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Automatic Selection of Frequency Bands for Electroencephalographic Source Localization

Conference Paper

Automatic Selection of Frequency Bands for Electroencephalographic Source Localization

Abstract and Figures

This paper shows a method to locate actives sources from pre-processed electroencephalographic signals. These signals are processed using multivariate empirical mode decomposition (MEMD). The intrinsic mode functions are analyzed through the Hilbert-Huang spectral entropy. A cost function is proposed to automatically select the intrinsic mode functions associated with the lowest spectral entropy values and they are used to reconstruct the neural activity generated by the active sources. Multiple sparse priors are used to locate the active sources with and without multivariate empirical mode decomposition and the performance is estimated using the Wasserstein metric. The results were obtained for conditions with high noise (Signal-to-Noise-Ratio of -5dB), where the estimated location, for five sources, was better for multiple sparse prior with Multivariate Empirical Mode Decomposition, and with low noise (Signal-to-Noise-Ratio of 20dB), where the estimated location, for three sources, was better for multiple sparse prior without MEMD.
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Automatic Selection of Frequency Bands for Electroencephalographic
Source Localization
Pablo Andr´
es Mu˜
noz1,2, Eduardo Giraldo2, Maximiliano Bueno L´
opez3and Marta Molinas4
Abstract This paper shows a method to locate actives
sources from pre-processed electroencephalographic signals.
These signals are processed using multivariate empirical mode
decomposition (MEMD). The intrinsic mode functions are
analyzed through the Hilbert-Huang spectral entropy. A cost
function is proposed to automatically select the intrinsic mode
functions associated with the lowest spectral entropy values and
they are used to reconstruct the neural activity generated by
the active sources. Multiple sparse priors are used to locate the
active sources with and without multivariate empirical mode
decomposition and the performance is estimated using the
Wasserstein metric. The results were obtained for conditions
with high noise (Signal-to-Noise-Ratio of -5dB), where the
estimated location, for five sources, was better for multiple
sparse prior with Multivariate Empirical Mode Decomposition,
and with low noise (Signal-to-Noise-Ratio of 20dB), where the
estimated location, for three sources, was better for multiple
sparse prior without MEMD.
I. INTRODUCTION
Electroencephalographic (EEG) Source Localization (ESL)
has been widely used in different medical fields (neuroscience
studies or clinical applications) for its high temporal resolution
that allows to measure the changes of neural activity in time
intervals of the order of milliseconds. The main drawback of
ESL is to solve the neuromagnetic inverse problem which is
ill-posed and it does not have an unique solution. Therefore,
to obtain an approximated locations of neural current sources
from EEG, it is necessary to solve the inverse problem
using some a priori information or applying some constraints
over the source space [
1
], [
2
]. Nowadays, spatio-temporal
constraints have been used in different works, in [
1
] was
included, to improve the spatial resolution, a basis set for
smoothing the source space (localized areas that could be
potentially active brain regions) and based on a Markovian
assumption applied at each sample time to estimate the brain
activity, the time resolution was improved. Another spatio-
temporal constraints were incorporated as a small and locally
patches to reconstruct sparse brain activity; to smooth the
solution over the time, temporal constraint was imposed for
penalizing the difference between consecutive time points
[2].
Currently, some research have focused their studies to analyze
the neural activity in frequency bands, in this way, they have
1
Universidad del Quind
´
ıo, Colombia
pamunoz@uniquindio.edu.co
2
Universidad Tecnol
´
ogica de Pereira, Colombia
egiraldos@utp.edu.co
3
Universidad de la Salle, Colombia
maxbueno@unisalle.edu.co
4
Norwegian University of Science and Technology, Norway
marta.molinas@ntnu.no
found it e.g. some theta-band activities of low-amplitude
desynchronised were associated to visual areas when they
were compared among motion stimuli and static stimuli [
3
].
Besides, in [
4
], the authors focused the research in alpha-band
oscillations because they are the main frequency components,
associated to neural activity, present in EEG signals. Recently,
some works have proposed a method whose structure is
based on data-driven analysis. An example for this kind of
analysis is the empirical mode decomposition (EMD) and
some applications in brain activity reconstruction are shown
in [
5
], [
6
]. One of the results shown in [
6
] was the way how
the neural activity was split in frequency bands which can be
seen in the intrinsic mode functions (IMFs). Similar results
can be seen in [
5
], but these results were analyzing according
to the retained energy and the amount of entropy in each
IMFs. Despite of the relevant results, some issues associated
to EMD method were regarded in the full reconstruction,
namely, mode mixing and mode splitting.
