Optimization Driven Variational Autoencoder GAN for Artifact Reduction in EEG Signals for Improved Neurological Disorder and Disability Assessment

First define the low-pass filter (LPF) and high-pass filter (HPF): (1) LPFt=St⋅wt∑i=0T−1Si⋅wi LPF\left[ t \right] = {{S\left[ t \right] \cdot w\left[ t \right]} \over {\sum\nolimits _{i = 0}^{T - 1}S\left[ i \right] \cdot w\left[ i \right]}} (2) HPFt=δt−LPFt HPF\left[ t \right] = \delta \left[ t \right] - LPF\left[ t \right] where S[t],w[t], and δ[t] represent the sinc filter, the Hamming window, and the discrete unit impulse function. PVA consists of five main parts: feature extractor, encoder, sampler, feature generator, and signal reconstructor. The model's components work together to synthesize EEG signals. The feature extractor g_x(.) uses cascade filters to divide the input signal y into four amplitude-modulated subsets x ∈ {x_HH,x_HL,x_LH,x_LL}, which are the learning targets of the feature generator. The encoder g_e(.) learns the distribution parameters of the latent variable z and cutoff frequency θ. It makes two assumptions:

θ_k~u(o,1) for k = 1,2 ... .6 stands for six occurrences in the proposed model. The Bernoulli distributions approximates this distribution.

The samplers g_z(.) and g_θ(.) provide a distinct data distribution estimate. The method uses reparameterization for backpropagation, sampling z_j and θ_k to allow the gradients to flow across the network node. Using the encoder settings, feature generator g_z′(.) creates four feature signals for the signal reconstructor. Signal reconstructor g_y(.) uses the generated feature subsets to reconstruct the signals while preserving their fundamentals. Monte Carlo (MC) can be used to estimate the predicted log likelihood of reconstructing raw signals y from reconstructed feature signals x. (3) −Eq,(x,z,θ|y)[log p(y|x)]≈−1L∑l=1Llog py|xl - {E_{q,(x,z,\theta |y)}}[log p(y|x)] \approx - {1 \over L}\sum\nolimits _{l = 1}^L log p\left( {y|{x^{\left( l \right)}}} \right) where L is the number of samples. The mean square error (MSE) was reduced instead of the negative log likelihood from (4) to maintain convergence stability. (4) J(φy;y)=1N∑n=1Nyn−gnxn2 J({\varphi _y} ; y) = {1 \over N}\sum\nolimits _{n = 1}^N{\left( {{y_n} - {g_n}\left( {{x_n}} \right)} \right)^2} where the sample index and the total number of training samples are n and N, respectively. The optimization of the latent variable Z reduces the Kullback-Leibler divergence (KLD) compared to the previous ones. Latent variable Z optimization under variational inference for p(z) requires a reduction of the KLD relative to the prior. (5) Eq(z|y)q(θ|y)q(x|y,θ)log q(z|y)pz=KLD(q(z|y)pz {E_{q(z|y)q(\theta |y)q(x|y,\theta )\left[ {\log {{q(z|y)} \over {p\left( z \right)}}} \right]}} = KLD(q(z|y)p\left(z\right)

The Gaussian distribution KLD and a VAE reparametrization method were used for this optimization.

A GAN consists of two CNNs, a generator and a discriminator, with opposing conditional arguments. In the discriminator, we used the Patch-GAN to classify each patch as true or generated. The discriminator should punish local signal patches to accurately mimic high-frequency components. The GAN training total loss function is: (6) LGANG,D=Ex,ylog Dx,y+Ex,ylog 1−Dx,Gx,z {L_{GAN}}\left( {G,D} \right) = {E_{x,y}}\left[ {log D\left( {x,y} \right)} \right] + {E_{x,y}}\left[ {log \left( {1 - D\left( {x,G\left( {x,z} \right)} \right)} \right)} \right]

The generator (G) minimizes the loss function L_GAN(G,D), while the discriminator D maximizes it to discriminate between the generated samples G(x,y) and the actual samples y. We provide the discriminator estimate error loss feedback to guarantee successful training. Therefore, the final goal function is: (7) G*=ARGminG maxD LGANG,D+γLL1G {G^*} = ARG\mathop {\min }\limits_G \;\mathop {\max }\limits_D \;{L_{GAN}}\left( {G,D} \right) + \gamma {L_{{L_1}\left( G \right)}} where L_L1(G) is an extra L₁ norm based on the generator function loss to approximate the ground truth output. γ is an adjustable parameter set to 100. The multi-modal feature-fusion of image and interaction information L_GAN L_GAN causes the generative network to create the same pathological feature as the original signal: (8) LGAN=∑n=1Nlog DθxGθxIα,t {L_{GAN}} = \sum\nolimits _{n = 1}^N log D{\theta _x}\left( {G{\theta _x}\left( {{I^\alpha },t} \right)} \right) where t is the interactive information and N is the number of samples. We use the visual perceptual loss to maintain the perceptual similarity. The loss function is: (9) LGAN/i.j=1Wi,jHi,j∑i=1Wi,j∑j=1Hi,j(φi,jIf−φi,jGθgIα,t {L_{GAN/i.j}} = {1 \over {{W_{i,j}}{H_{i,j}}}}\sum\nolimits _{i = 1}^{{W_{i,j}}}\sum\nolimits _{j = 1}^{{H_{i,j}}}({\varphi _{i,j}}\left( {{I^f}} \right) - {\varphi _{i,j}}\left( {{G_{{\theta _g}\left( {{I^{\alpha ,t}}} \right)}}} \right)

