Mathematical Sciences: Improved Statistical Methods for Magnetic Resonance Spectroscopy

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Magnetic resonance spectra, used in scientific, engineering and medical research, depart from pure Lorentzian behavior in the presence of inhomogeneities such as those commonly encountered in many of these applications. This research will develop appropriate analytic methods using statistical theory drawn from semiparametric model analysis. This new methodology will be derived to remove distortions caused by magnetic field inhomogeneity and by temporal instability. Also, statistical theory and methodology will be developed to analyze repeated observations such as those taken to identify and study metabolic changes at intervals during an extended period of time.