Maximum likelihood estimation in signal analysis of MR spectroscopy

Abstract: Proton magnetic resonance spectroscopy (MRS) is used to determine the concentration of metabolites in organic tissues, or to study metabolic changes in a non-invasive way. The complex-valued magnetic resonance spectroscopy signals are assumed to be disturbed by additive white noise. The distributional properties of the stochastic noise are studied. A statistical model for the magnitude and phase of the Fourier transformed magnetic resonance spectroscopy signal is introduced. Maximum likelihood estimators of the distributional parameters of this model are derived and asymptotic properties such as consistency, asymptotic normality and efficiency of the estimators are verified. A simulation study is used to test the findings and the model is tested on magnetic resonance spectroscopy data from a spectroscopy phantom and human brain data.