Abstract
Current electroencephalogram (EEG) denoising methods struggle to remove the complex
physiological and environmental artifacts typical of real-world settings, which both hinders the
isolation of true neural activity and limits the technology’s translational potential. We present
the Generalized Eigenvalue De -Artifacting Instrument (GEDAI), a novel algorithm for
denoising highly contaminated EEG. GEDAI employs leadfield filtering to selectively remove
noise and artifacts that diverge from a theoretically defined EEG forward model. This approach
offers unique advantages over existing solutions, including 1) denoising of highly corrupt
recordings without “clean” reference data, 2) single -step correction of artifactual epochs and
bad channels, 3) unsupervised detection of brain and noise components based on the signal
and noise subspace alignment index (SENSAI). In ground-truth simulations with synthetic and
empirical EEG contaminated with realistic artifacts (EOG, EMG, n oise), GEDAI globally
outperformed leading denoising techniques based on principal component analysis (ASR) and
independent component analysis (IClabel, MARA), revealing large effect sizes in challenging
scenarios with simultaneous artifact mixtures, low s ignal-to-noise ratio ( -9 dB), and high
temporal contamination (up to 100%). Its superior denoising also enhanced neurobehavioral
predictions, yielding highest accuracies in ERP classification and brain fingerprinting. GEDAI’s
autonomy, computational speed and noise-resilience could find future applications in 1) real-
world medical, mobile and dry electrode EEG recordings 2) magnetoenecephalography
(MEG) denoising (given the shared M/EEG forward model), and 3) real-time brain-computer
interfaces (BCIs). The Matlab code for GEDAI is available as an open-source EEGLAB plugin
at https://github.com/neurotuning/GEDAI-master
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2
Introduction
Despite being well-researched and affordable, the multi-channel electroencephalogram (EEG)
struggles to expand beyond controlled research and clinical settings (Sawangjai et al., 2020).
A major hurdle to broader EEG use is contamination by non -cerebral signals, known as
artifacts (Mumtaz et al., 2021). EEG artifact removal often requires the supervision of a trained
operator, leading to reduced scalability and rel iability. Hence, tackling artifacts has recently
been rated by experts as the most important development needed in EEG research (Mushtaq
et al., 2024).
In the realm of medical applications (Fratangelo et al., 2025) , EEG artifacts can
obscure or mimic genuine brain activity, leading to inaccurate diagnoses and compromised
patient care (e.g. in epilepsy, intensive care or sleep monitori ng) (Amin et al., 2023) .
Furthermore, artifacts significantly hinder the development and reliability of brain -computer
interfaces (BCIs) (Mak & Wolpaw, 2009), which rely on consistent and accurate decoding of
neural signals to translate brain activity into commands for external devices or neurofeedback
(Ros et al., 2014). Artifacts introduce noise that can disrupt this decoding process, leading to
reduced accuracy, slower response times, and ultimately, a less effective BCI system.
Therefore, there remains a critical need for a fast, fully automated, and noise -agnostic EEG
Method
to reliably remove all types of artifacts, particularly in highly contaminated recordings
where clean reference data is unavailable.
Several previous strategies have been developed to clean multi-channel EEG signals.
The most popular of which is indep endent component analysis (ICA), which performs blind
source separation and can be used to remove temporally-independent components from the
signal. While effective at removing ocular (Jung et al., 2000) and muscular artifacts (Olbrich
et al., 2011) , ICA is computationally demanding, requires a case -by-case inspection of
components to reject that calls for expert human input or that from machine learning classifiers
(Frølich et al., 2015; Radüntz et al., 2017). Moreover, ICA cannot inherently identify Gaussian
distributed noise, which might be spread across the components or remain as unexplained
residual variance . ICA is therefore not an ideal choice for inexperienced users, large datasets
or online analysis (despite promising attempts e.g. Hsu et al., 2014).
Another algorithm, called artifact subspace reconstruction (ASR), directly uses
principal component analysis (PCA) to exclude EEG components exceeding a variance
threshold, but requires a portion of clean EEG data as a reference (Kothe & Jung, 2015). While
faster, relying solely on a variance threshold is not per se sufficient to distinguish between
signal and noise (de Cheveigné & Parra, 2014), as in the case when noise amplitude is below
that of the signal. Moreover, since ASR is based on PCA, it can only separate orthogonal
components (Cohen, 2022a), which may limit its effectiveness when trying to resolve complex
artifact mixtures.
To overcome the limitations of ICA and PCA, Generalized Eigenvalue Decomposition
(GEVD) offers a promising alternative (Koles, 1991; Y. Wang et al., 1999) . GEVD works by
taking a pair of EEG covariance matrices and decomposing them jointly – a process known
as "joint diagonalization" – to find common underlying components (de Cheveigné & Parra,
2014). The core objective of this joint diagonalization is to find a set of components that
maximizes the variance ratio between the signal and reference matrices (Cohen, 2 022a).
Another key advantage is that the resulting GEVD components do not need to be orthogonal
(unlike PCA) or conform to Gaussian assumptions (unlike ICA) (Cohen, 2022a; Parra & Sajda,
2003).
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GEVD is widely employed in the BCI field for mental classification tasks, where it is
known as the common spatial patterns (CSP) algorithm (Blankertz et al., 2008; Lotte & Guan,
2011). It has also been proposed for brain source separation (Cohen, 2022a; Parra & Sajda,
2003), correction of ocular artifacts (Gouy-Pailler et al., 2009), removal of stimulation artifacts
(Haslacher et al., 2021) and generic M/EEG data cleaning (Boudet et al., 2012; Somers et al.,
2018; F. Wang et al., 2025).
We refer to this work as the “return” of the GEDAI (Generalized Eigenvalue De -
Artifacting Instrument) because, while GEVD has been used in EEG denoising before, our
approach revisits it by addressing key limitations. An existing challenge in applying GEVD is
the need to specify the reference covariance matrix (refCOV) for decomposition. This typically
involves selecting empirical EEG segments deemed "clean" (Haslacher et al., 2021; F. Wang
et al., 2025) or "artifactual" (Gouy-Pailler et al., 2009; Somers et al., 2018) . However, this
process is often subjective and circular since identifying representative segments requires
prior knowledge of their typical characteristics. GEDAI addresses this by constructing the
refCOV theoretically, deriving it from EEG signal generation principles using the forward model
via the leadfield matrix (Weinstein et al., 2000) . This leadfield-based refCOV represents the
expected EEG signature of brain activity generated by internal sources, offeri ng a principled
way to define the "clean signal" subspace for decomposition. We refer to this forward-modeling
approach to separate brain signals from noise as leadfield filtering (LFF). An additional
challenge with GEVD is determining the cutoff that sepa rates 'signal' (brain activity) from
'noise' (artifacts) components. GEDAI addresses this by using the theoretical refCOV as a
benchmark, selecting the optimal threshold based on subspace similarity between the cleaned
EEG covariance and the refCOV (see Methods section).
To evaluate GEDAI's performance, we tested it against prominent artifact correction
techniques using both synthetic and empirical EEG data, following recommendations for
robust testing (Mumtaz et al., 2021). This comparison includes the fa st PCA-based method
ASR (Kothe & Jung, 2015) and two widely used ICA -based methods known for effective
Results
ICLabel (Pion-Tonachini et al., 2019) and Multiple Artifact Rejection Algorithm (MARA)
(Winkler et al., 2014). This comparative analysis aims to position GEDAI relative to current
state-of-the-art methods.
Methods
Section I of the methods describes the mathematical details of the GEDAI denoising
algorithm, whose code we also release as an open plugin for the EEGlab toolbox in MATLAB
(Delorme & Makeig, 2004).
Section II of the methods describes benchmarking using ground -truth simulations,
where GEDAI’s performance is compared to current state -of-the-art algorithms for EEG de -
artifacting, including ASR (Kothe & Jung, 2015) , ICLabel (Pion-Tonachini et al., 2019) and
MARA (Winkler et al., 2014) . The simulations were performed using both synthetic and
empirical EEG datasets to which noise and/or artifacts were added.
Section III of the methods describes each algorithm’s denoising performance in the
context of neurobehavioral prediction. Here, two publicly -available EEG datasets were used
to compare how the denoising algorithms influence the prediction accuracy of sensory stimuli
(“visual oddball”) and individual identity (“brain fingerprinting”).
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4
Section I: The GEDAI algorithm
Figure 1. An overview of the GEDAI algorithm
A) Schematics illustrating the GEDAI pipeline; dataCOV: empirical data covariance matrix; refCOV:
theoretical covariance matrix from a leadfield model. B) An example dataCOV of clean EEG data. C)
An example refCOV of a leadfield matrix. D) Graph illustrating similarity between the denoised data and
the refCOV across a range of artifact thresholds. SSSI: Signal Subspace Similarity Index, blue curve;
NSSI: Noise Subspace Similarity Index, red curve; SENSAI: SSSI - NSSI, black curve; vertical dashed
line: optimal artifacting threshold.
As illustrated in Figure 1A above, multi -channel EEG may be considered to be a linear
summation of electrical activities from a brain “signal” subspace with one containing different
types of non -cerebral noise or “artifact”. This mixture may be “unmixed” by linear
decomposition techniques (e.g. PCA or ICA) into separate components with individual source
locations (“topographies”) and respective time -courses (“waveforms”). However, as "blind"
source separation methods, PCA and ICA leverage statistical properties within mixed data to
recover underlying sources, functioning without a priori knowledge of the original signals or
their mixing process. GEDAI combines prior knowledge of the brain’s “signal” subspace (i.e.
its spatial covariance) with generalized eigenvalue decomposition (GEVD) to more effectively
separate source components belonging to the artifact -subspace from those of the brain -
subspace.
