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Abstract. The correction of baseline and phase distortions is an important problem in magnetic resonance spectroscopy. In this work, fast and automatic correction methods based on the adaptive construction of Wiener filters are presented. The proposed methods consist of estimating and classifying the model parameters of the measured spectrum and of approximating correlation operators for the measured and the corrected signal. Results of numerical simulations and applications to real data are given.

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Introduction

Magnetic resonance spectroscopy (MRS) is a powerful analysis tool with a variety of applications in chemistry, biology and medical diagnostics. In recent years, it has been used as a medical imaging technique in order to obtain spectral decompositions for each examined volume element. This application of MRS could - in principle - provide detailed maps of the concentration of various chemical bonds in e.g. a human brain, an information that cannot be obtained by other methods such as the related techniques of magnetic resonance imaging (MRI) and computed tomography (CT). Unfortunately, signal distortions like underlying baselines, phase distortions and noise severely complicate the quantitative analysis of MR spectra. Most methods used to compensate these distortions are either not suitable for in vivo spectra, or require user interaction and thus cannot be used for automatic correction of large data sets. The goal of this project is to develop fast, automatic and accurate correction algorithms of such distortions, with a special focus on in vivo spectra and on medical applications. The project has been carried out in cooperation with Bruker Daltonik GmbH at Bremen (formerly Bruker-Franzen Analytik GmbH) and the research group of Prof. Leibfritz, Institute for Organic Chemistry at the University of Bremen. 1.1

Magnetic Resonance Spectroscopy

The magnetic resonance phenomenon, discovered in 1946, is a quantum mechanical effect that affects atomic nuclei with an angular momentum (or

* E-Mail: [email protected] W. Jäger et al. (eds.), Mathematics - Key Technology for the Future © Springer-Verlag Berlin Heidelberg 2003

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spin) placed in an external magnetic field. If such nuclei are exposed to a high frequency electromagnetic excitation pulse, they respond by emitting a signal known as the free induction decay (FID), with a strength proportional to the number of responding nuclei. The frequency of the response signal (the resonance frequency) depends on the type of the nuclei and the magnitude of the magnetic field. Since the latter is also influenced by the molecular surrounding of the nuclei, the resonance frequency is not the same for all nuclei of a given type. Instead, nuclei in different chemical bonds emit signals with different resonance frequencies. This so called chemical shift forms the basis of magnetic resonance spectroscopy.l The time-domain FID signal f(t) obtained by a single MRS experiment is commonly described by the Lorentz model as a sum of K expo