## 4 Preprocessing of the Measured Data
### Data Augmentation Using Generative Adversarial Networks  
In our data set, the empty debris (noise) class initially contained only 20 real samples, which was significantly fewer than the respiration and movement classes. To address this imbalance and strengthen the model's ability to distinguish between classes, we leveraged  
Figure 7: Selected IMFs of the EMD analysis for a measured signal of a moving subject inside the debris with \(\phi=0^{\circ}\) orientation angle.  
GANs to augment the noise data. By synthesizing additional realistic noise samples, we created a more balanced data set that allowed the model to learn discriminative features effectively, helping mitigate potential bias and improve overall classification performance. The data set was augmented by generating synthetic samples, which increased the amount of training and testing data, thereby enhancing the performance of the classification models. GANs are a specific framework of a generative model that aims to implicitly learn the data distribution from a set of samples to further generate new samples drawn from the learned distribution. The main idea behind GANs is that the generator network learns to produce data that resemble examples from a target data distribution. Synthetic data examples are generated to mimic real data using random noise as input [74].  
The GAN comprises a generator and a discriminator, both of which are structured to facilitate efficient data generation and validation. The generator network starts with a feature input layer, followed by two fully connected layers and activation functions, resulting in a tanh layer to ensure the output ranges between \(-1\) and \(1\). The discriminator network, on the other hand, includes a sequence of fully connected layers interspersed with leaky ReLU activations, ending in a sigmoid layer for binary classification. This setup enables the generator to create data samples that the discriminator evaluates, iteratively improving the quality of the generated data. Training involves normalizing the real data to the \([-1,1]\) range and feeding noise through the generator to produce synthetic data. The discriminator then differentiates between real and generated data, computing losses that guide updates to both networks. Over 5000 epochs, this adversarial process refines the generator's ability to produce realistic data. The trained generator can then create new data samples, which are rescaled to match the range of the original data, demonstrating the effectiveness of the GAN in data synthesis. The samples of empty debris have been increased fivefold, using GAN to balance the number of samples compared to the other classes (respiration and movement).  
To further validate the quality of the GAN-generated samples and their relevance to real measurements, we compared both the amplitude (Figure 8) and phase (Figure 9) of original and augmented noise signals. The time domain waveforms after DC removal reveal similar magnitudes and fluctuation patterns, indicating that the GAN effectively captures key statistical characteristics of the real signals. Figures 8 and 9 demonstrate that the synthetic data closely resemble real data while preserving key signal features. These visual confirmations, combined with our subsequent classification experiments, indicate that integrating GAN-augmented data not only balances class distributions but also preserves important signal features to improve overall model performance.  
Figure 8: Comparison of original and GAN-augmented noise signals (Magnitude).