In this section, both study datasets are described. The CHB-MIT dataset [12] initially included 22 participants: 17 women aged 1.5–19 years and 5 men aged 3–22 years. The collection includes 198 seizures and 969 hours of EEG recordings. The number of seizures is lower than the number of seizure-free signals. The second dataset, KAU, was obtained at 256 Hz from two male scalp EEG patients aged 28 years. This dataset is similar to the CHB-MIT dataset. The subjects' ages were considered. The individuals in the CHB-MIT dataset are similar to these two cases. In both datasets, an age range of 1–28 years was chosen. This is significant as age considerably affects the clinical and electroencephalographic features of seizures [13]. Both individuals had 38-channel EEGs. They had two 495 s seizures and four 417 s seizures, respectively. The CHB-MIT dataset selects 18 out of 23 channels because they are similar to all recordings.

The time-step value in this study varied from 0 to m − t, with t set to 50. The prior and downstream tasks were each trained for 30 epochs with a batch size of 64. The network was trained using Python, PyTorch, and an RTX 3060Ti GPU. The BrOpt_VAGAN model with its complex VAE and GAN components can be very computationally intensive. Real-time EEG analysis requires significant hardware resources (e.g., GPUs, TPUs) that may not be available in all medical settings, especially for portable or low-power devices. Here, the modeling findings of the proposed artifact elimination method using the BrOpt_VAGAN network are quickly investigated. The simulation is performed by comparing the results with a number of well-known methods, including HEFS+DNN [12], VFCDM+CNN [14]. These are done to reduce artifacts due to random noise. The metrics used for assessment in this study include MSE and signal to noise ratio (SNR).

The MSE measure describes the difference between the real reaction and the intended response: (10) MSE=1NOn−Dn2 MSE = {1 \over N}{\left( {{O^n} - {D^n}} \right)^2}

Table 1 shows the accuracy and error calculation for the proposed BrOpt_VAGAN method in terms of pseudo-clean and noisy input.

Fig. 2 shows that BrOpt_VAGAN consistently achieves the lowest MSE % with values between 11.2 % and 12.6 % and thus has superior accuracy. In contrast, HEFS+DNN shows stable but higher MSE values (20.1 % to 20.9 %), while VFCDM+CNN has the highest MSE % across all channels (21.3 % to 21.76 %). This shows that BrOpt_VAGAN is the most effective method for error reduction regardless of the number of channels, outperforming both HEFS+DNN and VFCDM+CNN.

Fig. 2.

Comparison of MSE with the EEG+brain signal artifact.

Fig. 3 shows the MSE of HEFS+DNN, VFCDM+CNN, and BrOpt_VAGAN for EEG signals with eye signal artifacts across channels (2 to 10). HEFS+DNN has stable MSE values between 19.4 % and 19.5 % and thus shows a constant performance. VFCDM+CNN has the highest MSE % (21.5 % to 21.9 %), indicating that it is less effective at handling artifacts. BrOpt_VAGAN achieves lower MSE values (15.3 % to 15.9 %) than VFCDM+CNN but slightly higher than HEFS+DNN, suggesting moderate effectiveness in reducing artifacts. Overall, HEFS+DNN is the most stable, while BrOpt_VAGAN performs better than VFCDM+CNN in error minimization.

Fig. 3.

Comparison of MSE with the EEG+eye signal artifact.

Fig. 4 compares the MSE of the aforementioned methods when processing EEG signals with muscle signal artifacts over different numbers of channels. HEFS+DNN consistently shows the highest MSE %, ranging from 27.4 % to 28.6 %, indicating a significant error in handling muscle artifacts. VFCDM+CNN achieves lower MSE values, ranging from 19.2 % to 19.5 %, indicating moderate effectiveness in artifact reduction. BrOpt_VAGAN consistently achieves the lowest MSE %, with values between 12.3 % and 12.98 %, indicating superior performance in minimizing errors due to muscle artifacts. Overall, BrOpt_VAGAN is the most effective, followed by VFCDM+CNN, while HEFS+DNN is the least effective in this context.

Fig. 4.

Comparison of MSE with the EEG+muscle signal artifact.