Harmonic hidden Markov models for the study of EEG signals

A new approach for modelling multichannel signals via hidden states models in the time-frequency space is described. Multichannel signals are expanded using a local cosine basis, and the (time-frequency labelled) coefficients are modelled as multivariate random variables, whose distribution is governed by a (hidden) Markov chain. Several models are described, together with maximum likelihood estimation algorithms. The model is applied to electroencephalogram data, and it is shown that variance-covariance matrices labelled by sensor and frequency indices can yield relevant informations on the analyzed signals. This is examplified by a case study on the characterization of alpha waves desynchronization in the context of multiple sclerosis disease.