Time-varying EEG Signal Reconstruction Based on Local Graph Signal Smoothness

Electroencephalography (EEG) signals record the electrical activity of the brain and have significant applications in neuroscience and medicine. However, accurately reconstructing EEG signals has been a challenge due to potential signal missing and noise interference during signal acquisition. The paper exploits the underlying structure of EEG signals and presents an efficient method for reconstructing EEG signals based on local graph signal smoothness (LGS-based). Firstly, we introduce the concept of local graph signal smoothness according to distinct functional areas of the cerebral cortex. Then, considering the graph that does not properly represent similar relationships between signals will have a negative impact on the reconstruction performance, we propose a joint graph learning and EEG signal reconstruction optimization method. Since it is not jointly convex, we utilize the alternating direction method of multipliers (ADMM) to solve it. In experiments, it is shown that the proposed LGS-based method outperforms benchmark methods in EEG signal reconstruction. Additionally, the proposed method achieves a higher signal-to-noise ratio (SNR) as well as a smaller normalized mean square error (RMSE).