A wavelet-based energetic approach for the analysis of biomedical signals: Application to the electroencephalogram and electro-oculogram

Abstract

Wavelet transform has emerged over recent years as a favoured tool for the investigation of biomedical signals, which are highly non-stationary by their nature. A relevant wavelet-based approach in the analysis of biomedical signals exploits the capability of wavelet transform to separate the signal energy among different frequency bands (i.e., different scales), realizing a good compromise between temporal and frequency resolution. The rationale of this paper is twofold: (i) to present a mathematical formalization of energy calculation from wavelet coefficients, in order to obtain uniformly time distributed atoms of energy across all the scales; (ii) to show two different applications of the wavelet-based energetic approach to biomedical signals. One application concerns the study of epileptic brain electrical activity, with the aim of identifying typical patterns of energy redistribution during the seizure. Results obtained from this method provide interesting indications on the complex spatio-temporal dynamics of the seizure. The other application concerns the electro-oculographic tracings, with the purpose of realizing an automatic detector of a particular type of eye movements (slow eye movements), important to identify sleep phases. The algorithm is able to identify this eye movement pattern efficiently, characterizing it in rigorous energetic terms. The energetic approach built within the framework of the multiresolution decomposition appears as a powerful and versatile tool for the investigation and characterization of transient events in biomedical signals.