that the propagation
of signal (e.g., electric or magnetic field) from the source to the sensors is instanta-
neous. In such a case, the most straightforward optimality condition is that in a given
iteration
k
the atom
g
γ
k
is selected which explains the biggest amount of total energy
(summed over the channels) with the constraint that all the univariate atoms in in-
dividual channels have all the parameters identical, excluding the amplitude which
5
http://sccn.ucsd.edu/wiki/EEGLAB
.
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