Low-density EEG for Source Activity Reconstruction using Partial Brain

Models

Andres Felipe Soler

, Eduardo Giraldo

and Marta Molinas

Department of Engineering Cybernetics, Norwegian University of Science and Technology, Trondheim, Norway

Department of Electrical Engineering, Universidad Tecnol

ogica de Pereira, Pereira, Colombia

Keywords:

Low-density EEG, Partial Brain Model, Source Reconstruction, Brain Mapping, EEG Signals.

Abstract:

Brain mapping studies have shown that the source reconstruction performs with high accuracy by using high-

density EEG montages, however, several EEG devices in the market provide low-density conﬁgurations and

thus source reconstruction is considered out of the scope of those devices. In this work, our aim is to use a few

numbers of electrodes to reconstruct the neural activity using partial brain models, therefore, we presented a

pipeline to estimate the brain activity using a low-density EEG on brain regions of interest, the partial brain

model formulation and several criteria for channel selection. Two regions have been considered to be studied,

the occipital region and motor cortex region. For the presented study synthetic EEG signals were generated

simulating the activation of sources with a frequency in the beta range at the occipital region, and mu rhythm

range at the motor cortex areas. Novel methods for electrode reduction and models for speciﬁc brain areas

are presented. We assessed the quality of the reconstructions by measuring the localization error, obtaining a

mean localization error below 7 mm and 16 mm with sLORETA and MSP methods respectively, by using a

low-density EEG with eight channels and partial brain models.

1 INTRODUCTION

Electroencephalography (EEG) is a non-invasive

technique that allows measuring the electrical brain

activity from the scalp with a high temporal resolu-

tion compared with other techniques like Functional

Magnetic Resonance Imaging (fMRI), Computed To-

mography (CT), and Positron Emission Tomography

(PET). Since the ﬁrst report about brain activity mea-

sured by electrodes was presented by Hans Berger in

1924 (O’Leary, 1970), EEG technique has been used

to study various brain processes like memory and

emotions, brain diseases like Parkinson and epilepsy,

and human behavior, in attempts to understand the

complexity underlying processing capabilities of the

brain. Source analysis based on brain mapping tech-

niques are allowed to reconstruct the cortical activ-

ity from electrodes on the scalp solving the EEG

inverse problem. Several methods have been pro-

posed to provide a estimation of the neural activity,

like minimum norm estimation MNE (H

ainen

and Ilmoniemi, 1994) or low-resolution tomography

LORETA (Pascual-Marqui et al., 1994).

In brain mapping research, it has been established

that a high number of electrodes is required to localize

accurately and reconstruct the cortical activity. How-

ever, a few studies have shown the possibility to apply

brain mapping methods using a small number of elec-

trodes. E.g, in (Jatoi and Kamel, 2018), the authors

proposed and evaluated the use of seven electrodes

to map the activity of the whole brain using several

brain mapping methods, obtaining a localization ac-

curacy around 15 mm using multiple sparse priors

method MSP (Friston et al., 2008). In (Soler et al.,

2019), a low-density approach to BCI was presented,

in which the occipital activity was mapped using MSP

and a partial brain model of the occipital region, ob-

taining an accuracy around 23 mm in the location of

the source with four electrodes using simulated activ-

ity, however, a channel selection criteria were not es-

tablished and the partial brain model was brieﬂy for-

mulated.

The aim of this current study is to establish a

pipeline to apply low-density EEG conﬁgurations for

source activity reconstruction using partial brain mod-

els, presenting the formulation to map the brain based

on regions of interest. Additionally, several criteria

are proposed to perform a selection of the channels

to be used for brain mapping, two criteria are consid-

ered, one based on local electrodes around the target

Soler, A., Giraldo, E. and Molinas, M.

Low-density EEG for Source Activity Reconstruction using Partial Brain Models.

DOI: 10.5220/0008972500540063

In Proceedings of the 13th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2020) - Volume 2: BIOIMAGING, pages 54-63

ISBN: 978-989-758-398-8; ISSN: 2184-4305

zone, and a second one based on a relevance crite-

rion. In this work, we presented a pipeline to esti-

mate the brain activity, to test our methodology, we

used synthetic EEG signals, simulating sources over

two brain regions, the occipital region, and motor cor-

tex region. We use the localization error to evaluate

the reconstructions comparing the position of the es-

timated sources versus the simulated one.