First, refCOV is derived from a precomputed leadfield matrix for standard 10-5 system
electrode locations or, for non -standard electrode locations, from an interpolated leadfield
matrix calculated ‘on -the-fly’ via spherical interpolation. Next, the whole in put EEG signal
(including artifacts) is epoched in circa 1-second windows, and an individual data covariance
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matrix (dataCOV) is generated for each epoch. Then, each data covariance matrix is
decomposed with GEVD, using refCOV as a fixed reference matrix a cross all epochs. After,
the output EEG data is reconstructed and evaluated using the Signal & Noise Subspace
Alignment Index (SENSAI), in order to determine the optimal cutoff that separates brain from
artifactual components, sweeping across a range of ar tifacting strengths. By respectively
maximising and minimizing the subspace similarities of the retained and removed data with
the refCOV, across different thresholding strengths, GEDAI estimates the optimal cutoff for
component removal. For the final step , the denoised time -series of each epoch is then
reconstructed by using only the GEVD components belonging to the brain-subspace.
Estimation of the refCOV
The GEDAI EEGlab plugin offers two options for refCOV estimation. The first method uses a
pre-computed covariance matrix of 343 standard EEG electrode locations (10-5 system), from
which the plugin automatically matches the electrode labels present in the EEG recording (e.g.
Fp1, Pz, etc.). This leadfield matrix was generated with the Brainstorm Toolbox (Tadel et al.,
2011) using the OpenMEEG algorithm (Gramfort et al., 2010) and the ‘fsaverage’ adult head
model (FreeSurfer’s default template based on 40 normative brains), employing the Boundary
Element Method (BEM) with 3630 unconstrained brain dipolar sources (1210 vertices × 3
orientations).
For non -standard EEG recording montages, there is a second option: spherically
interpolating the precomputed leadfield to custom electrode locations. This method requires
that the electrodes’ spatial coordinates are provided within EEGlab. Although slightly less
accurate, this approach is computationally much faster than estimating a custom BEM
leadfield, taking only a couple of seconds compared to the several minutes required to
recompute with OpenMEEG.
The leadfield matrix parametrizes the “forward model” of how the EEG is generated by
sources of neuronal activity in the brain, i.e., the EEG_ac tivity with dimensions [channels x
time], the leadfield_matrix with dimensions [channels x sources], and the
brain_source_activities with dimensions [sources x time]:
From this, the spatial covariance matrix, refCOV, with dimensions [channels x channels] can
be simply computed as:
GEDAI's source -space to electrode -space projection relies on two main theore tical
assumptions (de Munck et al., 1988, 1992): electrode potential is a weighted sum of underlying
dipolar sources, and each source's strength is independent of other source parameters. Under
these conditions, de Munck et al. demonstrated a linear relationship between electrode signal
covariance and the summed, weighted covariance of individual dipolar sources.
We provide a simple empirical example supporting the aforementioned assumptions
in Figure 1 where a leadfield -generated covariance matrix (panel C) may be qualitatively
compared to the covariance matrix calculated from clean EEG data (panel B) (Subject #2
from the Ehrlich dataset, see Methods). Both matrices were normalised [channel x c hannel]
(i.e. zero mean with a standard deviation of one) for visualisation.
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Generalized Eigenvalue Decomposition
Threshold-based artifact rejection methods rely on the principle that artifacts are usually large
and relatively rare events occurring in th e signal. Artifacts can therefore be identified as
appearing in the upper tail of the eigenvalue distribution of EEG signals, and be excluded
based on a defined cutoff (Lazarevic & Kumar, 2005; Li et al., 2023). The large magnitude of
artifacts is exploited by PCA -based procedures such as ASR, but these are constrained by
orthogonality and blind to the spatial origin of the signal components.
In contrast, GEDAI employs GEVD to isolate and remove artifactual components from
the signal. However, GEVD alters the significance of the largest eigenvalues. Instead of
representing "components with high variance," they now signify "components with high
variance that maximally deviate from the reference co variance matrix (refCOV)." Given that
the refCOV encodes components that spatially originate only within the brain, this a priori
provides GEVD with extra “supervision” for separating artifactual from neural sources.
The GEVD may be summarised in one line of MATLAB/Python code, where e is the epoch
number:
Mathematically, the GEVD decomposition follows the linear algebra equation:
Where dataCOV is the covariance matrix of a single epoch extracted from the EEG data,
refCOV is the predetermined reference covariance matrix, Λ is the diagonal matrix containing
the generalized eigenvalues and V is the matr ix containing the generalized eigenvectors. In
GEDAI, a regularization technique is applied to refCOV before GEVD to enhance numerical
stability, manage singular matrices, and reduce overfitting (Cohen, 2022a).
The SENSAI algorithm: separating neural from artifactual components
Akin to finding the boundary that separates oil from water, differentiating artifacts from neural
signals depends on the exact magnitude of the eigenvalues, represented by the threshold T.
SENSAI (Signal & Noise Subspace Alignment Index) essentially estimates the correct
threshold T by evaluating the “improvement” in the output EEG signal quality by sweeping
over multiple threshold values of T. Here, the output EEG signal quality is represented by the
SENSAI score, which is proportional to the cosine similarity between the refCOV matrix and
the empirical covariance of the retained (i.e. Signal) and the removed (i.e. Noise) data.
As can be seen in Figure 1D, the SENSAI function computes a similarity index of the
retained and removed EEG data for each threshold tested. The similarity index is calculated
first by taking the covariance matrix of the cleaned EEG data and the refCOV, and performing
a classical ei gendecomposition separately on both (i.e. equivalent to PCA). The principal
angles between the top components (i.e. eigenvectors) of the refCOV and cleaned data
subspaces are then estimated (Knyazev & Argentati, 2002). Here, given two subspaces with
their orthonormal bases A (from refCOV) and B (from cleaned data), the principal angles θ i
between these subspaces can be computed as follows:
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Compute the projection matrix C:
Perform Singular Value Decomposition on the projection matrix :
where W is related to the orthonormal basis of the subspace A, Q is related to the orthonormal
basis of the subspace B, and Σ is a diagonal matrix containing the cosines of the principal
angles between the two subspaces. The principal angles θ i are obtained from the singular
values σi in the diagonal matrix Σ:
To estimate the Signal Subspace Similarity Index (SSSI), we take the cosine of each principal
angle and multiply them together:
Where 𝜃1, 𝜃2 and 𝜃3 are the principal angles between the top 3 eigenvectors of the cleaned
data and the top 3 eigenvectors of the refCOV. Similarly, the Noise Subspace Similarity Index
(NSSI) is also estimated between the top 3 eigenvectors of the residual noise data (removed
from the EEG) and the refCOV. By estimating the SSSI and NSSI through a broad range of
artifacting thresholds, it becomes possible to optimize the tradeoff between either removing or
retaining too many artifactual components. For example, increasing the threshold strength at
first increases the similarity of the cleaned EEG covariance with refCOV, as non -cerebral
components are initially removed. Past a certain point, however, the threshold becomes too
aggressive and cerebral activity starts to be removed from the EEG recording, thus reducing
the similarity of the cleaned EEG covariance with refCO V. Similarly, by calculating the NSSI
for the data being removed from the EEG in the cleaning process, we can quantify how much
potentially cerebral EEG activity gets included as noise.
SENSAI calculates a tradeoff score, called the SENSAI score, by subtr acting the subspace
similarity index of the noise from the similarity index of the cleaned EEG, or mathematically:
The optimal threshold for cleaning the dat a is simply the eigenvalue that corresponds to the
maximum of this score.
Denoised signal reconstruction
Cleaned EEG signal reconstruction occurs epoch -by-epoch. Within each epoch, artifactual
components are first identified (eigenvalues > T), and a spati al filter targeting these artifacts
is formed using the corresponding eigenvectors. Concurrently, the activation patterns (or
inverse spatial filters) for these artifactual components are derived from the pseudo-inverse of
the eigenvector matrix. The artifactual activity is then estimated in sensor space by combining
these activation patterns with their respective time courses (calculated using the spatial filter
and the original EEG). Finally, subtracting this reconstructed artifact activity from the origi nal
epoch yields the denoised EEG signal. To prevent signal discontinuities that can arise from
concatenating independently processed EEG epochs, GEDAI employs a 50% overlapping
window approach during its epoch-by-epoch reconstruction. These overlapping segments are
combined using cosine weighting to ensure smooth transitions at epoch boundaries, mitigating
the edge effects inherent in segmented processing.
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Multiresolution GEDAI
Although GEDAI can be applied end-to-end solely to broadband data (e.g. 1-45 Hz), we have
found that multiresolution -based denoising performs significantly better on pilot data.
Multiresolution analysis decomposes the signal into frequency sub -bands across multiple
scales, which permits perfect reconstruction, ensuring lossless re covery of the original EEG
data from its components (Clark et al., 1995). Hence, following an initial GEDAI denoising step
on broadband EEG to remove the largest artifacts, the GEDAI cleaning al gorithm is
subsequently applied to spectrally decomposed EEG data using a maximum overlap discrete
wavelet transform (MODWT). The benefit of this extra step comes from the fact that artifact
distributions clearly differ between EEG bands (ranging from delt a to gamma). Thus,
frequency-specific thresholds are needed to ensure that high -frequency artifacts (e.g. in the
gamma band) are not rejected using the same eigenvalue threshold estimated for lower
frequency bands (e.g. the delta band). Hence, the GEDAI al gorithm consists of a secondary
step on MODWT decomposed signals filtered in 10 dyadic frequency bands, using the ‘Haar’
wavelet. Among the wavelet families, the Haar wavelet has the best temporal localization,
which is an important property for pinpointing abrupt changes, discontinuities, or spikes typical
of artifactual signals. Compared to other types of wavelet analysis, the MODWT offers
advantages like conservation of signal energy (perfect reconstruction) and time alignment
(zero-phase filtering, shif t invariance) across decomposition levels. For an EEG recording
sampled at 256 Hz, the wavelet bands produced by the MODWT are as follows: 64 -128 Hz
(band 1), 32-64 Hz (band 2), 16 -32 Hz (band 3), 8 -16 Hz (band 4), 4 -8 Hz (band 5), 2 -4 Hz
(band 6), 1-2 Hz (band 7), 0.5-1 Hz (band 8), 0.25-0.5 Hz (band 9), 0.125-0.25 Hz (band 10).
Then, for each narrow -band the optimal artifacting threshold is estimated separately via the
SENSAI algorithm, and the final clean signal is reconstructed by adding up all the deno ised
wavelet bands.
