Matching Pursuit Algorithm based on L1 norm
Tomasz Spustek (University of Warsaw, Faculty of Physics, ul. Hoża 69, 00-681 Warszawa, Poland), Rafał Kuś (University of Warsaw, Faculty of Physics, ul. Hoża 69, 00-681 Warszawa, Poland), Urszula Malinowska (University of Warsaw, Faculty of Physics, ul. Hoża 69, 00-681 Warszawa, Poland), Piotr Durka (University of Warsaw, Faculty of Physics, ul. Hoża 69, 00-681 Warszawa, Poland)
In most cases MP provides a detailed description of structures present in EEG (electroencephalogram) time series. Signal patterns are described not only in terms of their frequency and amplitude, but also their exact time positions and durations are determined. However it is expected, that such procedure applied to a periodic signal would result in a Fourier expansion instead of preferred explicit parameterization of separate structures, as in Figure 1A.
Due to the described problem new Matching Pursuit procedure has been implemented. The idea was to change function selection criterion in such way, to use L1 norm instead of L2. Pilot application of this algorithm to the EEG signal from EEG-fMRI (functional magnetic resonance
imaging) coregistration allowed for a new approach dealing with EEG artifacts. Instead of filtering the signal before further processing, which may lead to a potential bias of further analyses, relevant structures of interest (in this case sleep spindles) have been detected directly in the raw signal (Figure 1B). Identification of the sleep spindle was made according to :
frequency 10-15 Hz, width 0.5-2.5 Hz, amplitude above 12 μV.
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 P. J. Durka. Matching Pursuit and Unification in EEG Analysis, Artech House 2007, ISBN 978-1-58053-304-1
 U. Malinowska, P. J. Durka, K. J. Blinowska, W. Szelenberger, A. Wakarow. Micro- and macrostructure of sleep EEG. IEEE Engineering in Medicine and Biology Magazine, 2005.