Assessment of the complexity/regularity of transient brain waves (EEG) during sleep, based on wavelet theory and the concept of entropy



In this paper we describe a new approach to quantify the concepts of order and complexity of EEG signals during sleep. Based on the concepts of entropy and wavelet transform, we introduce a measure named Wavelet-Entropy and we will show the results of its application to real sleep EEG signals and artificial data. The definition of wavelet entropy is very similar to the definition of entropy in information theory or spectral entropy in signal processing but its most important difference is the usage of time-frequency representation of the signal and its wavelet coefficients. Time-frequency methods proved to be very useful for signals like EEG with fast changing dynamics and high non-stationarity. This characteristic of EEG limits the usage of other complexity evaluation methods like chaos analysis and parameters like correlation dimension or Lyapunov exponent.