Section II: Benchmark EEG simulations
Using EEGlab v2025.0.0 we compared the GEDAI algorithm to 3 state -of-the-art (SOTA)
denoising algorithms (ASR, MARA and ICLabel) in terms of ground-truth signal reconstruction
on both synthetic and empirical EEG data.
Denoising algorithms: ASR, IClabel, MARA, GEDAI
Three established automated denoising algorithms were used to benchmark GEDAI, namely
ASR, IClabel and MARA. Like GEDAI, these are all projection algorithms that “correct” artifacts
by subtracting them from EEG data, and which technically incur no temporal data loss. A
panoply of pipelines also exists for denoising EEG data that involve wholesale “rejection” of
EEG segments, but these are designed to solve a different problem, where full recovery of the
original EEG signal is not the objective (Bailey et al., 2023; Gabard -Durnam et al., 2018;
Hajhassani et al., 2024). We have also not included deep learning based denoising algorithms
(X. Zhang, 2024) , as these techniques rely on extensive training datasets and can exhibit
limited generalizability when applied to out-of-sample data. This could be investigated in future
work and is beyond the scope of this paper.
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Raw
As a sanity-check, we provide the “raw” unprocessed data for comparison, which was used
as the direct input to each denoising algorithm. Hence, the raw condition did not contain any
denoising and/or preprocessing, and consisted of the original EEG contaminated with artifacts.
ASR
As the first denoising algorithm, we included ASR (i.e. EEGlab’s clean_raw_data v2.91), as it
is a fast, real -time capable method for EEG cleaning (Kothe, 2013) . The ASR algorithm
performs a standard eigendecomposition using one covariance matrix as input (i.e. PCA),
instead of a generalized eigendecomposition that utilizes two covariance matrices as input
(i.e. GEVD). We used EEGlab’s ASR plugin default burst criterion value of 20 SD (Chang et
al., 2020) . Given that bad (i.e. noisy) channels negatively affect ASR performance, we
activated clean_raw_data’s bad chan nel detection only for artifact categories where noisy
channels were present, i.e. NOISE or NOISE + Electromyography (EMG) +
Electrooculography (EOG). Since bad channel detection was not universally applied over all
artifact categories, the benchmark was not fully "noise-agnostic” and slightly advantaged ASR.
IClabel
The second denoising algorithm was ICLabel v1.6 (Pion-Tonachini et al., 2019) . This ICA -
based technique can automate artifact rejec tion by evaluating ICA topographies with a
machine learning based classifier trained on ICA topographies from over 6,000 datasets. Here,
the Infomax -extended ICA algorithm (Lee et al., 1999) was used based on its superior
performance compared to other ICA algorithms (Delorme et al., 2012). Firstly, given that bad
channels may impair the quality of ICA decomposition, the ICA was pre ceded by EEGlab’s
clean_raw_data bad channel rejection step only for artifact categories where noisy channels
were present (i.e. NOISE or NOISE + EMG + EOG). Moreover, if the artifact category
contained only EMG or EOG artifacts, IClabel was configured to remove only those ICA
components identified as EMG or EOG artifacts (all other components were retained). On the
other hand, if the artifact category contained noise (i.e. NOISE or NOISE + EMG + EOG),
IClabel was configured to only retain components that w ere classified as ‘brain’ or ‘other’.
Since the above settings were not universally applied over all artifact categories, the
benchmark was not fully "noise-agnostic” and provided a marginal advantage to IClabel.
MARA
For the third denoising algorithm, we selected MARA v1.2, the Multiple Artifact Rejection
Algorithm (Winkler et al., 2014). This ICA-based technique also involves a machine learning
classifier trained on a large datab ase of expert -labeled artifactual topographies. MARA is
integrated within popular denoising pipelines, such as the Harvard Automated Processing
Pipeline for Electroencephalography (HAPPE) (Gabard-Durnam et al., 2018). Unlike IClabel,
MARA directly classifies ICA components as artifactual (or not), and hence only those
components were removed. To facilitate comparisons to IClabel, the Infomax -extended ICA
algorithm was used (Lee et al., 1999), which was preceded by EEGlab’s clean_raw_data bad
channel rejection step only for artifact categories where noisy channels were present (i.e.
NOISE or NOISE + EMG + EOG). Since bad channel detectio n was not universally applied
over all artifact categories, the benchmark was not fully "noise -agnostic”, which slightly
favoured MARA’s performance.
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GEDAI
We executed EEGlab’s GEDAI v1.0 plugin using its default settings: with denoising strength
set to ‘auto’, an epoch size of 1.0 seconds, and a ‘precomputed’ BEM lead field matrix. No
bad channel rejection step was applied to any of the artifact categories. The above settings
were universally applied across all datasets, hence the GEDAI benchmark results can be
considered as effectively "noise-agnostic".
Denoising scenarios: signal-to-noise ratio, temporal contamination, artifact type
Each denoising algorithm was run with its default parameter settings across the complete
range of noise scenarios descri bed below. Fixing the parameter settings was necessary to
test each algorithm’s automation and/or generalization to a range of real -world “noise”
scenarios, which were varied across 3 key axes:
● Signal to Noise Ratio (SNRbefore ) of clean EEG power relative to artifact power (-9, -
6, -3, 0 dB)
where SNRbefore = 10 * log10(original_clean_signal_power / original_artifact_power)
was estimated across all epochs (i.e. the whole EEG recording)
● Temporal contamination of EEG contaminated by artifacts (25, 50, 75,100%)
where % reflects the proportion of samples containing artifacts. For example, for a
dataset of 60 seconds and sampled at 200 Hz, we added artifact segments with
random offsets into a total of 4000, 6000, 8000, or all 12000 samples. The artifact
segment duration was randomized, ranging from 1 sample to 1 second..
● Artifact type (EOG, EMG, NOISE, or their combination), where different artifact types
were linearly superimposed within each epoch.
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11
Denoising Benchmark: Synthetic and Empirical EEG Simulations
Figure 2. Simulated EEG data generation
Background
“ground -truth” EEG ( signal) was obtained either from clean empirical recordings or
synthetic data generated by a forward model with 100 -300 sources. Contaminated ( simulated EEG)
data were generated by a sensor -space summation of the signal (blue trace) with different types of
artifacts (red trace) (Ille et al., 2002). In this example, muscle artifact was generated by multiplying the
time-series (“waveforms”) of EMG electrode activity with source locations (“topographies”) consistent
with EMG artifact. Artifact waveforms were derived from the EEGdenoiseNet dataset, which consisted
of direct recordings from individual EO G and EMG electrodes, respectively placed over the eyes and
facial muscles (H. Zhang et al., 2021).
Synthetic EEG simulations
Synthetic data for these simulations were generated using a combination of the EEG forward
modelling toolbox SEREEGA (Krol et al., 2018) and the EEGdenoiseNet dataset based on
real EOG and EMG electrode recordings (H. Zhang et al., 2021).
Clean EEG signal generation
Here, we exclusively used the SEREEGA toolbox to generate clean “background” EEG data.
A total of 10 independent datasets were simulated with distinct spatio -temporal dynamics,
including: 2 datasets with autoregressive noise, 6 datasets with varying combinations of
colored noise (white, blue, brown) plus amplitude-modulated oscillations (in delta, theta, alpha
and beta bands), and 2 datasets with simulated epileptic spiking activity (small or large spikes).
The forward model consisted of the New York head model (i.e. ICBM152 average template)
with a precomputed Finite Element Method (FEM) leadfield (Huang et al., 2016). Here, 100-
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300 dipolar sources, randomly distributed within the brain volume, were used to generate a
multi-channel time series across 100 independent 1-second epochs. Each output dataset had
a duration of 100 seconds and consisted of 6 4 channels (standard Biosemi montage) with a
sampling frequency of 256 Hz. See Fig S1 for examples of clean synthetic EEG that was used.
EOG and EMG artifacts
In order to make the synthetic artifacts as realistic as possible, we used the real -world
recordings of sensor data directly overlying the eyes (EOG, electro -oculogram) and facial
muscles (EMG, electromyogram) from the EEGdenoiseNet dataset
https://github.com/ncclabsustech/EEGdenoiseNet (H. Zhang et al., 2021). Then, as shown in
Figure 2, these EOG/EMG single time-series (“waveforms”) were multiplied by dipolar source
patterns (“topographies”) to generate multi -channel EEG in sensor-space. In order for these
topographies to be consistent with EOG/EMG generation, we utilized the HArtMuT head model
(Harmening et al., 2022), which enables simulating EEG activity originating from extra-cerebral
sources located in the eyes and muscles. Here, we extracted a random sample of 16 eye and
10 scalp muscle source locations (as illustrated in Figure S3). Then, for each dataset, a
minimum of 2 sources of EOG and 1 -3 sources of EMG were randomly selected and their
topographic information (i.e. source location and orientation) was retained. Finally, these
EOG/EMG topographies were respectively multiplied by the EOG/EMG single time -series
from EEGdenoiseNet (with 50 randomly sampled e pochs of 2 seconds) to construct multi -
channel datasets containing only artifacts. All EOG signals were band -pass filtered between
0.3 and 10 Hz. EMG signals were band-pass filtered between 1 to 120 Hz and notched at the
powerline frequency of 50 Hz. See Fig S2 for examples of artifactual semi-synthetic EEG that
was used.
NOISE artifacts
Datasets with noise artifacts were identical in size to those with EOG/EMG, and were
generated to contain the following types of synthetic (i.e. MATLAB simulated) “noise” across
5 datasets: with 3 bad channels (white noise, 1 dataset), 5 bad channels (sawtooth wave, 1
dataset), 6 bad channels (square wave, 1 dataset), spike artifact (synthetic, 1 dataset),
impulsive noise (1 dataset).
Artifact mixtures
In order to challen ge the denoising algorithms with more complex scenarios of artifact
mixtures, the baseline EOG, EMG, and/or NOISE datasets were z -score normalised and
linearly combined with each other to produce a mixed artifact category: “ NOISE + EMG +
EOG ”. To generate a total of 5 datasets in this category, only datasets with matching numbers
were added across categories (e.g. EOG dataset 1 + EMG dataset 1 + NOISE dataset 1).
