Electroencephalographic (EEG) signals are fundamental to neuroscience research and clinical applications such as brain-computer interfaces and neurological disorder diagnosis. These signals are typically a combination of neurological activity and noise, originating from various sources, including physiological artifacts like ocular and muscular movements. Under this setting, we tackle the challenge of distinguishing neurological activity from noise-related sources. We develop a novel EEG denoising model that operates in the frequency domain, leveraging prior knowledge about noise spectral features to adaptively compute optimal convolutional filters for noise separation. The model is trained to learn an empirical relationship connecting the spectral characteristics of noise and noisy signal to a non-linear transformation which allows signal denoising. Performance evaluation on the EEGdenoiseNet dataset shows that the proposed model achieves optimal results according to both temporal and spectral metrics. The model is found to remove physiological artifacts from input EEG data, thus achieving efective EEG denoising. Indeed, the model performance either matches or outperforms that achieved by benchmark models, proving to efectively remove both muscle and ocular artifacts without the need to perform any training on the particular type of artifact.
The electroencephalographic (EEG) signal is a time series acquired with non-invasive sensors
(called electrodes) placed on a subject’s scalp and is characterized by time, frequency and spatial
information [
This means that besides recording neural signals, the EEG captures noise generated from ocular,
muscular, and cardiac movements as examples of biological artifacts, and noise related to
nonbiological sources like cable movement, electrical interference, and electrode bad positioning
[
Many attempts have been presented in the state-of-the-art to reduce or remove these types
of artifacts, but automatic EEG denoising remains an open challenge [
OAs are the most easily detectable artifacts due to their spiking shape similar to a V and
their pronounced presence on signals recorded by frontal electrodes [
Notice that even if reference electrodes (EOG and EMG) can be used to track artifacts, the
interference between them and the EEG related electrodes is bidirectional, i.e., the artifacts
contaminate the EEG signals, and the EOG and EMG electrodes capture both artifacts and
neural activity [
After a brief overview of current studies presenting DL-based denoising techniques (Section 2), EEGdenoiseNet is described to provide a better understanding of the exploited data (Section 3). Afterwards, the proposed DL model is detailed (Section 4). Section 5 reports the performed experiments, discuss both obtained and literature results, and provide future developments. Final considerations are presented in Section 6.
This study focuses on DL-based denoising techniques, which will be detailed in this section,
and thus will not provide a dissertation of traditional processing methodologies. The readers
are invited to consult insightful review papers on these topics provided by the EEG research
community [
Starting from the work related to the exploited dataset, Zhang et al. [
Subsequently, other approaches have been proposed in the literature, like Yu et al.’s
end-toend DL framework, called DeepSeparator [
Another proposal is EEGDnet [
A Multi-Module Neural Network (MMNN) [16] is developed to be used in real-time environments and considering single-channel EEG data. MMNN has a modular structure constituted by blocks containing convolutional and fully-connected layers. The model convergence and learning ability is supported by the residual connections intra- and inter-blocks.
Other proposals exploit Generative Adversarial Networks (GANs) to remove noise. For example, Brophy et al. [17] sample the generator input directly from noisy EEG signals and make a comparison with the corresponding clean EEG signals in the discriminator. The generator is constituted by a Long-Short Term Memory (LSTM) network, while the discriminator is composed by four 1D convolutional layers and a fully-connected layer.
Similarly, Wang, Luo, and Shen [18] generator consists of a Bidirectional-LSTM (BiLSTM) and a LSTM layer, while the discriminator comprises five CNN layers plus a fully-connected layer. The noisy EEG are passed to the generator, producing the denoised EEG, which is inputted to the discriminator with the ground truth data. Therefore, the authors’ main aim is to map the relationships between clean EEG and artifacts to iteratively reduce the noise.
Finally, OAs only removal strategies are reported. Ozdemir, Kizilisik, and Guren [19] focus on the use of BiLSTM and propose a benchmark combining EEGDenoiseNet and the DEAP dataset [20]. Notice that the inputs of the BiLSTM are the time-frequency features extracted from the augmented data. Instead, Yin et al. [21] propose a cross-domain framework integrating time and frequency domain information, demonstrating that the extracted features are able to improve the performance of state-of-the-art methods when provided as input to DL models.
The EEGdenoiseNet [
In fact, Zhang et al. construct a dataset exploiting EEG, EOG and EMG signals of publicly available datasets, processing these data to obtain neural and noise signals that could be considered unafected by other sources and thus clean.