2 MATERIAL AND METHODS

2.1 Forward EEG Model

The relation between the EEG electrodes distributed

on the scalp and the source activity can be represented

by the forward problem equation:

y = M

x + ε (1)

where M

M ∈ R

d×n

represents the volume conductor

model, also known by leadﬁeld matrix. This matrix

represents the conductivity of the brain and explains

how the potentials ﬂow through brain from a set of

n distributed sources to d number of electrodes on

the scalp. This volume conductor model in realis-

tic brain representations considers the head anatomy

and the conductivity of the different tissues and lay-

ers between current sources and electrodes, like white

matter, gray matter, CSF, skull and scalp (Vorwerk

et al., 2012; Huang et al., 2016). y

y ∈ R

d×k

represents

the signals recorded by the electrodes in k number

of samples, the source activity matrix is represented

by x

x ∈ R

n×k

, it contains the amplitude of distributed

sources over the brain cortical areas. ε represents the

noise covariance, and it is assumed to follow a normal

distribution with zero mean.

2.2 Partial Brain Model Formulation

Consider the problem of EEG generation for a time

instant given by the forward EEG equation in 1. This

model can be rewritten by considering two subsets of

brain activity x

x as follows:

y =







+ ε

ε (2)

being M

and x

being the leadﬁeld matrix and its

corresponding neural activity for a speciﬁc brain zone

of interest or target zone, and M

and x

the lead-

ﬁeld matrix and its corresponding neural activity of

the remaining brain. It can be seen that the (2) can be

rewritten as

y = M

+ η

η (3)

η being a vector that holds the noise and the activity

in the part of the brain related to M

and x

. In addi-

tion, if the vector x

is close to zero (which means that

the neural activity outside the target zone is closed to

zero), the following approximation can be performed

y ≈ M

+ ε

ε (4)

By using an approximated model as described in

(4) the inverse problem for

can be solved. How-

ever, the activity outside the target zone could affect

the estimation because all the recorded activity by the

electrodes will be projected in the target zone. There-

fore, an additional stage to reduce the effect of M

over y

y can be added before performing the inverse

problem, by considering that the source in the target

zone appears in a known frequency, then, the EEG

is ﬁltered using band-pass ﬁlters leading to an atten-

uation of the activity outside the region of interest.

In addition, by assuming that the electrodes mostly

record activity in the neighbor spaces around it, a re-

duction in the number of electrodes can be made as

≈ M

+ ε

(5)

where the resulting estimation of x

is an approxi-

mation of x

obtained by using a reduced number of

channels.

A partial brain model is a section of the brain

based on a speciﬁc zone of interest and it is gener-

ated from a complete brain model. For that purpose,

we used the brain model denominated as the New

York Head (ICBM-NY) presented in (Huang et al.,

2016), this is based on the computation of a ﬁnite ele-

ment method (FEM) over a non-linear average of 152

individual MRI (ICBM152 v2009) from the Interna-

tional Consortium for Brain Mapping (Fonov et al.,

2009). The New York Head was calculated consider-

ing the conductivity of six tissue types: scalp, skull,

CSF, gray matter, white matter and air cavities with

a resolution of 0.5mm

. The lead ﬁeld matrix of the

New York Head was calculated for 74382 distributed

sources and 231 electrodes, however, several strict

subsets of sources with 10016, 5008 and 2004 vertices

are available at https://www.parralab.org/nyhead/.

We selected the model of 10016 and performed

an electrode reduction to 60 positions of the 10-20

international system (Fig.1A), this model is referred

to the paper as 10K model and it is used to compare

the performance of a high-density montage versus the

partial brain models with low-density EEG.

We generated a partial brain model of two brain

areas: occipital cortex area (Fig.1B) referred to OC

model, and the motor cortex area referred to MC

model (Fig.1C). The number of distributed sources

for the partial brain models is 3054 for the OC model

and 2162 for the MC model.

Low-density EEG for Source Activity Reconstruction using Partial Brain Models

Figure 1: Head model with 60 electrodes and 10016

sources, 10K model (A), Brain section for occipital cortex

area partial brain model, OC model (B), and Brain section

for motor cortex area partial brain model, MC model (C).

