As a time-varying non-linear and non-stationary signal, scalp EEG is susceptible to exogenous artifacts and physiological artifacts. Physiological artifacts are caused by a variety of internal body sources: EOG, EMG, electrocardiographic (ECG), etc. Traditional methods assume that the artifacts and scalp EEG signals are statistically independent of each other and that the signals we observe are composed of linear combinations of source signals as equation (1) (Parra et al., 2005), where f denotes the loss function of the transmission medium (skull) to the clean EEG signal and gi denotes the loss function of the transmission medium (skin surface) to each artifact signal.

In reality, however, there is a bidirectional contamination between scalp EEG and artifacts, forming a coupled system (David and Friston, 2003). Exogenous artifacts can be removed by adjusting the acquisition environment and filtering. In contrast, endogenous artifacts and clean scalp EEG activity signals are interacting with each other during transmission through the scalp to the electrodes and are more difficult to remove. This can be modeled as equation (2):

where artifactiendo denotes endogenous artifacts and artifactjexo denotes exogenous artifacts. gi and gj represent the transmission loss functions for endogenous and exogenous artifacts of different transmission mediums, respectively. We wished to construct a network structure that can simulate this mutual antagonism of the source signal during the scalp transmission process. The schematic diagram illustrating the coupling model framework of scalp electroencephalography can be found in Figure 1. Therefore, we propose the following dual-pathway denoised autoencoder model. We fit the coupling between the two types of loss functions, by means of a multiscale dual-pathway structure and a fusion block to extract the feature coding of clean scalp EEG signals.

Considering the coupled system, the clean scalp EEG signals and the artifact signals interfere and contaminate each other, which ultimately constitutes the observed scalp EEG signals composed of signals from multiple sources. In this paper, a dual-pathway autoencoder (DPAE) network architecture is designed for extracting the encoding of the target signal which is also the clean scalp EEG signal.

Firstly, at the time of extracting the primary features, the original input is mapped to subspaces of different dimensions to obtain feature representations at different scales. Secondly, through the fusion module, the joint representation features of different scales are compressed and reconstructed to obtain the scale-independent common feature information. Finally, the clean scalp EEG signal is reconstructed based on this common feature information. Notably, we associate the neural network layers at both ends of the fusion module through residual connections, i.e., the input and output layers of the fusion module are summed before feeding into the decoder. In view of the fact that the depth of the network structure increases with the addition of the fusion module, the residual connection can ensure that there is no gradient vanishing in the backpropagation (Drozdzal et al., 2016). Furthermore, the residual connection is added to construct an identity mapping of the joint representation based on the residual connection, which is more conducive to the model learning the common feature information in the different scale features. This model structure has the advantage of automatically modeling the contamination relationship between multiple interference source signals. It also learns multiscale feature representations in a dual pathway format and uses the coding of the target source signals as its learning target. This helps the fusion module to obtain common feature representations at different scales that contain more information about the target source signals.

In addition, to better illustrate the generalization of the network frame, the dual-pathway autoencoder network architectures based on MLP, CNN, and RNN are constructed in this paper, respectively. Specifically, taking CNN as an example, we construct two sets of convolutional layer pathways with different sizes of convolutional kernels (1×3 vs. 1×5) and different steps (1×2 vs. 1×4) on the input layer of the network, respectively. In contrast to MLP, two sets of fully connected layer pathways are constructed with different neuron shrinkage ratios (0.45 vs. 0.75). Compared to RNN, two sets of GRU (gate recurrent unit) pathways are constructed with different unit shrinkage ratios (0.45 vs. 0.75). The two hidden layer pathways are followed by the fusion module. The fusion module is constructed based on a fully connected layer, which constructs the joint representation based on the two hidden layer pathways, and reconstructs the joint representation by compression coding first and then reconstructing the joint representation. The whole fusion module is a symmetric structure, as shown in Figure 2. The reconstructed joint representation is further compression coded by combining the residual connections after the fusion module. Finally, decoding is performed based on the decoder to synthesize clean scalp EEG signals. In addition, we added a batch normalization (Santurkar et al., 2018) layer after the joint representation layer every time, which is to regularize the features from two pathways to a uniform interval, reduce the degree of data divergence, and construct independently and identically distributed recombination features.

