From EEG Dependency Multichannel Matching Pursuit to Sparse Topographic Decomposition

In this work we present a multichannel EEG decomposition model based on an adaptive topographic time-frequency approximation technique. It is an extension of the Matching Pur- suit algorithm and called Dependency Multichannel Matching Pursuit (DMMP). It takes the physiologically explainable and statistically observable topographic dependencies between the channels into account, namely the spatial smoothness of neighboring electrodes that is im- plied by the electric lead¯eld. DMMP decomposes a multichannel signal as a weighted sum of atoms from a given dictionary where the single channels are represented from exactly the same subset of a complete dictionary. The decomposition is illustrated on topographical EEG data during di®erent physiological conditions using a complete Gabor dictionary. Further the extension of the single-channel time-frequency distribution to a multichannel time-frequency distribution is given. This can be used for the visualization of the decomposition structure of multichannel EEG. A clustering procedure applied to the topographies, the vectors of the corresponding contribution of an atom to the signal in each channel produced by DMMP, leads to an extremely sparse topographic decomposition of the EEG.