2.3 Synthetic EEG Generation

With the purpose to evaluate the performance of the

partial brain models for source reconstruction, we

generated 400 trials of simulated EEG activity at ﬁve

levels of noise: 0, 5, 10, 15, and 20dB (80 trials per

level). Each trial has two simulated sources over-

lapping between 37.5% and 40% . Each simulated

source activity was computed using a windowed si-

nusoidal activity using the following equation:

) = e

−

(

−c

)

sin(2π f

) (6)

where σ = 0.12 determines the Gaussian window

width. The ﬁrst source s

was simulated in the oc-

cipital areas, with a frequency f

of 20Hz (simulating

a source in the range of Beta wave), and centered at

= 300ms. The second source s

was simulated in

the motor cortex areas, with a frequency f

of 10Hz

(simulating a source in the range of mu rhythm), and

centered at c

= 800ms. The positions were randomly

selected between a set of pre-deﬁned positions dis-

tributed on the corresponding target zone. The pre-

deﬁned set of positions has six locations, three in each

hemisphere, the positions were: 3727, 8735, 2734,

7742, 3461, and 8469 for the source s

at occipital ar-

eas and 3837, 8845, 2284, 7292, 2271, and 7279 for

the source s

at motor cortex areas. An example of the

simulated activity is shown in Fig.2. It shows the lo-

cation of the simulated sources at the center of activity

and the time courses of the sources during the simu-

lated trial, in addition, the EEG related to the simu-

lated activity is presented with the electrodes labeling.

2.4 Channel Selection

We applied two criteria to select the electrodes: us-

ing local electrodes around the region of interest as

presented in (Soler et al., 2019), and using a channel

relevance analysis applying the Q-α method proposed

by (Wolf and Shashua, 2005). Those criteria are ex-

plained below:

2.4.1 Local Electrodes

The concept of local electrodes is based on the hy-

pothesis that the electrodes mostly record the electri-

cal activity of the near space around it. To select an

electrode conﬁguration we considered the results of

the previous work of (Soler et al., 2019), in which

a four-electrode conﬁguration was used to map one

source in the occipital region with a mean localiza-

tion error of 23 mm. Therefore, to evaluate the con-

cept of local electrodes and compare if increasing the

number of electrodes decreases the error, we selected

a conﬁguration of eighth electrodes around the tar-

get zone, maintaining an equal number of electrodes

across both brain hemispheres. Those conﬁgurations

are shown in Fig.3 for the OC and MC partial brain

models.

BIOIMAGING 2020 - 7th International Conference on Bioimaging

Figure 2: Example of source activity (top), source activ-

ity one simulated between 0-0.7s at 20Hz in the occipital

area (red), source activity two simulated between 0.4-1.2s

at 12Hz in the motor cortex (blue). EEG and channel infor-

mation (bottom). The overlap between the source activity

one and two is around a 37.5% to 42% (marked in the gray

area).

2.4.2 Relevance Analysis

We performed a relevance analysis based on the Q-α

method, applying the Standard Power-Embedded Q-α

algorithm. This method was originally proposed for

feature selection in unsupervised and supervised in-

ference problems (Wolf and Shashua, 2005; Wolf and

Shashua, 2003), in which a set of features is weighted

with an α vector coefﬁcient according to the cluster-

ing quality of data points. Under this approach, let

deﬁne the EEG data y

y as the data points matrix with

k samples, and each row correspond to an electrode

containing the voltage information of a speciﬁc loca-

tion as a feature to weight. Each electrode denoted

Figure 3: Electrode layout and selected local electrodes, lo-

cal electrodes for OC partial brain model (green), and local

electrodes for MC partial brain model (red).

by y

, ..., y

is pre-processed such that each electrode

is centered around zero and its L

norm equal to one

(||y

|| = 1). Let deﬁne a vector α

α ∈ R

, which con-

tains the weight value associated with each electrode,

being α

α = (α

, ..., α

)

. Let A

be the correspond-

ing afﬁnity matrix deﬁned as A

∑

i=1

and

Q ∈ R

k×m

whose columns are the ﬁrst m eigenvec-

tors of A

associated with the highest eigenvalues

≥ ... ≥ λ

. The values of α

α and Q

Q are unknown

and they can be calculated solving the following opti-

mization problem:

maxtrace

Q,α

subject to α

α = 1, Q

Q = I

(7)

by applying the Standard Power-Embedded Q-α

algorithm to solve the optimization problem, the α

weights are calculated. This method was applied be-

fore in a source reconstruction setting to weight the

electrodes in an inverse problem solution algorithm

presented by (Giraldo et al., 2012). In contrast, our

proposed approach is to select a set of channels with

the highest weights to perform the brain source recon-

struction using the partial brain models. We deﬁned

three levels of relevance, based on the 4, 8 and 16

most relevant electrodes.