Solutions for reducing the mode mixing have been highlighted
in [
7
] e.g. Noise aided EMD computation (EEMD) and
multivariate empirical mode decomposition (MEMD). In this
paper is presented a method, based on data-driven analysis
using MEMD, to improve the localization of the actives
sources in the brain and for reducing the mode mixing
problem. To separate the frequency bands is used MEMD
method and the relevant IMFs are chosen from marginal
Hilbert-Huang spectrum (MHHS) and entropy analysis. A cost
function based on entropy is proposed to dismiss the IMFs
with Hilbert-Huang Spectral Entropy (HHSE) greater than
the estimated HHSE threshold, and those IMFs with lower
HHSE are chosen to located the actives sources. The proposed
method is evaluated by comparing ESL using multiple sparse
prior (MSP) with and without MEMD, and the performance is
measured with Wasserstein metric on simulated brain activity.
II. MATERIAL AND METHODS
A. Multivariate Empirical Mode Decomposition (MEMD)
Signals represented in multivariate form should have a
coherent treatment to obtain a suitable time-frequency esti-
mation, because these signals contain generalized oscillations
(joint rotational modes). Therefore, it is important to remark
that when the single EMD is applied (channel by channel)
to multichannel signals, this approach is obstructed by [7]:
Nonuniformity. Each channel would not be decomposed
with the same number of IMFs using standard EMD.
Scale alignment. It is possible that the scales across data
channels do not have the same-index.
Nature of IMFs. It is not convenient to enforce the
same number of IMFs for each channel, because the t-f
estimation could be affected, as such IMFs are typically
not monocomponent.
Common mode alignment and nonuniqueness have been the
greatest obstacles for application of the EMD in studies where
is necessary same-index IMFs within of the same scale for the
corresponding information (synchrony, causality, data/image
fusion), being a problem in applications data/image fusion
[
7
]. For multivariate signals, the local maxima and minima
can not be calculated directly and, the notion of ”oscillatory
modes” to define an IMF is confuse in this case [
8
]. This
method proposes to take a signal projections along of multiple
directions that have been distributed in a uniform way within
of a n-dimensional space to obtain multiple envelopes which
are averaged and then, interpolated (using cubic spline) their
extrema to estimate the local n-dimensional mean. Especial
attention is required to choose a suitable set of directions
from the signal projections taken in the n-dimensional space
[7].
The following algorithm summarizes how the MEMD
works [7]:
1)
Using the Hammersley sequence, as a uniformly sam-
pling a n-dimensional sphere, generate a P-point.
2)
Projections
qθp(tk)
of the signal
y(tk)
must be calcu-
lated in the same direction vector
xθp
, for
p= 1, ..., P
and then to obtain a set of projections {qθp(tk)}P
p=1.
3)
Find the time instants
{ti
θp}P
p=1
that correspond to
the maxima of the set of projections of signals
{qθp(tk)}P
p=1.
4)
Interpolate [
ti
θp
,
s
(
ti
θp
)] to obtain the envelope curves
{eθp(tk)}P
p=1.
5)
Calculate the mean of the P multidimensional envelopes
m(tk) = 1
P
P
X
p=1
eθp(tk)(1)
6)
Extract the “detail”
d(tk) = s(tk)m(tk)
. If
d(tk)
fulfills the stoppage criterion for a multivariate IMF,
apply the above procedure to
s(tk)d(tk)
, else repeat
for d(tk).
B. Hilbert-Huang Spectral Entropy
Spectral entropy can be defined as a measure of the amount
of disorder and this definition is based on the spectrum of
a signal. The Hilbert-Huang Epectral Entropy (HHSE), for
non-stationary signals, is calculated from Hilbert spectrum
following these steps [9]:
1)
The signal
x(t)
is decomposed into a series of IMFs
(IMFj).
2)
The hilbert transform is applied to
IMFj
(
1jn
)
to obtain YIM Fj
3) The analytical signal is calculated for each IMFj:
ZIM Fj(t) = I M F j(t) + iYI M Fj(t) = aj(t)ej(t)
(2)
where
aj(t)=[I M F 2
j(t) + Y2
IM Fj(t)] 1
2(3)
and
θj(t) = arctan( YIM Fj
I M F j(t))(4)
4)
The instantaneous frequency is calculated for
IMFj
(1jn):
ωj(t) = j(t)
dt ,(5)
The time series is expressed as:
x(t) =
n
X
j=1
aj(t)exp(iZωjdt)(6)
The equation 6 represents, as function on time, the
amplitude and the instantaneous frequency, therefore, this
equation corresponds to the Hilbert Transform
H(ω, t)
. The
Hilbert spectrum is the energy-time-frequency distribution
over the signal
x(t)
y HHSE es calculated using the frequency
marginal by integrating the Hilbert spectrum over the time-
axis.
