Matching Pursuit Algorithm based on L1 norm

Abstract

Event Abstract Back to Event Matching Pursuit Algorithm based on L1 norm Tomasz Spustek1*, Rafał Kuś1, Urszula Malinowska1 and Piotr Durka1 1 University of Warsaw, Faculty of Physics, ul. Hoza 69, 00-681 Warszawa, Poland, Poland Matching pursuit algorithm (MP), introduced by Mallat and Zhang [1], is a greedy iterative algorithm used for adaptive decomposition of a given signal. The idea of Matching Pursuit is to provide a suboptimal solution to the problem of finding a best linear expansion of a signal in a redundant set of functions. In each of the consecutive steps, a waveform is matched to the signal. Choosing best matching function is most commonly done, by means of largest dot product (called L2 norm) with the residual signal, left after subtracting results of previous iterations [2]. 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 [3]: frequency 10-15 Hz, width 0.5-2.5 Hz, amplitude above 12 μV. [1] S. Mallat and Z. Zhang. Matching pursuit with time-frequency dictionaries. IEE Transactions on Signal Processing, 41:3397-3415, 1993. [2] P. J. Durka. Matching Pursuit and Unification in EEG Analysis, Artech House 2007, ISBN 978-1-58053-304-1 [3] 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. Figure 1 Keywords: computational neuroscience, Matching pursuit algorithm (MP), linear expression, EEG signal processing, neuroinformatics Conference: 5th INCF Congress of Neuroinformatics, Munich, Germany, 10 Sep - 12 Sep, 2012. Presentation Type: Poster Topic: Neuroinformatics Citation: Spustek T, Kuś R, Malinowska U and Durka P (2014). Matching Pursuit Algorithm based on L1 norm. Front. Neuroinform. Conference Abstract: 5th INCF Congress of Neuroinformatics. doi: 10.3389/conf.fninf.2014.08.00015 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 21 Mar 2013; Published Online: 27 Feb 2014. * Correspondence: Dr. Tomasz Spustek, University of Warsaw, Faculty of Physics, ul. Hoza 69, 00-681 Warszawa, Poland, Warsaw, Poland, tspus@fuw.edu.pl Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers Tomasz Spustek Rafał Kuś Urszula Malinowska Piotr Durka Google Tomasz Spustek Rafał Kuś Urszula Malinowska Piotr Durka Google Scholar Tomasz Spustek Rafał Kuś Urszula Malinowska Piotr Durka PubMed Tomasz Spustek Rafał Kuś Urszula Malinowska Piotr Durka Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.