Stochastic Modelling and Optimal Spectral Estimation of EEG signals

The study of a time-frequency image is often the method of choice to address key issues in cognitive electrophysiology. The quality of the time-frequency representation is crucial for the extraction of robust and relevant features, thus leading to the demand for highly performing spectral estimators. We consider a stochastic model, known as Locally Stationary Processes, based on the modulation in time of a stationary covariance function. The flexibility of the model makes it suitable for a wide range of time-varying signals, in particular EEG signals. Previous works provided the theoretical expression of the mean-square error optimal kernel for the computation of the Wigner-Ville spectrum. The introduction of a novel inference method for the model parameters permits the computation of the optimal kernel in real-world data cases. The obtained MSE optimal time-frequency estimator is compared with other commonly used methods in a simulation study, confirming the error reduction. Optimal spectral estimates are presented for the case study, consisting of EEG data collected within a research on memory retrieval.