In summary, 5 separate artifact datasets were generated for each of the following 4 artifact
categories:
1. EMG (muscle activity)
2. EOG (eye blinks and/or movement)
3. NOISE (empirical or synthetic noise)
4. NOISE + EMG + EOG
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Bad channels
Out of the above total of 20 artifactual datasets, there were 6 datasets containing bad channels
(3 datasets in the NO ISE category, and 3 datasets in the NOISE + EMG + EOG category).
Thus, bad channels were present in 30% (6/20) of all synthetic simulations.
Mixed clean EEG + artifact signal generation
In line with the model shown in Figure 2, each of the 10 clean recordings was pairwise “mixed”,
through linear summation, with each of 5 datasets from a specific artifact category. This
resulted in 50 contaminated datasets within each one of the 4 artifact categories (EMG; EOG;
NOISE; and EMG + EOG + NOISE).
Thus, the synthetic simulations consisted of 200 unique datasets (50 datasets x 4 artifact
categories), varied across 4 temporal contamination levels x 4 SNR levels, yielding a
“synthetic” benchmark sample of 3,200 datasets . Each dataset had 64 channels and a
length of 100 seconds, sampled at 256 Hz (i.e. each data matrix: 64 channels x 25,600
samples).
Empirical EEG simulations
Clean EEG signal generation
Here, we used Stefan Ehrlich’s experimentally-acquired recordings of clean EEG
https://github.com/stefan-ehrlich/dataset-automaticArtifactRemoval (Ehrlich, 2019/2024) ,
where 10 separate subjects were selected from the Ehrlich dataset in the ‘eyes-closed’ resting
condition with a duration of 100 seconds. These recordings were visually inspected for the
presence of any artifacts, and any samples that were suspected of contamination were
wholesale rejected (i.e. removed across all channels). For every subject, clean EEG segments
of at least 2 seconds were concatenated and low-pass filtered at 60 Hz. Each output dataset
had a duration of 60 seconds and consisted of 27 channels with a sampling frequency of 200
Hz. See Fig S4 for examples of clean empirical EEG that was used.
Artifact signal generation
EOG and EMG artifacts
Even dedicated scalp EEG recordings of extra -cerebral artifacts inevitably contain brain
signals. Consequently, ground-truth brain and artifact signals cannot be established, which is
necessary for reliably evaluating denoising performance. To address this problem, we used
empirical recordings of sensor data directly overlying the eyes (EOG, electro-oculogram) and
facial muscles (EMG, electromyogram) from the EEGdenoiseNet dataset
https://github.com/ncclabsustech/EEGdenoiseNet (H. Zhang et al., 2021). Then, as shown in
Figure 2, the EOG/EMG single time-series (“waveforms”) can be multiplied by their relevant
spatial patterns (“topographies”) to generate multi -channel EEG in sensor -space. For these
topographies to be consistent with EOG/EMG generation, we separately performed (Infomax-
extended) ICA on multichannel EOG/EMG artifact recordings from the Ehrlich dataset (Ehrlich,
2019/2024). Here, for each dataset, a minimum of 2 components of EOG and 4 components
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of EMG were manually selected and only their topographic information was retained. Finally,
as described above, these EOG/EMG topographies were respectively multiplied by the
EOG/EMG single time-series from EEGdenoiseNet (with 30 randomly sampled epochs of 2
seconds) to construct multi -channel datasets containing only artifacts. The use of ICA in
generating the artifactual EEG data could raise concerns about circularity (i.e. "double
dipping”), potentially favouring ICA -based algorithms (IC label, MARA). Such a bias would
indeed be possible if we had used the independent, non-Gaussian time courses generated by
ICA itself (i.e. the time -courses matching the Ehrlich dataset topographies). However, we
circumvented this issue by instead using dir ect EOG/EMG sensor recordings from the
EEGdenoiseNet dataset as the artifact time courses. These physiological signals were
obtained without imposing ICA's assumptions of independence or non -Gaussianity, thereby
ensuring a fairer evaluation of the ICA -based algorithms. All EOG signals were band -pass
filtered between 0.3 and 10 Hz, and then re-sampled to 200 Hz. EMG signals were band-pass
filtered between 1 to 120 Hz and notched at the powerline frequency of 50 Hz, and then
resampled to 200 Hz. See Fig S5 for examples of artifactual empirical EEG that was used.
NOISE artifacts
Datasets with noise artifacts were identical in size to those with EOG/EMG, and were
generated to contain the following types of empirical (e.g. based on Stefan Ehrlich’s empirical
recordings) and synthetic (i.e. MATLAB simulated) “noise” across 10 datasets: with 3 -7 bad
channels (synthetic, 4 datasets), movement artifact (empirical, 1 dataset), electrode pop
(empirical, 1 dataset), step artifacts (synthetic, 1 dataset), temporally non-stationary noise
(synthetic, 1 dataset), and spatially non-stationary noise (synthetic, 2 datasets). See Fig S6
for examples of noisy empirical EEG that was used.
Artifact mixtures
In order to challenge the denoising algorithms with more complex scenarios of artifact
mixtures, the baseline EOG, EMG, and/or NOISE datasets were z -score normalised and
linearly combined to produce a mixed artifact category: “NOISE + EMG + EOG ”. To generate
a total of 10 datasets in this category, only datasets with matching numbers were added across
categories (e.g. EOG dataset 1 + EMG dataset 1 + NOISE dataset 1).
In summary, 10 separate artifact datasets were generated for each of the following 4 artifact
categories:
1. EMG (muscle activity)
2. EOG (eye blinks and/or movement)
3. NOISE (empirical or synthetic noise)
4. NOISE + EMG + EOG
Bad channels
Out of the above total of 40 purely artifactual datasets, there were 8 datasets containing bad
channels (4 datasets in the NOISE category, and 4 datasets in the NOISE + EMG + EOG
category). Thus, bad channels were present in 20% (8/40) of all empirical simulations.
Mixed clean EEG + artifact signal generation
For the final step, and according to the model shown in Figure 2 above, each of the 10 clean
recordings was pairwise “mixed”, through linear summation, with each of 10 datasets from a
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specific artifact category. This resulted in 100 contaminated datasets within each one of the 4
artifact categories (EMG; EOG; NOISE; and EMG + EOG + NOISE).
Thus, the empirical simulations consisted of 400 unique datasets (100 datasets x 4 artifact
categories), varied across 4 temporal contamination levels x 4 SNR levels, yielding an
“empirical” benchmark sample of 6,400 datasets . Each dataset had 27 channels a nd a
length of 60 seconds, sampled at 200 Hz (i.e. each data matrix: 27 channels x 12,000
samples).
Measures of denoising performance: SNR, relative root mean square error
(RRMSE) and correlation coefficient
Here, clean EEG recordings served as the ground truth. Denoising algorithms were evaluated
on their accuracy in recovering this signal from contaminated data using 3 standard metrics,
allowing comparison with prior work (Mumtaz et al., 2021).
● SNR: higher is better
where: original_clean_signal_power is the variance of the original clean signal elements:
residual_artifact_power is the variance of the error signal (difference between denoised and
original clean signal elements):
● Relative Root Mean Square Error (RRMSE): lower is better
where: RMSE is the standard deviation of the error signal (difference between denoised and
original clean signal elements) and RMS is the amplitude of the original clean signal
elements.
● Correlation Coefficient (R): higher is better
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where:
is the mean of the original clean signal elements
and
is the mean of the denoised signal elements
Statistical Analysis
To compare the benchmark performance of GEDAI against the other algorithm s (ASR,
ICLabel, MARA) paired, non -parametric, statistical tests were employed due to a) the same
dataset(s) were denoised by all algorithms, and b) the potential non -normal distribution of
performance metrics. The primary performance metrics evaluated wer e the Correlation
Coefficient R, SNR, and RRMSE) between the denoised signal and the ground -truth clean
signal. Statistical significance was set at an alpha level of 0.05. Here, we used a Friedman
test (i.e. a non-parametric equivalent of a repeated-measures ANOVA) to assess if there was
a statistically significant difference in the distributions of denoising performance scores
between the algorithms (GEDAI, ASR, ICLabel, MARA) when applied to the same
contaminated datasets (varied by SNR before, temporal contamination, and artifact type).
Following a significant two -sided Friedman test result (i.e. p < 0.05) on SNR after, post -hoc
pairwise two -tailed comparisons between algorithms were conducted using MATLAB's
multcompare function with a Bonferro ni multiple-comparison correction to control for family -
wise error rate. Effect sizes for each pairwise comparison were reported using the
standardized Z-score effect size (r = Z/√N ), where Z is the Z -score from the Wilcoxon test
and N is the number of pairs (where r ≈ 0.1 is small, r ≈ 0.3 is medium, and r ≈ 0.5 is large).
All statistical analyses were performed using MATLAB (v2024b).
Section III: Neurobehavioral Prediction
This section investigated GEDAI's denoising performance using real-world EEG data, moving
beyond simulated environments. While genuine ground-truth EEG data is unobtainable in such
circumstances, EEG can still be used to predict specific objective information from an
experiment. Our central hypothe sis was that superior denoising would preserve the crucial
neural information necessary for more accurate predictions. We tested this hypothesis across
two distinct datasets and scenarios below.
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Classification of visual stimuli based on single -trial Event Related Potentials
(ERP)
Here, we used publicly available data ( https://zenodo.org/records/7495536) from a visual
oddball study by Omejc and colleagues (Omejc et al., 2023) . A total of 70 healthy adult
individuals passively viewed frequent (white square) and rare (Einstein's face) stimuli while
being recorded with a 32 -channel EEG sampled at 256 Hz. Each participant was presented
with 124 frequent (84%) and 23 rare (16%) stimuli. For full details of the experiment please
see (Omejc et al., 2023) . After 1 -40 Hz band -pass filtering and average referencing the
continuous EEG data, we ran each denoising algorithm with its default settings (as described
in the EEG simulations) without any bad epoch rejection. Accordingly, ASR’s bad channel
rejection step was enabled for this algorithm, as well as prior to running IClabel or MARA. No
explicit bad channel rejection was utilized for GEDAI. For IClabel, only components flagged
as "brain" or "other" were retained as clean EEG data. The open MATLAB analysis code
(https://github.com/NinaOmejc/VEP_classification_aging) was then utilized for the extraction
of single-trial ERP features (Omejc et al., 2023) . Time-independent statistical ERP features
were extracted ba sed on four ERP components: P1, N170, P2, and P3. Each of these
components was parameterized by four metrics: peak amplitude, mean amplitude, peak
latency, and fractional 50% peak latency. After feature selection based on mutual information,
eight time-independent features were used for classification, specifically the peak amplitudes
and fractional 50% peak latencies at four electrode clusters (occipital, parietal, central, and
frontal).
