IEEE Signal Processing - May 2018 - 82

we stress the current limitations that need further investigation. We also report results obtained in concrete applications
in both normal and pathological brain states. Additionally, we
discuss future directions in terms of signal processing methods and applications.

Introduction
Over the past decades, neuroscience research has significantly
improved our understanding of the normal brain. There is now
a growing body of evidence suggesting that brain functions
are generated by large-scale networks of highly specialized
and spatially segregated areas of the nervous system. From a
theoretical viewpoint, network science in general and graph
theory in particular have progressively entered the fields of
neuroscience and neurology. A relatively new research field,
referred to as network neuroscience [1], offers researchers a
unique opportunity to assess, quantify, and ultimately understand the multifaceted features of complex brain networks.
This interdisciplinary field has also been accelerated by enormous advances in neuroimaging techniques, which now allow
for the visualization of brain structure and function at unprecedented space and time resolution using, e.g., functional magnetic resonance imaging (fMRI), magnetoencephalography
(MEG), and EEG.
In this rapidly growing and thought-provoking context, the
identification of normal and pathological functional networks
from neuroimaging data has become one of the most promising prospects in brain research [2]. Among the neuroimaging
techniques that are able to provide relevant information about
the dynamics of functional brain networks, EEG has considerably progressed over the past two decades. A key advantage
of EEG systems is the noninvasiveness and the relative ease
of use. Information conveyed in EEG signals can be highly
informative about the underlying functional brain networks if
those signals are appropriately processed to extract the relevant
information. In addition, an important advantage of EEG is its
excellent temporal resolution, which offers the irreplaceable
opportunity to not only track large-scale brain networks over
very short durations like in many cognitive tasks [3] but to also
analyze fast, dynamic changes that can occur during the resting
state [4] or in brain disorders, such as epilepsy, typically during
interictal periods (between seizures) or ictal events (seizures).
Studying the role of neural synchrony in brain function using
EEG has been reviewed in depth [5]. Most of the reported studies on EEG functional connectivity analyses were performed at
the sensor level. However, the interpretation of corresponding
networks is not straightforward, as signals are strongly corrupted by the volume conduction effect due to the electrical conduction properties of the head [6], [7] and the fact that multiple
scalp electrodes, to some extent, collect the activity arising from
the same brain sources. These two factors can result in an inaccurate estimation of the real functional connectivity between
brain areas. Several recent studies have clearly reported the limitations of computing connectivity at the EEG scalp level (see [8]
for a review). Recent years have witnessed a significant increase
of interest in the EEG analysis of functional brain networks at
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the cortical source level. A proposed approach to reducing the
aforementioned limitations is called EEG source connectivity.
It is conceptually quite attractive, as high spatiotemporal resolution networks can be directly identified in the cortical-source
space, provided that some methodological aspects are carefully
accounted for to avoid pitfalls.
Practically, the transition from the electrode space into the
source space involves solving an ill-posed inverse problem, the
biophysical basis of which relies on dipole theory. Among the
many inverse methods proposed so far (see the review in [9]),
some make use of physiologically relevant a priori knowledge
about both the location and orientation of dipole sources at the
origin of signals collected at the scalp. When this information
is combined with an accurate, possibly subject- or patient-specific representation of the volume conductor (the realistic head
model [10] obtained by MRI segmentation), these methods considerably increase both the precision of localized sources and
the estimation of associated time series, which are analogous to
local field potentials. These time series then become the input
information for so-called connectivity methods, which aim to
estimate brain networks directly in the source space. Such networks are much more informative from the application viewpoint (e.g., cognitive sciences and clinics) [11], [12].
EEG source connectivity approaches involve several steps,
each related to important topics in signal processing, such
as the preprocessing of raw EEG data (e.g., artifact removal
and denoising), EEG inverse solutions (e.g., source localization
and reconstruction, spatial/temporal hypothesis, sparsity, and
regularization constraints), estimation of statistical couplings
between signals [e.g., phase synchronization (PS)/entropy, mutual information, coherence function, and linear/nonlinear regression analysis], and graph theory-based analysis (e.g., network
segregation/integration and hubness). However, a complete
overview of EEG source connectivity in terms of methodological choices and limitations at each stage and the available tools
is still missing. The main objective of this tutorial is to address
this issue by providing a comprehensive description of the main
contributions of the signal-processing community to this relatively new research field. From the methodological viewpoint,
we also address future advances that could likely overcome
some limitations of the current techniques.
From the application viewpoint, we focus on results obtained
so far with EEG source-connectivity methods applied to data
recorded during either normal or pathological brain states. We
also present new results using this method in the tracking of
the dynamics of brain networks during cognitive activity at a
subsecond timescale. In particular, we highlight recent studies
reporting attempts to use EEG source connectivity to reveal
clinically valuable information about the topology and dynamics of dysfunctional networks involved in epilepsies and neurodegenerative diseases. Finally, we address some expectations
in the field of cognitive and clinical research.

The volume-conduction problem
Let X (t) be the time series recorded at the surface of the brain
using M scalp EEG electrodes. These M sensors record the

IEEE Signal Processing Magazine

May 2018

Table of Contents for the Digital Edition of IEEE Signal Processing - May 2018