title: SPHARA--a generalized spatial Fourier analysis for multi-sensor systems with non-uniformly arranged sensors: application to EEG.
abstract: Important requirements for the analysis of multichannel EEG data are efficient techniques for signal enhancement, signal decomposition, feature extraction, and dimensionality reduction. We propose a new approach for spatial harmonic analysis (SPHARA) that extends the classical spatial Fourier analysis to EEG sensors positioned non-uniformly on the surface of the head. The proposed method is based on the eigenanalysis of the discrete Laplace-Beltrami operator defined on a triangular mesh. We present several ways to discretize the continuous Laplace-Beltrami operator and compare the properties of the resulting basis functions computed using these discretization methods. We apply SPHARA to somatosensory evoked potential data from eleven volunteers and demonstrate the ability of the method for spatial data decomposition, dimensionality reduction and noise suppression. When employing SPHARA for dimensionality reduction, a significantly more compact representation can be achieved using the FEM approach, compared to the other discretization methods. Using FEM, to recover 95% and 99% of the total energy of the EEG data, on average only 35% and 58% of the coefficients are necessary. The capability of SPHARA for noise suppression is shown using artificial data. We conclude that SPHARA can be used for spatial harmonic analysis of multi-sensor data at arbitrary positions and can be utilized in a variety of other applications.
authors.affiliation: Institute of Biomedical Engineering and Informatics, Faculty of Computer Science and Automation, Technische Universität Ilmenau, Ilmenau, Germany.
authors.forename: Uwe
authors.initials: U
authors.lastname: Graichen
authors.affiliation: Institute of Biomedical Engineering and Informatics, Faculty of Computer Science and Automation, Technische Universität Ilmenau, Ilmenau, Germany.
authors.forename: Roland
authors.initials: R
authors.lastname: Eichardt
authors.affiliation: Institute of Biomedical Engineering and Informatics, Faculty of Computer Science and Automation, Technische Universität Ilmenau, Ilmenau, Germany.
authors.forename: Patrique
authors.initials: P
authors.lastname: Fiedler
authors.affiliation: Institute of Biomedical Engineering and Informatics, Faculty of Computer Science and Automation, Technische Universität Ilmenau, Ilmenau, Germany.
authors.forename: Daniel
authors.initials: D
authors.lastname: Strohmeier
authors.affiliation: eemagine GmbH, Berlin, Germany.
authors.forename: Frank
authors.initials: F
authors.lastname: Zanow
authors.affiliation: Institute of Biomedical Engineering and Informatics, Faculty of Computer Science and Automation, Technische Universität Ilmenau, Ilmenau, Germany; Biomagnetic Center, Department of Neurology, University Clinic Jena, Jena, Germany.
authors.forename: Jens
authors.initials: J
authors.lastname: Haueisen
mesh_terms: D000328:Adult; D000465:Algorithms; D001921:Brain / Q000502:physiology; D001931:Brain Mapping; D004569:Electroencephalography; D005583:Fourier Analysis; D006801:Humans; D007091:Image Processing, Computer-Assisted; D008297:Male; D059629:Signal-To-Noise Ratio