C. Neuromagnetic Inverse Problem
The neural activity can be generated through the following
model of EEG generation:
y(tk) = M x(tk) + (tk)(7)
being the EEG at sample time
tk
termed
y(tk)Rd×1
,
the lead field matrix
MRd×n
and the neural activity
x(tk)Rn×1
. The forward problem indicated in
(7)
, allows
to define that the estimation of the neural activity can be
obtained by solving the inverse problem based on the EEG
measurements
y(tk)
and the knowledge of the lead field
matrix
M
. Besides, to get an unique solution, it is necessary
to consider some spatio-temporal dynamics of EEG signals,
which can improve the approximated location of the active
sources [
1
]. The MSP method was proposed by [
10
] and this
method apply a hierarchical or empirical Bayes model as
spatio-temporal constraints to reconstruct the inverse problem
in a distributed way, and multiple cortical sources with a
spatial support, specified in terms of empirical priors, are
automatically selected.
III. EXP ER IM EN TAL SE TU P
Studies in neuroscience have set five frequency bands,
namely: delta-band (0-4 Hz), theta-band (4-8 Hz), Alpha-band
(8-14 Hz), beta-band (14-30 Hz) and gamma-band (30-150Hz)
[
3
]. The aim was to simulate brain activity for three sources
and five sources, these sources were randomly located in three
(delta, alpha and beta bands) and five (delta, theta, alpha, beta
and gamma bands) different frequency bands, they were also
located randomly in different areas in the brain. The activity
in each source was simulated using the following expression:
xi(tk) = e1
2tkci
σ2
sin (2πfitk),(8)
being
ci
the center of the windowed signal in seconds
(
1
,
3
and
5
seconds for three sources and
1
,
2
,
3
,
4
and
5
seconds for five sources), the frequency of the signal (
fi
)
was chose randomly within of the ranges according with the
frequency bands mentioned above and
σ= 0.2
. In this work
were simulated 30 trials for Signal-to-Noise-Ratio (SNR) of
20
dB,
10
dB,
0
dB and
5
dB using the model of generation
(7).
After applying the HHSE to each trial and each noise level,
It was possible to find that the lowest spectral entropy values
were associated to the IMFs where the simulated activity was
observed in the frequency bands. For this reason, the subset
of of IMFs whose entropy was under a threshold
τe
were
chosen to locate the active sources.
The proposed entropy function is the following:
ej=X
k
kI M F j(t)k2
2log(kI M F j(t)k2
2)(9)
It is applied over each
I M F j(t)
and where
ej
is the entropy
of each IMF, and
e= [e1. . . eN]
. The estimated EEG signal
˜
y(t)
from IMFs with lowest entropy (chosen automatically)
is rebuilt according to the measured entropy ei.
˜
y(t) = X
iO
I M F j(t)(10)
Access to a standard EEG database is important because
it is necessary to know the underlying source activity to
evaluate the methods for solving the inverse problem. We
used a model with
n= 8,196
sources and
32
electrodes for
simulation, as described by ([1]).
IV. RES ULTS
After to analyze all of trials in the four noise levels, it
could be found that the most suitable threshold, to choice
the relevant IMFs for locating the active sources, was the
IMFs with lowest spectral entropy and the chosen IMFs
were those whose sum did not exceed 40 percent of the
normalized HHSE for all IMFs. To show the results, for this
work were done two simulations with controlled conditions,
especially with respect to the location of the active sources,
which were located for a clear visualization.
The first one was simulated for three active sources with
f1= 2Hz
,
f2= 9Hz
and
f3= 22Hz
, the SNR was of
20dB
. In fig. 1 are shown three of the six IMFs chosen by
entropy cost function; the simulated EEG fig. (1A), IMF2
Fig. (1B) associated to frequency beta-band (
f3= 22Hz
),
IMF5 fig. (1C) associated to frequency alpha-band (
f2=
9Hz
) and IMF8 fig. (1D) associated to frequency delta-band
(f1= 2Hz).
Each IMF used to locate the active source can be seen in
fig. 2 whose sum allows to obtain the full location for the
three active sources fig. 2B. The Wasserstein metric for this
Fig. 1. Selected IMFs for 3 sources with SNR 20dB
estimation was the 3.1467 and the location without MEMD
was 3.2313 fig. 2C, this measurements compared with the
ground truth fig. 2A.