We performed the binary classification task by concatenating all subjects’ trials together, and
used a linear support vector machine (Matlab’s fitcsvm function) with tenfold cross-validation,
averaging the validation scores over 100 runs. In order to assess each algorithm’s full potential
for signal recovery, we did not perform any “bad” ERP trial rejection before or after denoising.
Hence, all trials were classified based on whether they contained a frequent or infrequent
stimulus. Given the strong class imbalance, classification performance was reported as the
area under the curve (AUC) of the receiver operating characteristic (ROC), averaged across
all subjects. DeLong’s test (DeLong et al., 1988) was used to estimate the statistical
significance of AUC between models, with Bonferroni multiple comparison correction.
Subject identification based on brain fingerprinting
Here, we used each person's unique resting-state EEG activity to identify them among a group
of 100 individuals, also known as “brain fingerprinting”. For this, we utilised the Dortmund Vital
Study dataset, freely accessible at OpenNeuro
(https://doi.org/10.18112/openneuro.ds005385.v1.0.3). This dataset contained EEG
recordings of adult subjects (mean age: 44 years) in a test -retest design, where the retest of
the same individuals was rec orded at 5 years follow -up. From this dataset, we included the
first n=100 subjects that contained recordings of both Session 1 (“test”) and Session 2 (“retest
“). Each test and retest file consisted of 180 seconds of eyes-open resting state before a
cognitive task, recorded with 62 channels and a sampling rate of 100 Hz. After 1-45 Hz band-
pass filtering and average referencing, all EEG recordings were then denoised with ASR,
IClabel, MARA, or GEDAI using default settings (identical to the EEG simulations) . Hence,
bad channel rejection was enabled for ASR, IClabel and MARA, but not GEDAI. For IClabel,
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only components flagged as "brain" or "other" were retained as clean EEG data. In order to
conduct fingerprinting, we first calculated the spatial covariance matrix (i.e. channel x channel)
of the denoised data using MATLAB’s cov function. Then, the correlation distance (with range
-1 to +1) between the Session 1 recordings’ and Session 2 recordings’ covariance matrices
was calculated using MATLAB’s pdist2 function. The values from this square distance matrix
were subtracted from 1, yielding a 100 x 100 similarity matrix between Sessions 1 (test) and
Sessions 2 (retest), also known as the Identifiability matrix (Amico & Goñi, 2018) . The
Identifiability matrix has subjects as rows and columns, and encodes the information about
the self-similarity (Iself, main diagonal elements) of each subject with themself, across the
test/retest sessions, and the similarity of each subject with the others (or Iothers, off-diagonal
elements). The overall goal is to predict the identity of a single subject from Session 1 based
on the similarity of that recording with multi -subject data from Session 2. As a measure of
fingerprinting performance, we used the success rate (Sorrentino et al., 2021) from code
available at https://github.com/eamico/Clinical_fingerprinting/blob/master/FC_fingerprint.m.
The success rate (%) indicates how many times an Iself value is higher than the Iothers values
on the same row and column of the Identifiability matrix. In other words, th e success rate
represents the percentage of the number of individual off-diagonal comparisons when the self-
correlation “wins”, which is a more granular comparison rather than a binary correct/incorrect
prediction of the subject. To estimate the variabilit y in fingerprinting performance for each
algorithm, we performed 50 random resamples of the denoised EEG data. Each resample
consisted of a total of 10 seconds (i.e. 1000 random data samples), from which the spatial
covariance matrix was calculated and the success score estimated. Following a significant
Kuskall-Wallis test result (p <0.05), post -hoc comparisons between algorithms were
conducted using MATLAB's multcompare function with a Bonferroni correction to control the
family-wise error rate.
Hardware and Software Platform
All computations were carried out using MATLAB software v2024b running on a Windows
desktop PC with an Intel-Core Ultra 9 285K CPU with 24 parallel cores and 64GB of RAM. All
tests were performed with the CPU using parallel processing, with no GPU acceleration.
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Results
Here, we compared the GEDAI algorithm to three established denoising algorithms (ASR,
MARA and ICLabel) in terms of ground -truth (i.e. clean background signal) recovery. We
principally report the SNR after and RRMSE effect sizes. Matching figures for RRMSE can be
found in Fig. SX of the Supplementary Results. For the Correlation Coefficient R, we show its
values in the global comparisons at the end of each section.
Denoising Benchmark of Synthetic EEG
We compared the denoising of 3,200 contaminated datasets, each containing 100 seconds of
64-channel EEG, which varied across 4 levels of temporal contamination, baseline SNRs, and
artifact type. These datasets combined synthetic background EEG (simulated in s ilico via
forward modelling) with semi-synthetic EOG/EMG artifacts and synthetic noise (see Methods
for more details).
For example videos of synthetic ground-truth, noise -contaminated and GEDAI -denoised
EEG, see Synthetic_Video_1 and Synthetic_Video_2.
Figure 3. Denoising of Synthetic EEG
A) By temporal contamination (%). Results are pooled across all SNRbefore and all artifact types. For
every temporal contamination level, each coloured data point represents 1 of 800 datasets (50 datasets
x 4 SNR levels x 4 artifact types). B) By SNR before (dB). Results are pooled across all tem poral
contamination levels and all artifact types. For every SNR before, each coloured data point represents 1
of 800 datasets (50 datasets x 4 artifact types x 4 temporal contamination levels). C) By artifact type.
Results
are pooled across all SNRbefore and temporal contamination levels. For each artifact type, each
coloured data point represents 1 of 800 datasets (50 datasets x 4 SNR levels x 4 temporal
contamination levels). D) Computational time (seconds). Lower values indicate faster calculations.
An asterisk indicates the winning algorithm (p < 0.05 Bonferroni corrected). If no asterisk is present, it
signifies a statistical tie.
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Figure 3 above shows benchmarking across different aggregation levels (temporal
contamination levels, SNRbefore , artifact type and computational time). Higher SNRafter and lower
RRMSE (for RRMSE see Supplementary Fig. S7 ) values indicate better denoising,
respectively. Differences in SNRafter and RRMSE are reported below (effect size r = Z/√N).
By temporal contamination (Fig 3A):
For 25% , GEDAI (median = 14.54 dB, IQR = 12.67 − 16.35) outperformed all algorithms
except for MARA (median = 16.34 dB, IQR = 9.91−21.63), with non-significant differences in
SNRafter (r = -0.13, p = 0.24) and RRMSE (r = 0.0082, p = 0.4 6); following a Friedman test:
χ²(3) = 257, p = 2.6 x 10-55.
For 50% , GEDAI (median = 13.00 dB, IQR = 10.71 −14.99) outperformed all algorithms,
including the next-best MARA (median = 12.00 dB, IQR = 4.82−17.95) in SNRafter (r = 0.090,
p = 0.0036) and RRMS E (r = -0.22, p = 0.0015); following a Friedman test: χ²(3) = 519, p =
2.9 x 10-112.
For 75% , GEDAI (median = 12.43 dB, IQR = 10.12 −14.63) outperformed all algorithms,
including the next-best MARA (median = 10.12 dB, IQR = 2.93−14.65) in SNRafter (r = 0.34, p
= 6.4e-15) and RRMSE (r = -0.46, p = 1.9 x 10-18); following a Friedman test: χ²(3) = 899, p =
1.50 x 10-194.
For 100% , GEDAI (median = 12.38 dB, IQR = 9.96 −14.55) outperformed all algorithms,
including the next-best MARA (median = 6.75 dB, IQR = -0.28−11.47), the closest competitor,
in SNR after (r = 0.59, p = 4.7 x 10 -51) and RRMSE (r = -0.70, p = 1.8 x 10 -60); following a
Friedman test: χ²(3) = 1028, p = 1.6 x 10-222.
By SNRbefore (Fig 3B)
For -9 dB, GEDAI (median = 12.68 dB, IQR = 10.28 −15.16) outperformed all algorithms,
including the next-best MARA (median = 9.39 dB, IQR = 0.23−13.59), the closest competitor,
in SNRafter (r = 0.46, p = 1.40 x 10 -30) and RRMSE (r = -0.56, p = 3.7 x 10 -33); following a
Friedman test: χ²(3) = 657, p = 4.3 x 10-142.
For -6 dB, GEDAI (median = 13.00 dB, IQR = 10.59 −15.24) outperformed all algorithms,
including the next -best MARA (median = 10.19 dB, IQR = 2.63 − 15.81), the closest
competitor, in SNRafter (r = 0.33, p = 2.0 x 10-16) and RRMSE (r = -0.46, p = 1.3 x 10-19); following
a Friedman test: χ²(3) = 607, p = 2.4 x 10-131.
For -3 dB, GEDAI (median = 13.23 dB, IQR = 10.72 −15.43) outperformed all algorithms,
including the next-best MARA (median = 11.36 dB, IQR = 4.01−17.78), the closest competitor,
in SNRafter (r = 0.14, p = 0.0025) and RRMSE (r = -0.30, p = 3.7 x 10-05 ); following a Friedman
test: χ²(3) = 565, p = 3.2 x 10-122.
For 0 dB , GEDAI (median = 13.37 dB, IQR = 11.06 −15.52) outperformed all algorithms
except for MARA (median = 13.04 dB, IQR = 6.97−19.05), with non-significant differences in
SNRafter (r = -0.03, p = 1) and RRMSE (r = -0.14, p = 0.83); following a Friedman test: χ²(3) =
493, p = 1.8 x 10-106.
