title: Reconstruction of electroencephalographic data using radial basis functions.
abstract: OBJECTIVE
  In this paper we introduce a new interpolation method to use for scalp potential interpolation. The predictive value of this new interpolation technique (the multiquadric method) is compared to commonly used interpolation techniques like nearest-neighbour averaging and spherical splines.
  
  
  METHODS
  The method of comparison is cross-validation, where the data of one or two electrodes is predicted by the rest of the data. The difference between the predicted and the measured data is used to determine two error measures. One is the maximal error in one interpolation technique and the other is the mean square error. The methods are tested on data stemming from 30 channel EEG of 10 healthy volunteers.
  
  
  RESULTS
  The multiquadric interpolation methods performed best regarding both error measures and have been easier to calculate than spherical splines.
  
  
  CONCLUSIONS
  Multiquadrics are a good alternative to commonly used EEG reconstruction methods.
  
  
  CONCLUSIONS
  Multiquadrics have been widely used in reconstruction on sphere-like surfaces, but until now, the advantages have not been investigated in EEG reconstruction.
authors.affiliation: Justus-Liebig-Universität Gießen, Lehrstuhl für Numerische Mathematik, Heinrich-Buff-Ring 44, 35392 Gießen, Germany. Electronic address: janin.jaeger@math.uni-giessen.de.
authors.forename: Janin
authors.initials: J
authors.lastname: Jäger
authors.affiliation: Justus-Liebig-Universität Gießen, Physiologisches Institut, Aulweg 129, 35392 Gießen, Germany.
authors.forename: Alexander
authors.initials: A
authors.lastname: Klein
authors.affiliation: Justus-Liebig-Universität Gießen, Lehrstuhl für Numerische Mathematik, Heinrich-Buff-Ring 44, 35392 Gießen, Germany.
authors.forename: Martin
authors.initials: M
authors.lastname: Buhmann
authors.affiliation: Justus-Liebig-Universität Gießen, Physiologisches Institut, Aulweg 129, 35392 Gießen, Germany.
authors.forename: Wolfgang
authors.initials: W
authors.lastname: Skrandies
mesh_terms: D001921:Brain / Q000502:physiology*; D001931:Brain Mapping / Q000295:instrumentation / Q000379:methods*; D004566:Electrodes; D004569:Electroencephalography / Q000295:instrumentation / Q000379:methods*; D005260:Female; D006801:Humans; D008297:Male; D012535:Scalp / Q000502:physiology; D062206:Spatial Analysis; D013223:Statistics as Topic / Q000379:methods*
keywords: 3D interpolation; EEG; Radial basis functions; Spherical interpolation; Spherical splines