Fig. 2. Wasserstein metric with and without MEMD for 3 active sources
located with SNR of 20dB
The second simulation was done for 5 sources with
f1=
1.5Hz
,
f2= 4Hz
,
f3= 9Hz
,
f4= 20Hz
and
f5= 45Hz
,
the SNR was of
5dB
. The high level of noise can be seen
in fig. 3A and the another figures are shown 5 of the 6 IMFs
chosen. The advantage by using the MEMD is to be able
to separate the activity in different bands of frequency e.g.,
in fig. 3B corresponds to gamma-band (
f5= 45Hz
) and
was decomposed in the IMF2 with some noise. In the IMF4
(fig. 3C) was located the frequency associated to beta-band
(
f4= 20Hz
) and the same way, it can be seen in fig. 3D the
IMF5 with the frequency in alpha-band (
f3= 9Hz
), in fig.
3E the IMF7 with the frequency in theta-band (
f2= 4Hz
)
and in fig. 3F the IMF9 with the frequency in delta-band
(f1= 1.5Hz).
In the fig. 4 is presented that the Wesserstien metric for
MSP with MEMD (fig. 4B) was lower than the metric for
MSP without MEMD (fig. 4C), compared with the ground
truth fig. 4A.
V. CONCLUSION
A method based on data-driven analysis, for improving the
accuracy for EEG source localization (ESL), was evaluated.
Fig. 3. Selected IMFs for 5 sources with SNR -5dB
Fig. 4. Wasserstein metric with and without MEMD for 5 active sources
located with SNR of -5dB
The MEMD was used in order to decomposed the EEG signal
in its main modes and separate the noisy components and
reaching to locate the active sources with a minimum noise.
It could also be seen that the EEG signal was decomposed
in IMFs according with frequency bands and each IMF was
associated a specific spectral entropy values. Those IMFs
with incorporated frequency band or source activity allow to
reconstruct the brain activity of that source. The cost function
of entropy was proposed for choosing the IMFs with lowest
spectral entropy (calculated by using HHSE) and up to a
maximum of the 40 percent, with this cost function, all the
active sources were located and the performance of MSP with
MEMD, according to the Wesserstein metric, was better both
SNR 20db and SNR -5dB than MSP without MEMD. In both
cases, the method for choosing the IMFs took in account
additional IMFs, because the mode splitting generated by
MEMD method is present.
ACKNOWLEDGMENT
This work was carried out under the funding of COL-
CIENCIAS. Research project: 111077757982: Sistema de
identificacin de fuentes epileptognicas basado en medidas de
conectividad funcional usando registros electroencefalogrficos
e imgenes de resonancia magntica en pacientes con epilepsia
refractaria: apoyo a la ciruga resectiva.
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... An entropy based cost function is applied over each IMF γ i (t k ) as follows ( Bueno-López et al. (2019), Muñoz-Gutiérrez et al. (2019)): ...
Preprint
Full-text available
Several approaches can be used for estimating neural activity. The main differences between them are in the apriori information used and their sensibility to high noise levels. Empirical Mode Decomposition (EMD) has been recently applied to Electroencephalography EEG-based neural activity reconstruction to provide apriori time-frequency information to improve the neural activity estimation. EMD has the specific ability to identify independent oscillatory modes in non-stationary signals with multiple oscillatory components. The various attempts to use EMD in EEG analysis, however, did not provide yet the best reconstructions due to the intrinsic mode mixing problem of EMD. Some previous works have used a single-channel analysis and in other cases, multiple-channel have been used for other applications. In this paper, we present a study about multiple-channel analysis using Multivariate Empirical Mode Decomposition (MEMD) as a method to attenuate the mode mixing problem and to provide apriori useful time-frequency information to the reconstruction of neuronal activity using several low-density EEG electrode montages. The methods were evaluated over real and synthetic EEG data, in which the reconstructions were performed using multiple sparse priors (MSP) method with several electrode numbers of 32, 16, and 8, and the source reconstruction quality was measured using the Wasserstein Metric. Comparing the solutions when no pre-processing was made and when MEMD was applied, the source reconstructions were improved using MEMD as apriori information in the low-density montage of 8 and 16 electrodes. The mean source reconstruction error on a real EEG dataset was reduced a 59.42% and 66.04% for the 8 and 16 electrodes montages respectively, and on a simulated EEG with three active sources, the mean error was reduced an 87.31% and 31.45% for the same electrodes montages.
