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Quantitative magnetic resonance spectroscopy: Semi‐parametric modeling and determination of uncertainties
Author(s) -
Elster Clemens,
Schubert Florian,
Link Alfred,
Walzel Monika,
Seifert Frank,
Rinneberg Herbert
Publication year - 2005
Publication title -
magnetic resonance in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.696
H-Index - 225
eISSN - 1522-2594
pISSN - 0740-3194
DOI - 10.1002/mrm.20500
Subject(s) - parametric statistics , baseline (sea) , mathematics , bayesian probability , nuisance parameter , spectral line , regularization (linguistics) , parametric model , parameter space , calibration , statistics , algorithm , physics , computer science , artificial intelligence , oceanography , astronomy , estimator , geology
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 Cramér–Rao lower bounds, which tend to overestimate accuracy. Magn Reson Med 53:1288–1296, 2005. © 2005 Wiley‐Liss, Inc.