IEEE Signal Processing - May 2018 - 85

automatically, depending on the type of artifact. A simple way
is to reject the data segment where the artifact is visually
clear. This is the case, for instance, for movement artifacts (a
participant's head moving during an experiment) that simultaneously affect a large number of channels over a given time
period. This step is still subjective, as the visual inspection is
user dependent.
Artifacts can also be detected and removed automatically. The simplest method involves comparing the EEG signal amplitude to an arbitrarily defined threshold signal to
remove nonphysiological, often saturated segments of very
high amplitude compared to the usual ±80 μV amplitude of
the background activity. Bad channels also can be recovered
by interpolation, using the surrounding electrodes (which is
more efficient when dense electrode arrays are available).
More sophisticated methods include filtering, which is now
widely available with any EEG reviewing software. Eye
blinks are often present during EEG experiments, and they
can be removed using the independent component analysis
method, which is performed manually or automatically
[4]. Recording the electrooculography signal simultaneously
with the EEG signals could help to precisely and automatically remove the eye blinks. In this case, adaptive filtering
has proven to be relatively efficient [15]. Muscle artifacts can
also severely corrupt EEG signals. They are more difficult to
remove because of the overlap with the EEG frequency band.
Several studies on simulated and real data have shown that
the use of blind source separation methods, such as canonical
correlation analysis, are powerful tools for removing muscle
artifacts [16], [17].

Reconstruction of EEG sources
To localize brain sources and reconstruct their time courses,
the following data are required:
■ the scalp-recorded EEG signals
■ the three-dimensional (3-D) positions of the electrodes
positioned on the head
■ the head model, which contains information about the electrical and geometrical characteristics of the head
■ the source model, which provides information about the location and orientation of the dipole sources to be estimated.
A template file for the 3-D electrode locations is often available
with the acquisition systems. However, in a patient- or subjectspecific context, the actual position may be required. A number
of 3-D digitizing devices allow for the registration of the electrode positions on the head, such as Fastrak Digitizer (Polhemus
Inc.) and Geodesic Photogrammetry System (EGI Inc.).
Realistic head models employing the boundary element method
(surfacic case) or the finite element method (volumic case)
allow for an accurate calculation of the electrical fields in the
brain. Compared to simple spherical head models, improved
realism in the description of the head geometry and in the tissues with their associated conductivities increases the quality of
the EEG forward/inverse solution. The source model is computed from the segmentation of the anatomical MRI (template or
subject specific). Usually, the white/gray matter interface is

chosen as the source space for the neocortical sources that
mostly contribute to EEG. The MRI anatomy and channel locations are coregistered using the same anatomical landmarks
(the left and right preauricular points and the nasion). In the following, we complement the aforementioned qualitative description of EEG source reconstruction with more formal aspects.
According to the dipole theory, EEG signals X (t) recorded
from M channels can be considered as linear combinations of
P time-varying current dipole sources S(t):
x 1 (t)
s 1 (t)
X (t) = f g p = G. f g p + N (t) = G.S (t) + N (t),
x M (t)
s p (t)
where G (M # P) is called the lead field matrix and N (t) is
the noise. G reflects the contribution of each brain source to
the sensors [9]. It is computed from a head model (volume
conductor) and from the positions of the electrodes. In the
case where the source distribution is constrained to a field of
current dipoles homogeneously distributed over the cortex and
normal to the cortical surface, the position and the orientation
of the sources are defined. For the methods described next, the
EEG inverse problem consists of estimating the source magnitude of
St (t) = W.X (t).

(1)

Several algorithms have been proposed to solve this problem
and estimate W based on different assumptions related to
the spatiotemporal properties of the sources and regularization constraints (see [9] for a review). Here, we describe two
methods widely used in EEG source connectivity analysis,
based respectively on a minimum norm estimate and a beamformer filter.
Weighted minimum norm estimation (wMNE) is one of the
most popular approaches. Here, W is estimated in such a way
as to produce the source distribution with the minimum power
that fits the measurements in a least-square error:
W wMNE = BG T (GBG T + mC) -1,
where m is the regularization parameter and C represents the
noise covariance matrix. The wMNE algorithm compensates
for the tendency of MNE to favor weak and surface sources
[18]. Matrix B adjusts the properties of the solution by reducing the bias inherent to the standard MNE solution.
Classically, B is a diagonal matrix built from matrix G with
nonzero terms inversely proportional to the norm of the lead
field vectors. Note that B = I in the case where the weighting
is null. Practically, m is computed based on the signal-to-noise
ratio (SNR): m = 1/SNR.
The SNR depends on the data type. For instance, in the taskrelated paradigm, the prestimuli are usually considered to be
noise and the poststimuli to be the useful signal. The SNR can
be computed using the ratio of the signal variance over these
two periods. In addition, the prestimuli period can also be used
to compute the noise covariance matrix C. In resting-state data,

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May 2018

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