Development of filtering methods based on spectral decomposition for analyzing cognitive performance using electroencephalogram (EEG) signals

This study aims to implement, detail, and optimize a filtering method based on spectral decomposition to noise removal and analysis of EEG signals focused on cognitive performance. Popular filtering techniques, such as ICA, PCA, and wavelet transforms, often face limitations in precise feature extraction, scalability for large datasets, and high computational demands, especially in modern applications. Our approach incorporates a two-stage process: first, an optimal rank is selected based on the statistical properties of eigenvalues derived from Hankel matrices; second, the denoised signal is reconstructed using SVD, and the rank obtained from the first stage. To address the high complexity of computing spectral decomposition and simulated series, we tested strategies such as parallelization and GPU acceleration with CuPy, which resulted in processing improvements reducing simulation times by over 99% and enhancing eigen-value computation efficiency by 38–47%. We evaluated the methodology using both synthetic and real data. With synthetic signals, we obtained an RMSE of 2.04% and an SNR of 19.08 dB. In real data, we employed a machine learning framework based on ensemble learning, confirming improved cognitive performance classification with top results of 90% accuracy. Finally, the results show that this method provides good reconstruction and noise reduction, along with suitable metrics for its application, but continued research is needed to improve its performance. Future work will focus on better leveraging parallel processing to improve the effectiveness of the proposed method across multiple EEG channels and enable its integration into real-time applications for cognitive performance experiments.

• Egile nagusia: Marcillo Vera, Ana Gabriela (author)
• Formatua: bachelorThesis
• Hizkuntza: eng
• Argitaratua: 2025
• Gaiak: Electroencefalografía; Descomposición espectral; Spectral decomposition; Noise removal
• Sarrera elektronikoa: http://repositorio.yachaytech.edu.ec/handle/123456789/942