2.5 Brain Source Reconstruction

The source reconstruction is an estimation of the cor-

tical activity using the registered voltages by elec-

Low-density EEG for Source Activity Reconstruction using Partial Brain Models

trodes on the scalp. To estimate the neural activity

in cortical regions, the EEG inverse problem must

be solved. This problem is considered ill-posed and

ill-conditioned due to the information available on

the scalp, which is limited to hundreds of electrodes,

while, the number of unknowns or sources to estimate

is in the order of thousands.

Several methods provide a solution for the elec-

tromagnetic inverse problem based on electrodes in-

formation and the model of the conductivity. We se-

lected two methods for brain mapping: the standard-

ized low-resolution tomography sLORETA (Pascual-

Marqui, 2002), and multiple sparse priors MSP (Fris-

ton et al., 2008). sLORETA was selected due to the

low localization error presented by its author, even in

some cases, zero error localization(Jatoi et al., 2014).

On the other hand, MSP has been tested with low-

density EEG montages by (Jatoi and Kamel, 2018)

and has shown lower localization error than other

methods like minimum norm estimation MNE and

LORETA (L

opez et al., 2014).

The MSP implementation used is a freely avail-

able software package SPM12 (Wellcome Trust Cen-

tre for Neuroimaging), we set up the number of

patches to 1100 according to the ﬁndings using seven

electrodes in (Jatoi and Kamel, 2018). The method

sLORETA was implemented based on the code pro-

vided in by (Biscay et al., 2018).

2.6 Pipeline

The followed pipeline is summarized in Fig.4A. The

procedure started with the simulation of the neural ac-

tivity using Eq.6, two sources s

and s

were simu-

lated. To generate the EEG signals, the activity matrix

x is created and the sources were located in random

positions, s

in occipital areas and s

in motor cortex

areas, none of the sources was located outside the tar-

get to avoid a projection of an external source in the

partial brain model. With the computed source activ-

ity x, and using the 10K model, the forward problem

was calculated applying the Eq.1, the estimated EEG

was contaminated with noise at ﬁve levels of signal-

noise-ratio SNR of 0, 5, 10, 15, and 20dB. For detailed

information of the EEG generation we refer to section

2.3.

Each EEG trial is ﬁltered by using a high order

FIR band-pass ﬁlters, the cutoff frequencies were set

up at 19 and 21Hz for the ﬁrst source s

, and for the

second source s

were at 9 and 11Hz. The ﬁlters were

applied in both direction of time to prevent losing in-

formation. As the output of the ﬁlter stage, two ﬁl-

tered set of EEG signals were obtained y

and y

for

the respective simulated source.

After ﬁltering, several EEG reductions were cal-

culated according to the channel selection criteria,

loe

and y

loe

by the local channel criterion,

rel4e

and y

rel4e

by the ﬁrst level of relevance with

four electrodes, y

rel8e

and y

rel8e

by the second

level of relevance with eight electrodes, and y

rel16e

and y

rel16e

by the third level of relevance with 16

electrodes.

The source reconstruction was performed with

both methods MSP and sLORETA over all the ten

EEG data, therefore, 20 source reconstructions were

computed, four using the high-density montage with

60 electrodes and the 10K model, eight applying the

channel selection criteria and the OC model, and

eight applying the channel selection criteria and the

MC model. A diagram with the name of each EEG

data and the respective reconstructions is presented in

Fig.4B.

Finally, the localization error was calculated com-

paring the resulting source position versus the original

simulated position, using the following equation:

LocE = ||

− P

ˆx

(8)

where P

is the position in a 3D coordinated space

of the simulated activity and P

ˆx

the position of the

maximum amplitude source of the estimated activity.

To provide a view of the effects of ﬁltering, the

same 20 reconstructions were calculated eliminating

the ﬁltering stage from the pipeline, making y

and

equal to y

y, however, the same respective models

were used to perform the source reconstruction stage.

Because the source s

has higher mean power than

due to the higher frequency, we were interested in

evaluating the performance of the channel selection

criteria and the brain mapping methods without iso-

lating the sources using the ﬁltering process.