By artifact type (Fig 3C)
For EOG , GEDAI (median = 13.12 dB, IQR = 11.41 −14.71) outperformed all algorithms
except for MARA (median = 11.70 dB, IQR = 6.35−18.62), with non-significant differences in
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SNRafter (r = 0.049, p = 0.79) and RRMSE (r = -0.16, p = 0.79); following a Friedman test: χ²(3)
= 1127, p = 4.1 x 10-244.
For EMG , GEDAI (median = 13.33 dB, IQR = 10.87 −14.65) outperformed all algorithms,
including the next-best MARA (median = 10.62 dB, IQR = 3.22−17.75) in SNRafter (r = 0.25, p
= 1.9 x 10-10) and RRMSE (r = -0.36, p = 1.6 x 10-10); following a Friedman test: χ²(3) = 614,
p = 1.0 x 10-132.
For NOISE, GEDAI (median = 17.54 dB, IQR = 14.35 - 18.88) outperformed all algorithms,
including the next-best ASR (median = 14.75 dB, IQR = 9.28−19.51) in SNRafter (r = 0.073, p
= 3.8 x 10-06) and RRMSE (r = -0.33, p = 5.2 x 10-11); following a Friedman test: χ²(3) = 315,
p = 5.9 x 10-68.
For NOISE + EOG + EMG, GEDAI (median = 10.82 dB, IQR = 9.16−12.02) outperformed all
algorithms, including the next-best MARA (median = 8.10 dB, IQR = 1.43 −12.50) in SNRafter
(r = 0.44, p = 3.4 x 10 -21) and RRMSE (r = -0.52, p = 4.7 x 10 -24); following a Friedman test:
χ²(3) = 942, p = 7.7 x 10-204.
Computational time (Fig 3D)
For EOG, GEDAI (median = 4.62 s, IQR = 4.38−4.97) outperformed all algorithms, including
the next-best ASR (median = 5.30 seconds, IQR = 4.33 - 6.16) in Time (r = -0.44, p = 5.1 x
10-05); following a Friedman test: χ²(3) = 2180, p < m.p.
For EMG, GEDAI (median = 4.61 s, IQR = 4.34−4.96) outperformed all algorithms except for
ASR (median = 3.77 seconds, IQR = 3.10−5.18), with a significant difference in Time (r = 0.40,
p = 2.1 x 10-9); following a Friedman test: χ²(3) = 2199, p < m.p.
For NOISE, GEDAI (median = 4.48 s, IQR = 4.26 −4.82) outperformed all algorithms except
for ASR (median = 4.00 s, IQR = 3.36−4.97), with a significant difference in Time (r = 0.24, p
= 1.6 x 10-9); following a Friedman test: χ²(3) =2200, p < m.p.
For NOISE + EOG + EMG , GEDAI (median = 4.52 s, IQR = 4.27 −4.89) outperformed all
algorithms except for ASR (median = 5.04, IQR = 3.83−5.99), with a non-significant difference
in Time (r = -0.29, p = 0.13); following a Friedman test: χ²(3) = 2165, p < m.p.
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Figure 4. Global statistics for synthetic EEG benchmark
Global means and 95% conf idence intervals for synthetic EEG denoising across all temporal
contamination levels, baseline SNRs and artifact types for: Correlation (top left panel, higher is better),
SNRafter in dB (top right panel, higher is better), RRMSE (bottom left panel, lower is better),
Computational time in seconds (bottom right panel, lower is better). Confidence intervals are plotted
but are very narrow due to the large sample size.
Globally: following a Friedman test χ²(3) = 2252, p < m.p. across all datasets and conditions,
GEDAI outperformed all algorithms in post -hoc pairwise comparisons, with absolute means
and 95% confidence intervals illustrated in Fig. 4. GEDAI significantly differed from MARA,
the closest competitor in SNRafter (r = 0.23 ; GEDAI mean = 13.1 dB ; MARA mean = 10.8 dB),
RRMSE (r = -0.37 ; GEDAI mean = 0.24 ; MARA mean = 0.51) and Correlation Coefficient (r
= 0.37 ; GEDAI mean = 0.96 ; MARA mean = 0.87). GEDAI did not significantly differ from
ASR, the closest competitor in Time (r = -0.03 ; GEDAI mean = 4.6 s; ASR mean = 4.7 s).
Denoising Benchmark of Empirical EEG
We contrasted the denoising of 6,400 contaminated datasets, each containing 60 seconds of
27-channel EEG, which varied across 4 levels of temporal contamination, baseline SNR
(SNRbefore), and artifact type. These datasets combined genuine background EEG (serving as
the ground truth) with actual EOG/EMG/NOISE artifacts (see Methods for more details).
For example videos of empirical ground-truth, noise -contaminated a nd GEDAI -denoised
EEG, see Empirical_Video_1 and Empirical_Video_2.
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Figure 5. Denoising of Empirical EEG
A) By temporal contamination (%). Results are pooled across all SNRbefore and all artifact types. For
every temporal contamination level, each coloured data point represents 1 of 1,600 datasets (100
datasets x 4 SNR levels x 4 artifact types). B) By SNRbefore (dB). Results are pooled across all temporal
contamination levels and all artifact types. For every SNR before, each coloured data point represents 1
of 1,600 datasets (100 datasets x 4 artifact types x 4 temporal contamination levels). C) By artifact
type. Results are pooled across all SNRbefore and temporal contamination levels. For each artifact type,
each coloured data point represents 1 of 1,600 datasets (100 datasets x 4 SNR levels x 4 temporal
contamination levels). D) Computational time (seconds). Lower values indicate faster calculations.
An asterisk indicates the winning algorithm (p < 0.05 Bonferroni corrected). If no asterisk is present, it
signifies a statistical tie .
Figure 5 above shows benchmarking across different aggregation levels (temporal
contamination levels, SNRbefore , artifact type and computational time). Higher SNRafter and lower
RRMSE (for RRMSE see Supplementary Fig. S7 ) values indicate better denoising,
respectively. Differences in SNRafter and RRMSE are reported below (effect size r = Z/√N).
By temporal contamination (Fig 5A)
For 25%, GEDAI (median = 9.84 dB, IQR = 8.77-11.06) outperformed all algorithms, including
the next-best ASR (median = 9.79 dB, IQR = 7.97-11.97) in SNRafter (r = -0.07, p = 0.032) and
RRMSE (r = 0.0046, p = 0.02); following a Friedman test: χ²(3) = 1855, p < m.p.
For 50%, GEDAI (median = 8.66 dB, IQR = 7.43-10.03) outperformed all algorithms, including
the next-best MARA (median = 6.95 dB, IQR = 4.34-9.33) in SNRafter (r = 0.55, p = 4.8 x 10-90)
and RRMSE (r = -0.60, p = 2.2 x 10-91); following a Friedman test: χ²(3) = 1134, p = 1.6 x 10-
245.
For 75%, GEDAI (median = 7.98 dB, IQR = 6.67-9.45) outperformed all algorithms, including
the next-best MARA (median = 6.06 dB, IQR = 2.67-8.92) in SNRafter (r = 0.53, p = 1.0 x 10-65)
and RRMSE (r = -0.60, p = 1.1 x 10-73); following a Friedman test: χ²(3) = 1356, p = 1.3 x 10-
293.
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For 100%, GEDAI (median = 7.98 dB, IQR = 6.60-9.27 ) outperformed all algorithms, including
the next-best MARA (median = 5.01 dB, IQR = 0.76 -8.34) in SNRafter (r = 0.62, p = 6.2 x 10 -
105) and RRMSE (r = -0.67, p = 2.3 x 10-112); following a Friedman test: χ²(3) = 1615, p < m.p.
by SNRbefore (Fig 5B)
For -9 dB, GEDAI (median = 8.24 dB, IQR = 6.69−9.60) outperformed all algorithms, including
the next-best MARA (median = 5.73 dB, IQR = 0.97−8.74) in SNRafter (r = 0.61, p = 1.92 x 10-
101) and RRMSE (r = -0.66, p = 2.1 x 10-104); following a Friedman test: χ²(3) =1334, p = 8.3 x
10-289.
For -6 dB, GEDAI (median = 8.46 dB, IQR = 7.07−9.83) outperformed all algorithms, including
the next-best MARA (median = 6.49 dB, IQR = 2.77−9.03) in SNRafter (r = 0.58, p = 3.0 x 10 -
91) and RRMSE (r = -0.64, p = 1.1 x 10-97) ; following a Friedman test: χ²(3) =1194, p = 1.5 x
10-258.
For -3 dB , GEDAI (median = 8.79 dB, IQR = 7.28 −10.24) outperformed all algorithms,
including the next-best MARA (median = 6.92 dB, IQR = 4.06−9.27) in SNRafter (r = 0.58, p =
9.8 x 10-92) and RRMSE (r = -0.63, p = 1.5 x 10-98); following a Friedman test: χ²(3) = 1078, p
= 2.7 x 10-233.
For 0 dB , GEDAI (median = 9.15 dB, IQR = 7.85 −10.62) outperformed all algorithms,
including the next-best ASR (median = 7.49 dB, IQR = 4.35 −10.34) in SNRafter (r = 0.47, p =
9.2 x 10-85) and RRMSE (r = -0.55, p = 5.9e-88); following a Friedman test: χ²(3) =1056, p =
1.6 x 10-228.
By artifact type (Fig 5C)
For EOG, GEDAI (median = 8.37 dB, IQR = 7.44−9.32) outperformed all algorithms, including
the next-best IClabel (median = 8.15 dB, IQR = 6.50 −9.45) in SNR after (r = 0.26, p = 0.003)
and RRMSE (r = -0.30, p = 0.003); following a Friedman test: χ²(3) = 1918, p < m.p.
For EMG, GEDAI (median = 9.97 dB, IQR = 9.04−10.99) outperformed all algorithms, except
for MARA (median = 10.39 dB, IQR = 8.04−11.76), with non-significant differences in SNRafter
(r = -0.06, p = 0.70) and RRMSE (r = -0.007, p = 0.70); following a Friedman test: χ²(3) =
1574, p < m.p.