In particular, the authors consider Cho et al.’s EEG dataset [22], presenting signals collected with 64 electrodes on 52 subjects during a motor execution and imagery experiment. The EOG signals have been instead taken from Kanoga et al. [23], and the BCI Competition IV dataset 2a and 2b [24], while the EMG signals are related to a facial EMG dataset [25].
Afterwards, the data are pre-processed as follows: 1. Signals are notch (50 Hz) and bandpass (EEG: 1-80 Hz, EOG: 0.3-10 Hz, and EMG: 1-120
Hz) filtered. 2. Signals are re-sampled, considering a sampling rate of 256 Hz or 512 Hz for the EEG, 256
Hz for the EOG, and 512 Hz for the EMG signals. 3. Signals are divided in segments of 2 s to provide data as cleaner as possible, and standardized. Segments are visually inspected by experts.
Notice that between point 1 and 2, EEG signals are processed with the independent component analysis based ICLabel toolbox [26] to obtain clean ground truth data. The data resulting from this process are 4,514, 3,400, and 5,598 pure (as defined by the authors) EEG, EOG, and EMG segments, respectively.
The pure EEG data are used as the ground truth and semi-synthetic data produced by linearly
combining these data with EOG or EMG segments, according to the following formula:
= +
(2)
where is the noisy signal, the pure EEG signal, the EOG or EMG noise, and a
hyperparameter controlling the SNR. For further information, please consult the original publication by
Zhang et al. [
In this work a novel denoising model leveraging data in the frequency domain is proposed.
The idea is that given a prior knowledge about the noise spectral features, an optimal convolutional filter, or a cascade of filters, can be computed to separate the noise from signal. Therefore the proposed model is trained to learn an empirical relationship which connects the spectral characteristics of noise and noisy signal to a non-linear transformation able to denoise that signal. The assumptions under which the model can operate are: • the PSD estimate of the noise is given; • the relation between signal and noise is known.
For the EEGdenoiseNet dataset this relationship is a linear mixture of the clean signal and the artifacts (OAs and MAs considered one at a time) as per Eq. 2.
The PSD related to noise , the PSD related to noisy signal , and the noisy signal are all given separately as multiple inputs to the model, which consists of two major components, repeatedly applied: the kernel evaluator and the convolutional filters applier. The kernel evaluator is used to evaluate the best convolutional filters from the frequencies that are characteristic of the noisy signal and noise. The convolutional filters applier then efectively apply the filters estimated by the kernel evaluator to the time domain signal. The overall pipeline of the model is depicted in Figure 1.
The model is inputted with two inputs not directly interacting with each other: the PSDs and the time series. The former is the concatenation of the PSD of the pure noise, the PSD of the noisy signal (which is always known) and the ratio between the noisy signal and the pure noise PSDs, which does not add any further information but facilitates model learning since the ratio is an operation not easily reproducible by the following convolutional operations. The PSDs and their ratio are processed by the kernel evaluator blocks only. The latter, i.e., the time series, is the noisy signal in the time domain, which is processed in cascade by the convolutional filters applier block in order to obtain the denoised signal.
For each convolutional step a kernel evaluator block, which structure is depicted in Figure 2, evaluates a set of convolutional filters (i.e., the kernels values) to be applied to the time series.
Each block is inputted with the PSDs, which are processed by two symmetric series of 1D convolutional layers with tanh activations. These branches independently estimate the real and imaginary part of the filters that will be subsequently applied to the time series. Remind that in this case the model is working in the frequency domain, dealing with PSDs.
To translate the filters into the time domain, where they will actually operate on the noisy signal, an inverse real fast Fourier transformation (IRFFT) is then applied to the complex 1D arrays obtained by assembling the two branches.
The IRFFT operation adds algorithmic capabilities to the model since the convolutional and activation layers in the pipeline cannot replace it by performing an analogous transformation.
The inverse fast Fourier transform (IFFT) is an algorithm that eficiently computes the inverse discrete Fourier transform (IDFT) of a sequence and is given as follows:
The IRFFT is a particular case of IFFT which returns real-valued sequences, as would be desired for the time-domain filters, without sacrificing the useful algorithmic capabilities of the Fourier transform.