3 RESULTS

A general view of the results is provided in Fig.5. At

the top, the mean localization errors of the source

reconstructions are presented, they were calculated

eliminating the ﬁltering stage from the pipeline. In

contrast, at the bottom, the mean localization errors

of the source reconstructions are presented using the

complete pipeline. Additionally, the results are sum-

marized in Table 1.

In a general point of view regarding the effects of

ﬁltering, when the ﬁlter stage was not applied (Fig.

5A and Table 1), the sources were mixed and the rel-

evance criteria tended to select the channels related to

the highest power source, in the case of the source s

BIOIMAGING 2020 - 7th International Conference on Bioimaging

Figure 4: The ﬂowchart of the followed pipeline (A), after the trial generation, the procedure is applied per trial (gray square).

Source reconstruction tree (B), gray squares contain the name of the reconstruction using the EEG signal at left, the region in

blue indicates the use of the 10K model, orange for the OC model, and green for the MC model.

due to the high frequency, it presents a higher power

than source s

, therefore it was reconstructed with

higher accuracy than s

. The accuracy obtained with-

out ﬁltering for the source s

shows that the methods

projected the s

in the MC model, which explains the

high mean localization error of the methods using the

full set of electrodes. By inspection of the selected

electrodes using the relevance criteria, in most of the

cases, the electrodes were near to the source s

due to

the lack of isolation by bypassing the ﬁltering stage.

The best reconstructions were obtained by the full

set of electrodes and the 10K model with ﬁltering

and without ﬁltering for the sLORETA, in the case

of MSP, the error increased signiﬁcantly from 4 to

24 mm removing the ﬁltering stage. Regarding the

reconstructions using the presented pipeline and the

partial brain models, the relevance channel selection

with 16 electrodes obtained the lowest localization er-

ror for both sources, followed by the second level of

relevance with 8 electrodes, the ﬁrst level with 4 elec-

trodes, and ﬁnally, the eight local electrodes. In all

the cases the MSP method presented a low accuracy

than sLORETA.

The local electrodes criteria presented a stable

value for the reconstruction even if the ﬁltering stage

was not applied. For the source s

with OC model, the

mean localization error was between 15 to 20 mm,

and for source s

and MC model, between 11 to 22

mm. In general, when used the partial brain models

and the channel selection by relevance, the localiza-

tion error remained below 10 mm for the sLORETA

method, and below 21 mm for the MSP reconstruc-

tions.

4 DISCUSSION

In this paper, we have presented a pipeline to recon-

struct the source activity over speciﬁc brain regions

using partial brain models and low-density EEG, us-

ing channel selection criteria.

In the presented simulations, we evaluated the per-

formance of partial brain models and the relevance

analysis for channel selection, the results showed by

using of sLORETA the mean localization error were

below 10mm, which in several cases is even low than

localization error values obtained by other methods

with high-density montages as explained in several

works by (L

opez et al., 2014; Jatoi and Kamel, 2018).

Comparing to (L

opez et al., 2014), we obtained a

similar error value around 5 mm for our high-density

montage with MSP.

The use of partial brain models constraint the

Low-density EEG for Source Activity Reconstruction using Partial Brain Models

Figure 5: Mean error localization, without applying the ﬁlter stage (A), and following the complete pipeline with the ﬁltering

stage (B).

BIOIMAGING 2020 - 7th International Conference on Bioimaging

Table 1: Mean error localization without applying the ﬁlter stage, and following the complete pipeline including the ﬁltering

stage.

Non-Filtered Data Filtered Data

Method

Head

Model

Source

Channel

Selection

Criteria

Number

Electrodes

Mean

Localization

Error (mm)

Mean

Localization

Error (mm)