For NOISE , GEDAI (median = 9.08 dB, IQR = 7.47 −11.16) outperfor med all algorithms,
including the next-best ASR (median = 8.08 dB, IQR = 3.76 −11.56) in SNRafter(r = 0.24, p =
6.5e-17) and RRMSE (r = -0.40, p = 7.9e-26); following a Friedman test: χ²(3) =2301, p < m.p.
For NOISE + EOG + EMG , GEDAI (median = 7.1 dB, IQR = 5.93−8.29) outperformed all
algorithms, including the next-best MARA (median = 4.21 dB, IQR = 1.83−6.36) in SNRafter (r
= 0.82, p = 8.4 x 10 -186) and RRMSE (r = -0.83, p = 1.9 x 10 -192); following a Friedman test:
χ²(3) = 2478, p < m.p.
Computational time (Fig 5D)
For EOG, GEDAI (median = 1.06 s, IQR = 1.03−1.11) outperformed all algorithms, including
the next-best ASR (median = 2.13 s, IQR = 1.80 −2.58) in Time ( r = -0.87, p = 6.0 x 10 -141);
following a Friedman test: χ²(3) = 4493, p < m.p.
For EMG, GEDAI (median = 1.07 s, IQR = 1.03−1.11) outperformed all algorithms, including
the next-best ASR (median = 1.99 s, IQR = 1.67−2.47), the closest competitor, in Time (r = -
0.87, p = 4.3 x 10-134); following a Friedman test: χ²(3) = 4562, p < m.p.
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For NOISE, GEDAI (median = 1.07 s, IQR = 1.03−1.12) outperformed all algorithms, including
the next-best ASR (median = 1.96 s, IQR = 1.58 −2.50) in Time (r = -0.85, p = 6.1 x 10 -161);
following a Friedman test: χ²(3) = 4098, p < m.p.
For NOISE + EOG + EMG , GEDAI (medi an = 1.08 s, IQR = 1.04 - 1.13) outperformed all
algorithms, including the next -best ASR (median = 2.22 s, IQR = 1.83 −2.77) in Time (r = -
0.87, p = 1.53 x 10-223 ); following a Friedman test: χ²(3) = 4018, p < m.p.
Figure 6. Global statistics for empirical EEG benchmark
Global means and 95% confidence intervals for empirical EEG denoising across all temporal
contamination levels, baseline SNRs and artifact types for: Correlation (top left panel, higher is better),
SNRafter in dB (top right panel, higher is better), RRMSE (bottom left panel, lower is better),
Computational time in seconds (bottom right panel, lower is better). Confidence intervals are plotted
but are very narrow due to the large sample size.
Globally: following a Friedman test χ²(3) = 4704, p < m.p. across all datasets and conditions,
GEDAI outperformed all algorithms in post-hoc pairwise comparisons (p < m.p.), with absolute
means and 95% confidence intervals illustrated in Fig. 6. GEDAI significantly differed from
MARA, the closest competitor in SNR after (r = 0.59 ; GEDAI mean= 8.67 dB ; MARA mean =
6.14 dB) and RRMSE (r = -0.64 ; GEDAI mean = 0.38 ; MARA mean = 0.57). GEDAI
significantly differed from ASR, the closest competitor, in Correlation Coeff icient (r = 0.63 ;
GEDAI mean= 0.92 ; ASR mean= 0.83) and Time (r = -0.86 ; GEDAI mean = 1.1 s; ASR mean
= 2.2 s).
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Neurobehavioral Prediction
Figure 7. Single-trial ERP Classification and Brain Fingerprinting
A) ROC curves for binary classification of ER Ps from a visual oddball task, after denoising
with each algorithm. Each curve is based on >10,000 trials (no bad trials were rejected). B)
Mean success rate (%) of individual identification from 100 subjects, after denoising with each
algorithm. Each poin t represents 1 of 50 resamples from each subject’s resting -state EEG
data. An asterisk indicates the winning algorithm (p < 0.05 Bonferroni corrected).
Single-trial ERP Classification
The goal here was to predict whether a subject observed either a freque nt (‘white
square’) or infrequent (‘Einstein’s face’) visual stimulus, based on a single -trial ERP.
Figure 7A shows the receiver -operating characteristics (ROCs) indicating binary
classification performance following denoising by each algorithm without any bad trial
rejection. DeLong tests on the area -under-the-curve (AUC) confirmed that GEDAI
(mean AUC = 0.80) statistically outperformed (p = 4.2 x 10-36) the next-best algorithm
ASR (mean AUC = 0.72), followed by MARA (mean AUC = 0.58) and IClabel (mean
AUC = 0.58). Basic average referencing plus 1 -40 Hz band -pass filtering, i.e RAW
(mean AUC = 0.52) performed close to chance level (AUC of 0.50, dotted-line).
Brain Fingerprinting
In the context of brain fingerprinting, and as shown in Figure 7B, following a significant
Kuskall-Wallis test χ²(3) = 187, p = 3.4 x 10 -40, post-hoc comparisons indicated that
GEDAI (mean success rate = 91%) demonstrated higher accuracy (r = 0.86, p = 9.4 x
10-5) than the next-best algorithm ASR (mean success rate = 76%), followed by MARA
(mean success rate = 63%), RAW (mean success rate = 55%) and IClabel (mean
success rate = 54%).
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Feature Comparison between Denoising Algorithms
Key features of state-of-the-art denoising algorithms
ASR ICLabel MARA GEDAI
Rank preservation ✓ - - ✓
Short data length (<1 second) ✓ - - ✓
Automatic thresholding / feature
selection
- ✓ ✓ ✓
Non-orthogonal artifacts - ✓ ✓ ✓
Gaussian artifacts ✓ - - ✓
Spatially non-stationary artifacts ✓ - - ✓
100% temporally contaminated data - ✓ ✓ ✓
Real-time capable ✓ - - ✓
Table 1. Algorithmic feature comparison of the tested denoising algorithms
Note: ✓ means that the performance of the function should not be affected in the listed
condition. However, edge cases in which a technique could perform to a satisfying level in a
condition for which it is not marked with an ✓ are possible.
Discussion
This paper introduces GEDAI, a novel algorithm designed to advance EEG artifact correction,
addressing a key challenge in advancing EEG technology, as highlighted in a survey by
Mushtaq and colleagues (Mushtaq et al., 2024) . Their study, involving 500 experts across
more than 50 countries, identified improved artifact correction as the top priority in the field.
Due to its theoretical underpinnings, GEDAI is fully automated, requiring no user expertise or
input, and may be used to recover brain signals from low signal -to-noise recordings (e.g. -9
dB) with up to 100% temporal contamination. Validated through rigorous simulations on
thousands of synthetic and real -world datasets, GEDAI marks a significant a dvance in EEG
artifact removal, delivering a unique blend of processing speed and denoising precision. As
elaborated below, GEDAI consistently performed better than, or on par with, competing
algorithms in simulations containing a single type of artifact (EMG or EOG only). Interestingly,
its most significant performance improvements were evident when handling multiple spatially
non-stationary and temporally overlapping artifacts, such as NOISE + EMG + EOG. This
makes it especially promising for use in real-world, noise-agnostic environments.
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Benchmark Simulations: synthetic and empirical EEG
Across both synthetic and empirical EEG benchmarks, GEDAI proved to be a highly effective
and robust method for artifact removal, demonstrating superior performance under diverse
and challenging conditions.
GEDAI's key strength was its superior performance on heavily contaminated data.
While comparable to other algorithms like ASR and MARA in datasets with sparse artifacts
(25% contamination), its superior ity grew significantly as contamination levels increased to
50%, 75%, and 100%, making it optimal for processing pervasively corrupted recordings.
Furthermore, GEDAI excelled at handling complex, mixed artifacts. While its
performance on isolated ocular or muscular artifacts was similar to that of ICA-based methods,
it showed a large effect size of |r| > 0.5 when disentangling mixtures of EOG, EMG, and
noise—a crucial capability for real-world applications.
Finally, the algorithm consistently outperformed competitors in low signal-to-noise ratio
(SNR) environments (from -9 dB to -3 dB). This ability to reliably recover weak neural signals
from substantial background noise confirms GEDAI's suitability for applications where data
quality is a significant challenge.
Neurobehavioral Prediction: ERP classification and brain fingerprinting
The neurobehavioral results demonstrate that the GEDAI algorithm significantly enhances the
quality of EEG data for machine learning applications, outperforming all other tested methods
in two distinct tasks. For single-trial ERP classification, GEDAI achieved a high mean AUC of
0.80, substantially better than the next-best algorithm, ASR (0.72), and far exceeding the near-
chance performance of raw data. This performance advantage was even more pronounced in
the brain fingerprinting paradigm, where GEDAI reached 91% accuracy in subject
identification, surpassing ASR (76%) and other methods that were only marginally better than
baseline.
GEDAI Compared to Existing Denoising Methods
The GEDAI algorithm offers a combination of advantages that, to the best of our knowledge,
is not currently exhibited by competing EEG denoising methods within a single package. As
shown in Table 1, GEDAI appears to globally encompass the major strengths of ASR, ICLabel,
and MARA, while their capabilities are limited to specific subsets of features. GEDAI's
favorable outcomes may be firstly attributed to the adaptability of GEVD decomposition,
consistent with previous reports (Gouy-Pailler et al., 2009; Somers et al., 2018). Unlike PCA,
GEVD is not limited by source orthogonality, nor is it restricted by Gaussianity, as is the case
with ICA (Cohen, 2022b).
With parallel processing, GEDAI was between 3 to 15 times faster than ICA -based
denoising, and achieved speeds comparable to PCA-based ASR, a real-time capable method
(Kothe & Jung, 2015). Hence, GEDAI is computationally light enough for BCI applications.
Perhaps GEDAI's biggest advantage is that it is fully automated and requires no
operator expertise or input for component selection and/or hyperparameter tuning. While these
capacities are partially shared with the other algorithms, GEDAI can achieve automation in
the absence of any calibration or training data. Harnessing a "noise -free" EEG leadfield as a
theoretical reference model allows GEDAI to avoid shortcomings rela ted to the identification
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of clean data, as is the case for PCA, or specific artifact types, as is the case for ICA. This
overall combination of features makes GEDAI a great candidate for noise -agnostic settings,
such as dry-electrode or mobile EEG recordings, where clean samples might not be available
or the noise could be out-of-distribution.
