Decomposition of EEG signal and detection of sleep spindle using sparse optimization

We proposed a signal decomposition algorithm for the electroencephalogram (EEG), which is separated into short oscillation, long oscillation, low frequency component, and the residual component. The decomposition problem is reduced to a sparse optimization one and the four components can be estimated by minimizing a convex objective function. A high-pass filter is applied to split the low frequency from the long oscillation. Meanwhile, two inverse short-time Fourier transforms are used to reconstruct the short oscillation and the long oscillation. After the EEG signal is decomposed, the sleep spindle is extracted from the long oscillation component. An EEG database is used to evaluate our method and the average F1 score 0.633 is obtained.