MSP 10K S1 - 60 24,41 40,22 4,19 0,82

sLORETA 10K S1 - 60 3,22 5,70 1,08 2,79

MSP OC S1 Relevance 4 28,67 18,97 20,37 11,63

sLORETA OC S1 Relevance 4 20,33 20,26 8,07 7,48

MSP OC S1 Relevance 8 22,19 19,69 12,58 11,72

sLORETA OC S1 Relevance 8 16,74 18,86 5,46 5,46

MSP OC S1 Relevance 16 18,68 20,29 9,14 7,02

sLORETA OC S1 Relevance 16 14,67 17,74 4,61 5,17

MSP OC S1 Local 8 19,47 12,54 18,73 9,89

sLORETA OC S1 Local 8 15,70 2,44 17,23 3,79

MSP 10K S2 - 60 91,09 38,32 15,94 5,71

sLORETA 10K S2 - 60 109,66 10,61 13,87 10,08

MSP MC S2 Relevance 4 48,90 23,16 15,17 11,13

sLORETA MC S2 Relevance 4 65,88 15,25 9,24 8,51

MSP MC S2 Relevance 8 53,09 24,39 16,05 10,82

sLORETA MC S2 Relevance 8 66,83 15,07 7,09 6,82

MSP MC S2 Relevance 16 51,93 23,19 13,64 12,17

sLORETA MC S2 Relevance 16 65,71 15,61 6,44 7,30

MSP MC S2 Local 8 18,14 12,27 21,44 6,22

sLORETA MC S2 Local 8 14,34 5,71 11,01 4,85

brain mapping methods to ﬁnd a solution in a pre-

deﬁned space, which will make it prone to error when

the source of interest originates from other areas. For

this reason, the application of partial brain models

should be restricted to applications in which the area

of interest that will be activated is well known, i.e,

in some visual evoked potentials VEP experiments

in which the interest is to know how the visual cor-

tex areas respond to certain stimuli (Vilhelmsen et al.,

2019; Van Der Meer et al., 2013), or in motor imagi-

nary task were is well known that the motor cortex is

activated (Burianov

a et al., 2013; Qiu et al., 2017).

Even if the results shown that the localization er-

ror was higher with the local electrodes than applying

the relevance criteria, this method can be applied in

settings in which a high quantity of electrodes is not

available. In addition, we consider that the use of lo-

cal electrodes can be applied in settings for which the

frequency of the source of interest is not well known.

As shown in Fig.5 and Table 1, the mean error was

kept below 22 mm regardless of the use of ﬁlters to

isolate the sources.

It is clear, regardless of the use of the ﬁltering

stage, that the best reconstructions were obtained by

the full set of electrodes. However, its noticeable that

with the presented pipeline using low-density EEG

montages and the proposed partial brain models, we

achieved with eight electrodes a mean localization er-

ror around 7 mm with sLORETA and 16 mm with

MSP, and slightly less with 16 electrodes, around 6

mm with sLORETA and 14 mm with MSP.

5 CONCLUSIONS

In this work, we presented a formal deﬁnition of the

partial brain models and tested the capability to map-

ping a target zone of the brain using a reduced model

of a region of interest. We presented a pipeline to

apply those models and performed experiments with

multiple synthetic EEG trials with two overlapped

sources at several levels of noise and several levels of

electrode resolution based on channel selection cri-

teria. We measured the quality of the source recon-

structions with the localization error, and based on

the accuracy of the results obtained herein, we con-

sider that partial brain models following the pipeline

can reconstruct the source activity using low-density

EEG montages of 8 and 16 electrodes with a precision

below 10 mm with sLORETA and 20 mm with MSP.

As presented, we focused on the localization error

obtained with sLORETA and MSP for brain source

Low-density EEG for Source Activity Reconstruction using Partial Brain Models

reconstruction, however, it is worth noticing that the

solutions by sLORETA are smooth (Pascual-Marqui,

2002), while the other hand, MSP present more sparse

solutions (L

opez et al., 2014; Friston et al., 2008).

Therefore in future works, we will consider the use

of error measurements that involve the temporal evo-

lution of the reconstructed sources and the sparseness

of the solutions.

The pipeline presented considers a basic ﬁlter

stage using band-pass ﬁlters with the intention to fo-

cus on the partial brain models to source activity

reconstruction. However, several studies (Mu

noz-

Guti

errez et al., 2018; Hansen et al., 2019) have

shown that the using of advanced techniques for fre-

quency decomposition like empirical mode decompo-

sition EMD, multivariate EMD, noise assisted EMD,

and wavelets can offer a solution for unmixing the

source activity improving the brain mapping algo-

rithms. Those techniques will be studied on partial

brain models in future publications.

AUTHOR CONTRIBUTIONS

This part was intentionally removed for reviewing

purposes All the authors conceived and designed the

experiments. AFS performed the experiments. All

the authors analyzed the data, wrote and reﬁned the

article.

ACKNOWLEDGMENT

This part was intentionally removed for reviewing

purposes This work was supported by the Norwegian

University of Science and Technology NTNU, project

”David and Goliath: single-channel EEG unravels its

power through adaptive signal analysis”.

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