Mathematical Sciences: Improved Statistical Methods for Magnetic Resonance Spectroscopy

在科学、工程和医学研究中使用的磁共振光谱，在存在诸如许多此类应用中常见的不均匀性的情况下，偏离了纯粹的洛伦兹行为。这项研究将利用半参数模型分析中的统计理论来开发适当的分析方法。这种新的方法将被用来消除由磁场不均匀和时间不稳定性引起的失真。此外，还将开发统计理论和方法来分析重复观察，例如在较长一段时间内以间隔时间识别和研究代谢变化的观察。

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.