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Mathematical Modelling and Data Analysis

Department 8.4

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Title: Quantitative magnetic resonance spectroscopy: semi-parametric modeling and determination of uncertainties
Author(s): C. Elster, F. Schubert, A. Link, M. Walzel, F. Seifert and H. Rinneberg
Journal: Magnetic resonance in medicine
Year: 2005
Volume: 53
Issue: 6
Pages: 1288--96
DOI: 10.1002/mrm.20500
ISSN: 0740-3194
Web URL: http://www.ncbi.nlm.nih.gov/pubmed/15906296
Keywords: Bayes Theorem,Brain Chemistry,Computer Simulation,Computer-Assisted,Humans,Least-Squares Analysis,Magnetic Resonance Spectroscopy,Magnetic Resonance Spectroscopy: methods,Models, Statistical,Regression,Signal Processing, Computer-Assisted,Statistical
Tags: 8.42, Unsicherheit, in-vivo
Abstract: A semi-parametric approach for the quantitative analysis of magnetic resonance (MR) spectra is proposed and an uncertainty analysis is given. Single resonances are described by parametric models or by parametrized in vitro spectra and the baseline is determined nonparametrically by regularization. By viewing baseline estimation in a reproducing kernel Hilbert space, an explicit parametric solution for the baseline is derived. A Bayesian point of view is adopted to derive uncertainties, and the many parameters associated with the baseline solution are treated as nuisance parameters. The derived uncertainties formally reduce to Cramér-Rao lower bounds for the parametric part of the model in the case of a vanishing baseline. The proposed uncertainty calculation was applied to simulated and measured MR spectra and the results were compared to Cramér-Rao lower bounds derived after the nonparametrically estimated baselines were subtracted from the spectra. In particular, for high SNR and strong baseline contributions the proposed procedure yields a more appropriate characterization of the accuracy of parameter estimates than Crémer-Rao lower bounds, which tend to overestimate accuracy.

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