In terms of parameter details, if we take the number of neurons at the input as 512, the specific parameters of the DPAE network model based on MLP are shown in Table 1. Additionally, it should be noted that the number of neurons in the high-dimensional layer is 682 (512/0.75) and the number of neurons in the low-dimensional layer is 230 (512*0.45). This is to map the input data to the low and high dimensional spaces, respectively, and thus ensure feature variability extracted by the subsequent dual-pathway structure. After that, the shrinkage ratio of the two pathway network layers stacked is always set to 0.45 and 0.75, respectively, so the shape of each network layer can be calculated in turn. In other words, our pathway with the high ratio is the first to carry out an expansion operation to upgrade dimensionality and a few contraction operations to reduce dimensionality. This is intended to improve the features’ expressiveness. In contrast, in the low ratio pathway, it is all shrinkage operations. In the decoder, the two-path network layers are concatenated together, then one layer of the network layers is stacked and output directly.

We propose a training strategy to facilitate the learning of the clean scalp EEG characteristic features from scalp EEG contaminated with artifacts. We designed clean scalp EEG and contaminated scalp EEG input-to-output pairs. We set clean EEG as the expected output and constructed contaminated scalp EEG frames with different signal-to-noise ratio EMG and EOG artifacts as the input. The dual-way autoencoder is trained in a supervised manner, using the Adam optimizer (Zhang, 2018) with the mean square error between the outputs and the expected reconstructed clean EEG as a loss function. Furthermore, all activation functions are SeLu.

Here, we adopted the evaluation criteria established by the creators of the dataset, consistent with their criteria for assessing denoising performance. Evaluating the network performance in terms of the root mean square error (RRMSE) of correlation on the time and frequency domains of the denoised EEG data, as well as the Pearson correlation coefficient values with the paired clean EEG.

First, we calculate the RRMSE of the denoised EEG from both the time domain and frequency domain, respectively. Here, we denote the denoised EEG by fy and the paired clean EEG by x as ground truth. Then, the RRMSE in the time domain is calculated as equation (6):

Considering that the scalp EEG signal is a non-linear time-variant signal, the RRMSE in the frequency domain introduces the power spectral density for calculating as equation (7):

The Pearson correlation coefficient (CC) is the classic measure of correlation of time-series data and is calculated as equation (8):

We start by explaining the source of the test data, which was constructed with the training set by sampling without replacement, which ensures that for the testing stage, either clean scalp EEG, EOG, or EMG are completely new and unseen. Some samples of our model noise reduction performance are given in Figures 4–6. For each segment of data, the normalization method has two steps: subtracting the standard deviation and then dividing by the maximum of the absolute values. It is important to highlight that when presenting the results of noise reduction through power spectrograms, we differentiated the various frequency bands of the EEG by employing distinct colors. This was done to accurately depict our method’s capacity to preserve the essential information within the power spectrum of each band. The frequency distribution intervals of each band are as follows: delta [1–4 Hz], theta [4–8 Hz], alpha [8–13 Hz], beta [13–30 Hz], and gamma [30–80 Hz].

To have a more comprehensive view of the performance of our model, we compare it with a fully convolutional neural network (FCNN), simple CNN, complex CNN (Emara et al., 2019), and RNN, which are proposed with the benchmark dataset and the latest novel CNN. Table 2 shows the scales in parameters and FLOPs (floating point operations) (Frølich and Dowding, 2018) of each network. Firstly, considering the number of parameters, it is evident that our methods belong to the forefront, characterized by a minimal parameter count. However, compared with the RNN model, the number of parameters is slightly increased, considering that the RNN only has three hidden layers, while our DPAE model has 16 hidden layers, so it can be said that the DPAE framework can increase the depth of the network while effectively reducing the number of parameters. FLOPs represent the amount of network computation when the model is propagated forward, which can be used to measure the computational complexity of the model. It can be seen that the FLOPs of the three network frameworks of the DPAE are extremely small, and are one-tenth or even one-twentieth of the other models, among which the FLOPs value of the DPAE MLP model is the smallest. This indicates that our method consumes very little memory and is very fast, which is conducive for applications.

We trained the above methods all in 200 epochs with batch size at 128, using the same optimizer and loss function as our method. We present the benchmark assessment metrics proposed with this dataset against the RRMSE temporal, RRMSE spectral, and Pearson correlation coefficients graphs at all SNR levels in Figure 7. The first column gives the performance for scalp EEG contaminated by EOG under the three noise reduction metrics, while the second column corresponds to the noise reduction results for EEG contaminated by EMG.