As a final step, the filters outputted by the IRFFT are linearly combined with a 1D convolutional layer with kernel size equal to 1. The last tanh activation forces the filters values in the range [− 1; 1], avoiding numerical problems coming from too high values and acting as a normalizer on filters.
The length of the filters evaluated by the kernel evaluator block is equal to the length of the input noisy signal itself, thus the filters are able to act on any signal frequency and to extract both local and global features. The kernel evaluator blocks contain all and only the trainable parameters of the model, specifically the kernels of the 1D convolutions applied to the PSDs. Therefore these parameters, which amount to 224192, depend only on the frequency characteristics of the signal and noise. The choice of the number of convolutional layers and the size of the kernels they apply are dictated by having a suficiently large receptive field that operates on correlated frequencies that are close to each other, without taking into account very distant frequencies.
The filters evaluated by the kernel evaluator blocks are inputted to the convolutional filter applier, which uses them without further changes. As depicted in Figure 3, on the first step this part of the model applies 1D convolutions directly to the noisy signal using the filters of the first kernel evaluator block and the resulting features are inputted to an ELU activation function. Subsequently, these features are convoluted with the filters evaluated by the second block and once again activated by the ELU function. This operation is repeated in cascade until the last convolution, which returns directly the denoised signal. No activation is applied in this last step and the range of possible values is therefore (−∞ ; +∞), which is also the range of the possible clean signals.
The number of convolutions applied in series and the number of filters applied at each convolutional step were sized based on domain knowledge and in a way that limited the total number of parameters trained in the kernel evaluator blocks.
The denoising capabilities of the proposed model are evaluated on the basis of the reconstruction
performance of pure EEG signals from the EEGdenoiseNet dataset when contaminated by EOG
or EMG artifacts, separately, following the paradigm proposed by the authors of the benchmark
model [
The original dataset has been randomly partitioned into two mutually exclusive subsets, i.e., a training dataset (60%) and a test dataset (40%). Therefore, the training dataset consists of 2,708 EEG, 3,358 EMG and 2,040 EOG samples while the test dataset consists of 1,806 EEG, 2,240 EMG and 1,360 EOG samples.
To synthesize the noisy signals from the pure samples, the linear relation defined in Eq. 2
has been used. The values are randomly sampled to obtain a uniform distribution of the
signal-to-noise ratio (SNR) in the range [− 7; 4] for the model training and in the range
[− 7; 2] for the model testing. This is a common range for OAs and MAs and the same
range has been used by the EEGdenoiseNet authors [
During the training phase, the noisy data synthesis is performed runtime in a random way, allowing the model to be trained with constantly new combinations of signal, noise and SNR.
Both noisy signal and pure noise are standardized using the mean and standard deviation of the noisy signal.
In order to quantitatively evaluate the performance of the model in the denoising task, standard metrics used for benchmarking on EEGdenoiseNet data are adopted.
The Root Mean Square Error (RMSE) is used to measure the variance between the output predicted by the model and the ground truth and it is defined by: = √︃ ∑︀=1( − ˜)2 (4) where denotes the EEG signal, ˜ the denoised signal and the total number of data points of the signal.
To avoid a metric depending on the absolute value of the signals, the Relative Root Mean Square Error (RRMSE) is used, which in the time domain is expressed as follows: √︃ ∑︀=1( − ˜)2 = ∑︀ =1 2 while when considering the frequency domain we obtain the following: = √︃ ∑︀=1( () − (˜))2
∑︀=1 ()2
The correlation coeficient (CC), also referred to as Pearson correlation coeficient , measures the degree of the statistical relationship between two variables, in this case the ground truth signal and the denoised signal. The CC takes values in the range [− 1; 1], where ± 1 indicates complete linear dependence between the variables, while 0 could mean their independence, and is defined as follows: = √︀∑︀ =1( − )2√︀∑︀
=1(˜ − )2 ∑︀=1( − )(˜ − ) where and are the means of the ground truth and of the model output, respectively.
Standardization helps to speed up the training process since input centering and scaling operations improve the rate at which the neural network converges [27]. Indeed, the learning algorithm is sensitive to the input scale, and if the input data are not standardized, it may take longer for the algorithm to find a good set of parameters, i.e., weights and thresholds of the network, or the learning algorithm may get stuck in a local minima. Moreover, the standardization of the input data makes the model capable of processing EEG signals with wider amplitude ranges. Nevertheless, only the mean and standard deviation of the noisy signal are always known. Therefore, the noisy signal , the pure EEG signal and the pure noise are processed in a similar manner according to: ^ = − , ^ = − , ^ = −
These signals, as well as the PSDs evaluated by them, are the actual inputs of the model.
