Discussion

Matching Pursuit with a time-frequency dictionary of Gabor functions is a powerful and general tool for parametrization of non-stationary signals. Described applications to analysis of sleep spindles and slow wave activity show new research possibilities opened by this approach in EEG analysis--presented framework can be used for description of other signals structures. Apart from sleep spindles analysis, adaptive decomposition into Gabor functions (in its dyadic form) was used for analysis of different signals e.g.: EEG recorded by depth and subdural electrodes [Franaszczuk et al., 1998], vibrotactile driving responses [Zygierewicz et al., 1998], vibroartrographic signals [Krishnan et al., 2000], phonocardiograms [Zhang et al., 1998] and otoacoustic emissions [Blinowska et al., 1997]. The MP method has been recommended as an approach especially suitable for analysis of non-stationary signals in the IVth edition of handbook "Electroencephalography..." [Niedermayer and Lopes Da Silva, 1999]. The features, which make MP unique among other time-frequency methods are high resolution and parametric description of all kinds of data structures. No other method possesses both these properties. Continuous wavelet transform or Cohen's class transforms do not provide parametric description, moreover Cohen's class transforms are biased by cross-terms. Discrete wavelet transforms give parametric description, but their time-frequency resolution is severely limited. Presented in this work MP with stochastic dictionaries removes bias of original MP algorithm and further improves time-frequency resolution. It makes the presented method a unique tool for investigation of dynamic changes of brain activity.

Complete software package for matching pursuit with stochastic time-frequency dictionaries, used in this work, is available at http://brain.fuw.edu.pl/mp.