Spectral analysis and magnetic resonance spectroscopy

Abstract: This dissertation is concerned with nonparametric approaches for spectral analysis (SA) and algorithms for magnetic resonance spectroscopy (MRS) data analysis.A method to obtain the optimal smoothing window for the class of SA methods based on local smoothing of the periodogram is proposed. Under a local smoothness assumption the Cramér-Rao lower bound on the estimation accuracy for nonparametric SA methods is derived. Furthermore, the maximum likelihood (ML) approach is considered and the relation between the ML approach and other SA methods is given.A novel nonparametric method for MRS data analysis is proposed. The method uses data dependent filterbanks to separate the MRS signal as a function of both frequency and damping. The two-dimensional interpretation leads to high resolution and estimation accuracy comparable with the best parametric approaches.A computationally convenient implementation of the ML estimator for MRS data incorporating maximum available a priori knowledge about model parameters to reduce the dimensionality of the problem is derived.Techniques that handle imperfections in the MRS data axe studied. A method based on maximum-phase finite impulse response filters for water peak suppression and frequency selective quantification of MRS data is presented. Finally a robust estimation algorithm using an unsuppressed water reference to model experimental imperfections is proposed. The algorithm is evaluated on MRS data acquired on a clinical magnetic resonance imaging scanner.