The loss function minimized in the training phase is a combination of three diferent terms, diferently weighted:
= + + − ℎ where is the temporal RRMSE defined in Eq. 5, is the spectral RRMSE defined in Eq. 6, and − ℎ the log-cosh error of the ground truth and predicted signals in the time domain, which is defined by the equation: (5) (6) (7) (8) (9)
This function provides a smooth approximation to the mean absolute error for values near 0. The , , and coeficients are empirically chosen for the training and are equal to 0.25, 0.25, and 0.5, respectively.
The optimization method used to find the best weights of the kernel evaluator blocks is AdaMax [28].
The code was developed in Python 3.8.10 and the proposed model was designed using the TensorFlow library, version 2.8. The experiments were run on an Nvidia Quadro RTX 4000 for a total training time of 61 hours.
A single model has been trained on both EMG and EOG artifacts at the same time in order to have a solution capable of handling both cases. In fact, the noisy signals are afected by either OAs or MAs. Therefore, both EMG only and EOG only afected signals are inputted to the model, as introduced at the beginning of Section 5.
Figure 4 shows the trend of loss as the epochs change for the training and test sets. For both datasets the loss values monotonically decrease and no significant overfit is present, indication that the model design and the runtime data synthesis approach used are efective in avoiding this issue.
Using the last epoch weights, we qualitatively demonstrate the denoising capabilities of the model on EOG and EMG artifacts in Figure 5. We can observe that both the high frequencies related to MAs and low frequencies related to OAs are filtered by the model while the majority of the structures related to the true EEG signals are preserved. Moreover, several amplitude ranges are properly managed by the model as well as diferent SNRs.
The quantitative results of the proposed model and of the literature benchmark models for MAs and OAs are reported in Table 1 and 2, respectively.
Regarding EEG afected by MAs, the reported values are in line with the benchmark models results. The proposed model demonstrated robust performance, achieving the third best results in the temporal domain metrics, and , and the second best result in the spectral metric . This latter metric provides insight into the method ability to efectively preserve the spectral information of the clean EEG signal.
Concerning OAs, our method achieves the best performance on all three metrics among the reported benchmark models. Furthermore, the similarity of the proposed model results in values on both muscular and ocular artifacts highlights the method stability and its ability to perform indiscriminately well on both high and low frequencies.
In contrast to the current state of the art, the proposed model is able to achieve these results using not only a single architecture but also a single set of trained parameters, valid on both MAs and OAs. This allows the two main sources of noise in EEG signals to be handled with a single solution. However, while the need to have as input an estimate of the PSD of the noise aflicting the signal makes the method more adaptable to new noise conditions with known characteristics, it also makes it sensitive to precise a priori knowledge of the frequency characteristics of this noise that cannot be easily estimated. In the future we will develop methods trained on the reference dataset to best estimate the PSD of the noise of each signal as a substitute for the exact PSD provided in the current work. Moreover, diferent activation functions and artifact amount estimation methodologies [29] will be considered to provide a better denoising of the EEG signals.
The significant issue of muscle and ocular artifact removal in EEG data has been tackled in this research. We introduced a unique solution capable of dealing with both artifact types using a single model. Our proposed method leverages dynamically assessed convolutional filters, which are determined based on the frequency features of the noise and the noisy signal. With this knowledge, our model has proven its efectiveness in both qualitatively and quantitatively cleaning EEG signals from muscle and ocular artifacts. This achievement either matches or exceeds the performance of existing state-of-the-art models, which typically require specicfi training on either ocular or muscle artifacts. Thus, this study marks a substantial step forward in EEG data processing by ofering a versatile spectral-based strategy for artifacts elimination and provides a baseline for subsequent work addressing the problem of estimating noise frequencies, whether with experimental solutions, algorithmic solutions, or a combination of the two.
This work was partially supported by the MUR under the grant “Dipartimenti di Eccellenza 2023-2027" of the Department of Informatics, Systems and Communication of the University of Milano-Bicocca, Italy. self-attention mechanism for denoising of electroencephalography signals, Neuroscience 505 (2022) 10–20. [16] Z. Zhang, X. Yu, X. Rong, M. Iwata, A novel multimodule neural network for eeg denoising,
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