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Several approaches can be used to estimate neural activity. The main differences between them concern the a priori information used and its sensitivity to high noise levels. Empirical mode decomposition (EMD) has been recently applied to electroencephalography EEG-based neural activity reconstruction to provide a priori time-frequency information to improve the estimation of neural activity. EMD has the specific ability to identify independent oscillatory modes in non-stationary signals with multiple oscillatory components. However, attempts to use EMD in EEG analysis have not yet provided optimal reconstructions, due to the intrinsic mode-mixing problem of EMD. Several studies have used single-channel analysis, whereas others have used multiple-channel analysis for other applications. Here, we present the results of multiple-channel analysis using multivariate empirical mode decomposition (MEMD) to reduce the mode-mixing problem and provide useful a priori time-frequency information for the reconstruction of neuronal activity using several low-density EEG electrode montages. The methods were evaluated using real and synthetic EEG data, in which the reconstructions were performed using the multiple sparse priors (MSP) algorithm with EEG electrode montages of 32, 16, and 8 electrodes. The quality of the source reconstruction was assessed using the Wasserstein metric. A comparison of the solutions without pre-processing and those after applying MEMD showed the source reconstructions to be improved using MEMD as a priori information for the low-density montages of 8 and 16 electrodes. The mean source reconstruction error on a real EEG dataset was reduced by 59.42% and 66.04% for the 8 and 16 electrode montages respectively, and that on a simulated EEG with three active sources, by 87.31% and 31.45% for the same electrode montages.
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Electroencephalogram (EEG) was used to investigate brain electrical activity of full-term and preterm infants at 4 and 12 months of age as a functional response mechanism to structured optic flow and random visual motion. EEG data were recorded with an array of 128-channel sensors. Visual evoked potentials (VEPs) and temporal spectral evolution (TSE, time-dependent amplitude changes) were analysed. VEP results showed a significant improvement in full-term infants’ latencies with age for forwards and reversed optic flow but not random visual motion. Full-term infants at 12 months significantly differentiated between the motion conditions, with the shortest latency observed for forwards optic flow and the longest latency for random visual motion, while preterm infants did not improve their latencies with age, nor were they able to differentiate between the motion conditions at 12 months. Differences in induced activities were also observed where comparisons between TSEs of the motion conditions and a static non-flow pattern showed desynchronised theta-band activity in both full-term and preterm infants, with synchronised alpha-beta band activity observed only in the full-term infants at 12 months. Full-term infants at 12 months with a substantial amount of self-produced locomotor experience and neural maturation coupled with faster oscillating cell assemblies, rely on the perception of structured optic flow to move around efficiently in the environment. The poorer responses in the preterm infants could be related to impairment of the dorsal visual stream specialized in the processing of visual motion.
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This article addresses data-driven time-frequency (T-F) analysis of multivariate signals, which is achieved through the empirical mode decomposition (EMD) algorithm and its noise assisted and multivariate extensions, the ensemble EMD (EEMD) and multivariate EMD (MEMD). Unlike standard approaches that project data onto predefined basis functions (harmonic, wavelet) thus coloring the representation and blurring the interpretation, the bases for EMD are derived from the data and can be nonlinear and nonstationary. For multivariate data, we show how the MEMD aligns intrinsic joint rotational modes across the intermittent, drifting, and noisy data channels, facilitating advanced synchrony and data fusion analyses. Simulations using real-world case studies illuminate several practical aspects, such as the role of noise in T-F localization, dealing with unbalanced multichannel data, and nonuniform sampling for computational efficiency.
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This paper describes an application of hierarchical or empirical Bayes to the distributed source reconstruction problem in electro- and magnetoencephalography (EEG and MEG). The key contribution is the automatic selection of multiple cortical sources with compact spatial support that are specified in terms of empirical priors. This obviates the need to use priors with a specific form (e.g., smoothness or minimum norm) or with spatial structure (e.g., priors based on depth constraints or functional magnetic resonance imaging results). Furthermore, the inversion scheme allows for a sparse solution for distributed sources, of the sort enforced by equivalent current dipole (ECD) models. This means the approach automatically selects either a sparse or a distributed model, depending on the data. The scheme is compared with conventional applications of Bayesian solutions to quantify the improvement in performance.
Localizing the focal origin of epileptic activity using eeg brain mapping based on empirical mode decomposition
  • P Muoz-Gutirrez
  • M Molinas
  • E Giraldo
  • M Bueno
P. Muoz-Gutirrez, M. Molinas, E. Giraldo, and M. Bueno, "Localizing the focal origin of epileptic activity using eeg brain mapping based on empirical mode decomposition," in Proceedings. (ITISE 2018). (International conference on Time Series and Forecasting, 2018., September 2018.