Sparse multi-wavelet-based identification of time-varying system with applications to EEG signal time-frequency analysis

The problem of identification in non-stationary time-varying system is investigated based on a time-varying parametric modelling algorithm, and is applied to time-frequency feature extraction analysis of electroencephalography (EEG) signals. The multi-wavelet basis function which has proved efficient for tracking the transient local changes in signals, is employed to approximate the time-varying coefficients, and thus the initial time-varying modelling problem is then simplified into a time-invariant regression model estimation problem. In addition, the regularized orthogonal least squares (ROLS) algorithm is used to construct a parsimonious model structure and estimate the model parameters effectively, which not only reduces the model complexity, but also avoids the overfitting problem. The simulation results show that, compared with traditional recursive least squares (RLS) algorithm and classical orthogonal least squares (OLS) algorithm, the proposed sparse multi-wavelet-based modelling method is capable of estimating time-varying parameters more accurately. Furthermore, the application of the proposed method to the real EEG signals during motor imagery has proven to have powerful tracking capabilities, and a time-frequency analysis is introduced based on the identified time-varying model. The high time-frequency resolution of the proposed method enables the characterizations of event-related desynchronization (ERD) and event-related synchronization (ERS) in alpha band precisely, and validates the applicability of the proposed modelling algorithm.