Analysis of functional magnetic resonance imaging time series by independent component analysis [Elektronische Ressource] / von Mandy Sohr

Analysis of Functional Magnetic Resonance ImagingTime Series by Independent Component AnalysisDissertationzur Erlangung des akademischen Gradesdoctor rerum naturalium(Dr. rer. nat)von Dipl.-Statistikerin MandySohrgeb. am 20.02.1980 in Lutherstadt Wittenberggenehmigt durch die Fakult¨at fur¨ Mathematikder Otto-von-Guericke-Universit¨at MagdeburgGutachterin: Frau Prof. Dr. Waltraud KahleGutachter: Herr Priv.Doz. Dr. Siegfried Kropfeingereicht am: 26.02.2007Verteidigung am: 22.06.2007ContentsList of Figures ivList of Tables viIndex of Symbols viiIndex of Abbreviations x1 Introduction 12 Fundamentals 62.1 Probability Spaces, Random Variables, and Stochastic Processes . . . . . . . 62.2 Independence and Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . 82.3 Measures of Independence and Nongaussianity . . . . . . . . . . . . . . . . . 112.3.1 Measuring Independence by Information-Theoretic Functions . . . . . 112.3.2 Measuring Nongaussianity by Kurtosis . . . . . . . . . . . . . . . . . 183 Functional Magnetic Resonance Imaging 203.1 Functional Magnetic Resonance Imaging . . . . . . . . . . . . . . . . . . . . 203.2 FMRI Time Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223.3 FMRI Time Series Regarded as Stochastic Processes . . . . . . . . . . . . . 233.4 Analyzing fMRI Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244 Classical Methods for Analyzing fMRI Time Series 264.