Leadfield Filtering: Theoretically Informed M/EEG Artifact Removal
GEDAI’s key strength is the use of a theoretical M/EEG leadfield matrix for guiding the artifact
removal, a process we refer to as ‘leadfield filtering’. Existing denoising methods that use
theoretical reference models include Signal Space Projection (SSP) (Uusitalo & Ilmoniemi,
1997), Signal Space Separation (SSS) (Taulu et al., 2004), PureEEG (Hartmann et al., 2014),
SPHARA (Graichen et al., 2015) and the SOUND algorithm (Mutanen et al., 2018). Of these,
PureEEG and SOUND explicitly leverage leadfield modeling based on head anatomy.
However, unlike SOUND, GEDAI’s algorithm does not require ill-posed inverse modeling used
for source activity estimation (Mutanen et al., 2018) . The PureEEG algorithm, in contrast to
GEDAI’s, separately compu tes the artifact covariance in the frequency domain using a
Bayesian estimator, with the assumption that brain and artifact components are statistically
uncorrelated (Hartmann et al., 2014).
Cutting through the Noise with SENSAI
In GEDAI, a reference covariance matrix (refCOV) models the expected spatial correlations
of brain activity based on a physical head model. Using joint diagonalization (de Cheveigné &
Parra, 2014), GEDAI decomposes recorded data into components. Those components with a
spatial covariance inconsistent with the brain model are identified as artifacts (large
eigenvalues), while consistent components are treated as neural signals (small eigenvalues).
Determining the optimal cutoff between the artifact and brain components is neither
obvious nor trivial. GEDAI solves this with its second key innovation: the Signal & Noise
Subspace Alignment Index (SENSAI). SENSAI aut omatically finds the best separation
threshold by calculating an alignment score for various cutoffs and selecting the one that
maximizes the similarity between the denoised data and the theoretical brain subspace
defined by refCOV. The resulting SENSAI sc ore is a relative, not absolute, measure of
denoised data quality (0 -100%), dependent on the specific head model used. Although
beyond the scope of this paper, it also has potential future use as a quantitative index for
comparing EEG recording quality or the performance of different denoising methods.
Theoretical vs. Empirical Denoising Frameworks
This subject concerns the apparent dichotomy between the theoretical (leadfield-driven)
Reference
matrix used by GEDAI, and the empirical (data-driven) reference matrix used by
existing GEVD implementations for M/EEG denoising (Haslacher et al., 2021; F. Wang et al.,
2025). The core trade -off between using a leadfield -based theoretical versus a n empirical
refCOV for M/EEG denoising centers on model accuracy versus data dependency. A data -
driven, empirical refCOV captures the actual spatial structure of noise or signal as it manifests
in that specific recording and subject, but still requires that suitable segments of EEG can be
reliably identified and/or denoised a priori. In contrast, using a theoretical refCOV bypasses
the often difficult challenge of identifying pure noise or clean signal EEG segments, but relies
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on a good fit between the theoretical model and the actual data. In this case, deviations from
the forward model that are specific to the subject (e.g. anatomical variations) or the recording
(e.g. electrode misplacement) will likely lead to greater inaccuracies in the denoising process.
Bad channels and how to deal with them
Traditional methods handle bad channels by rejecting them entirely (Bigdely-Shamlo et al.,
2015; Kumaravel et al., 2022) , which removes both artifactual and potentially useful neural
signals. GEDAI offers a novel alternative by avoiding this binary rejection. It instead treats
activity from compromised channels as artifactual components, which are identified via GEVD
and removed if their spatial character istics deviate from the theoretical brain signal model.
Although our benchmark datasets included bad channels, this study did not explicitly evaluate
GEDAI's effectiveness in correcting them at individual -channel level. Crucially, the other
algorithms bene fited from a bad -channel rejection pre -processing step only when bad
channels were present. This potential advantage was not extended to the fully noise-agnostic
GEDAI pipeline. Future work should assess whether a hybrid approach, combining dedicated
bad c hannel rejection with GEDAI, outperforms either method alone in specific noise
scenarios.
Potential Future Extensions of GEDAI
The simultaneous acquisition of EEG -fMRI or non -invasive brain stimulation (NIBS)
techniques like transcranial direct current sti mulation (tDCS), transcranial alternating current
stimulation (tACS), and transcranial magnetic stimulation (TMS) present significant denoising
challenges due to large, complex artifacts often contaminating the entire recording. Given that
GEDAI uses leadfield filtering to separate brain activity from extra -cerebral sources of noise,
it may also prove effective for removing fMRI gradient and/or brain stimulation artifacts
originating outside the head. Although beyond the scope of this paper, our preliminary tests
on concurrent fMRI-EEG and EEG-NIBS recordings indicated successful removal of very high-
amplitude electromagnetic noise components. Therefore, GEDAI’s automated, robust
denoising capabilities based on biophysical principles could make it a promising candidate for
improving data quality in challenging multimodal and stimulation experiments. Finally, as
GEDAI utilizes a shared M/EEG forward model, its potential applicability could also extend to
magnetoencephalography (MEG) recordings, especially opti cally-pumped magnetometers
(OPM-MEG) where sensors maintain a fixed position relative to the head (Brookes et al.,
2022).
Limitations
First, GEDAI’s performance is highly dependent on an accurate match between the theoretical
leadfield model and the actual EEG electrode positions. Any spatial mismatch will
proportionally degrade its efficacy, making precise electrode placement a prerequisite for
optimal results.
Second, because GEDAI defines artifacts as signals originating outside the brain, it is
not designed to remove artifacts that originate from within the brain volume, such as those
from deep brain stimulation, for example.
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Third, the current implementation assumes uniform and uncorrelat ed brain sources.
Incorporating a more neurophysiologically realistic source covariance model (e.g. one that
accounts for functional networks and differing regional power) could improve performance,
though this requires further research.
Finally, like PCA/ICA, the number of removable artifact components is limited by the
number of channels, making GEDAI unsuitable for single-channel EEG.
Conclusion
Taken together, these findings position GEDAI as a state -of-the-art tool for EEG denoising,
distinguished by its robust performance in heavily contaminated, low-SNR conditions and its
particular strength in resolving complex mixtures of artifacts.
Data and code availability
The open-source GEDAI plugin for EEGLAB is available at:
https://github.com/neurotuning/GEDAI-master
All simulated datasets and analysis codes used in this paper will be released as a standalone
resource upon publication, known as “ BEAR: Benchmarking EEG Artifact Removal with
Synthetic and Empirical Datasets”. The open EEGLAB code will allow users to consult and
modify the specific default parameters used in this study.
Acknowledgements
We would like to thank Michael X Cohen for his helpful discussions as well as tutorials on
EEG and GEVD, which have inspired this work. This study was supported by the Swiss
National Science Foundation (SNSF), grant number 215712.
Competing Interests Statement
T.R. is an inventor on a patent application related to the GEDAI algorithm described in this
manuscript. The other authors declare they have no competing interests.
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32
Supplementary Results
Fig S1: Clean synthetic data : example simulated ‘background’ EEG (i.e.noise-free)
simulated with https://github.com/lrkrol/SEREEGA
Fig S2. Artifactual synthetic data : example of simulated data containing only EOG (left panel) or
EMG artifacts (right panel) - using source locations from Fig S5
with https://github.com/lrkrol/SEREEGA
+ https://github.com/ncclabsustech/EEGdenoiseNet
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33
Fig S3. Synthetic artifact source locations for simulated EOG (left panel) or EMG artifacts (right
panel) from https://github.com/lrkrol/SEREEGA
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34
Fig S4: Clean empirical data : example resting-state EEG recordings (i.e.noise-free)
from https://github.com/stefan-ehrlich/dataset-automaticArtifactRemoval
Fig S5. Artifactual empirical EEG data : example of simulated data containing only EOG (left panel)
or EMG artifacts (right panel)
from https://github.com/stefan-ehrlich/dataset-automaticArtifactRemoval
+ https://github.com/ncclabsustech/EEGdenoiseNet
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35
Fig S6. Noisy empirical EEG data : example of simulated data containing step artifacts (left panel) or
line noise
from https://github.com/stefan-ehrlich/dataset-automaticArtifactRemoval
+ https://github.com/ncclabsustech/EEGdenoiseNet
+ https://github.com/vpKumaravel/NEAR/tree/main/SimulateArtifacts
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36
Figure S7. Relative Root Mean Square Error (RRMSE) . Lower values indicate better denoising .
Asterisks indicate the winning algorithm in each case. No asterisk signifies a statistical tie.
A) Synthetic denoising by temporal contamination. For every temporal contamination level, each
coloured data point represents 1 of 800 datasets (50 datasets x 4 SNR levels x 4 artifact types).
B) Empirical denoising by temporal contamination. Results are pooled across all baseline SNRbefore
and all artifact types. For every temporal contamination level, each coloured data point represents 1 of
1,600 datasets (100 datasets x 4 SNR levels x 4 artifact types).
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37
C) Synthetic denoising by SNRbefore. Results are pooled across all temporal contamination levels and
all artifact types. For every SNRbefore, each coloured data point represents 1 of 800 datasets (50 datasets
x 4 artifact types x 4 temporal contamination levels).
D) Empirical denoising by SNRbefore. Results are pooled across all temporal contamination levels and
all artifact types. For every SNR before, each coloured data point rep resents 1 of 1,600 datasets (100
datasets x 4 artifact types x 4 temporal contamination levels).
E) Synthetic denoising by artifact type. Results are pooled across all SNR before and temporal
contamination levels. For every artifact type, each coloured data point represents 1 of 800 datasets (50
datasets x 4 SNR levels x 4 temporal contamination levels).
F) Empirical denoising by artifact type. Results are pooled across all SNR before and temporal
contamination levels. For every artifact type, each colour ed data point represents 1 of 1,600 datasets
(100 datasets x 4 SNR levels x 4 temporal contamination levels).
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