In terms of trend, we can see that our noise reduction performance gets better as the SNR level increases. The fluctuation of our method is much more stable compared to other methods, which indicates the higher robustness of our method. The DPAE CNN model stably outperforms other models at all SNR levels in both temporal and spectral RRMSE metrics for EMG removal. The DPAE CNN also obtained the best performance on the removal of EOG as the signal-to-noise ratio went beyond -3 dB. In addition, the DPAE MLP model and the DPAE RNN model significantly outperform the baseline FCNN and RNN models, confirming the generalization of the DPAE frame across network structures. Secondly, the DPAE MLP model stably outperforms other deep learning algorithms on EOG removal after the SNR level exceeds -6 dB both on RRMSE temporal and spectral. In EMG removal, it outperforms other models in RRMSE spectral after the SNR level exceeds -3 dB, and in RRMSE temporal after the SNR level exceeds zero. The DPAE RNN, on the other hand, has a weaker performance improvement and does not outperform other deep learning algorithms, but only manages to completely outperform the simple CNN and outperform the complex RNN at the same SNR levels. As a side note, our method does not perform well on the Pearson correlation coefficient.

In addition, our encoder design scheme mainly consists of three elements: a dual-pathway network structure, fusion block module, and residual connection. We took the two-pathway network as the baseline and the complete network as the ablation object based on the MLP layer. The ablation study (Meyes et al., 2019) was set on two occasions: removing the fusion block module or removing the residual connection. In terms of control variables, we set the three networks under the same random seed with the same training set (using the EMG dataset) and consistent hyperparameters (batch size = 128, leaning rate = 0.001, epoch = 200). The experimental results are shown in Figure 8.

As we can see, the model with the fusion block removed has the slowest convergence speed and the worst final loss level. The model with the residual connections removed has a slightly higher convergence speed, and the final loss is better but not as good as the complete model. First, this result is consistent with the fact that residual connections can improve the convergence speed of the network. Second, it shows that the fusion block module can indeed effectively fuse and update the coding representation of scalp EEG signals, which can not only improve the convergence efficiency of the network jointly with the residual connection but also make the network converge to a better local optimum. Finally, according to the results of the comparison between eliminating the fusion block and eliminating the residual connections for the network performance degradation, the fusion block contributes more to the performance improvement of the neural network compared to the residual connections.

The clean scalp EEG of the EEGdenoiseNet dataset is one-dimensional although it comes from different electrode channels. That is, our model is currently not based on specific channels for noise reduction, but in the form of single-channel reuse of the same model. However, most of the real scalp EEG datasets are multichannel, coupled with the fact that the clean scalp EEG signals of EEGdenoiseNet extracted by ICA differ from the real scalp EEG data. Therefore, in order to verify the practicality of our method, we did another experiment on multichannel scalp EEG noise reduction.

The scalp EEG data were obtained from the BCI Competition IV dataset 2a (Brunner et al., 2008), a four-class motor image dataset with nine subjects and 288 trials per subject. The number of electrodes was 22, and the sampling rate was 250 Hz. We randomly sampled 192 trials of data from two subjects (with equal proportions for the four motor imagery tasks). We intercepted 2 s of EEG data from which the subjects started motor imagery and resampled the scalp EEG to 256 Hz as ground truth. Those data were then combined with EMG data from EEGdenoiseNet to simulate contaminated EEG data at different signal-to-noise levels.

For the training of the network model, we made the following changes: the original 1d DPAE model structure was still used, and the data from each trial were fed into the network channel by channel for noise reduction. Figure 9 shows the noise reduction results of the three model frameworks under different signal-to-noise levels. It can be seen that all three models maintain consistent noise reduction with the EEGDenoseNet dataset at different signal-to-noise ratio levels when facing real multichannel EEG data. Among them, 1dCNN DPAE consistently outperforms the other two models in EMG artifact removal until the signal-to-noise level is below 0 dB. This further illustrates the greater robustness of the 1dCNN DPAE model. The MLP DPAE model, on the other hand, maintains the trend of increasing noise reduction ability with increasing signal-to-noise ratio, whereas the other two models show a decrease in noise reduction ability at signal-to-noise ratios greater than 0 dB, suggesting that the MLP DPAE model is more capable of generalization.