Two-Dimensional Spectral Estimation Techniques with Applications to Magnetic Resonance Spectroscopy

Single-voxel proton magnetic resonance spectroscopy (MRS) is typically used in a clinical setting to quantify metabolites in the human brain. By convention, an MRS absorption spectrum is created by Fourier transformation of phase-corrected raw data acquired during an MRS experiment. An MRS absorption spectrum shows the relative concentrations of certain key metabolites, including N-Acetyl-aspartate (NAA), choline, creatine and others. Certain nonparametric techniques may also be used for MRS analysis. 2D Capon and 2D amplitude and phase estimation (APES) are two relatively new nonparametric methods that can be used effectively to estimate both frequency and damping characteristics of each metabolite. In this dissertation we introduce the weighted 2D Capon, weighted 2D APES, and combined weighted 2D APES/2D Capon methods. Under certain conditions these methods may provide improved estimation properties and/or reduced computation time, as compared to conventional 2D methods. Many clinicians routinely use multiple receive coils for magnetic resonance imaging (MRI) studies of the human brain. In conjunction with these exams, it is often desired to perform proton MRS experiments to quantify metabolites from a region of interest. An MRS absorption spectrum can be generated for each coil element; however, interpreting the results from each channel is a tedious process. Combining MRS absorption spectra obtained from an experiment in which multiple receive coils are used would greatly simplify clinical diagnosis. In this dissertation we introduce two methods for 2D spectral estimation in the case of multi-channel data. To date, no such methods have appeared in the literature. These new methods employ weighted signal averaging and weighted spectrum averaging and use any of the 2D techniques described above. We also introduce a method to optimally estimate the relative channel gains from observed data. The new techniques developed in this dissertation are evaluated and compared to conventional 2D spectral estimation based on extensive computer simulations written in MATLAB. They are also applied to phantom and in vivo MRS data