The problem of spectral quantification for magnetic resonance spectroscopic imaging (MRSI) is addressed in this thesis. We present a novel approach to solving this problem, incorporating both spatial and spectral prior information. More specifically, a new signal model is proposed which represents the spectral variations of each molecule as a subspace and the entire spectrum as a union-of-subspaces. The proposed model enables an efficient computational framework to quantify the unknown spectral parameters using both spectral and spatial prior information. Particularly, based on this model, the spectral quantification can be solved in two steps: (1) subspace estimation based on the empirical distributions of the spectral parameters obtained by initial spectral quantification imposing the spectral constraints, and (2) parameter estimation for the union-of-subspaces model imposing the spatial constraints. The proposed method has been evaluated using both simulated and experimental data, producing very impressive results. The resulting algorithm is expected to be useful for any metabolic imaging studies using MRSI. In this thesis, background materials including a brief review of the existing spectral quantification methods arefirstly presented. Then the proposed subspace spectral model is introduced followed by a detailed description of the resulting quantification algorithm. Finally, spectral quantification results from both simulated and in vivo MRSI data are presented to demonstrate the performance of the proposed method.
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A subspace approach to spectral quantification for MR spectroscopic imaging
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