Convex optimisation-based methods for K-complex detection

• We develop three convex optimisation-based models for automatic detection of K-complexes.
• They extract key features of an EEG signal (a biological application).
• They significantly reduce the dimension of the problem and the computational time.
• They enhance the classification accuracy of an EEG signal in presence of K-complex.
• K-complexes are successfully detected in an EEG background.

K-complex is a special type of electroencephalogram (EEG, brain activity) waveform that is used in sleep stage scoring. An automated detection of K-complexes is a desirable component of sleep stage monitoring. This automation is difficult due to the ambiguity of the scoring rules, complexity and extreme size of data. We develop three convex optimisation models that extract key features of EEG signals. These features are essential for detecting K-complexes. Our models are based on approximation of the original signals by sine functions with piecewise polynomial amplitudes. Then, the parameters of the corresponding approximations (rather than raw data) are used to detect the presence of K-complexes. The proposed approach significantly reduces the dimension of the classification problem (by extracting essential features) and the computational time while the classification accuracy is improved in most cases. Numerical results show that these models are efficient for detecting K-complexes.