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Mathematical analysis of the 1D model and reconstruction schemes for magnetic particle imaging

Magnetic particle imaging (MPI) is a promising new in vivo medical imaging modality in which distributions of super-paramagnetic nanoparticles are tracked based on their response in an applied magnetic field. In this paper we provide a mathematical analysis of the modeled MPI operator in the univari...

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Hauptverfasser: Erb, Wolfgang (VerfasserIn) , Weinmann, A. (VerfasserIn) , Ahlborg, M. (VerfasserIn) , Brandt, C. (VerfasserIn) , Bringout, G. (VerfasserIn) , Buzug, T. M. (VerfasserIn) , Frikel, J. (VerfasserIn) , Kaethner, C. (VerfasserIn) , Knopp, T. (VerfasserIn) , März, T. (VerfasserIn) , Möddel, M. (VerfasserIn) , Storath, Martin (VerfasserIn) , Weber, A. (VerfasserIn)
Dokumenttyp: Article (Journal)
Sprache:Englisch
Veröffentlicht: 20 April 2018
In: Inverse problems
Year: 2018, Jahrgang: 34, Heft: 5
ISSN:1361-6420
DOI:10.1088/1361-6420/aab8d1
Online-Zugang:Verlag, Volltext: https://doi.org/10.1088/1361-6420/aab8d1
Verlag, Volltext: https://doi.org/10.1088%2F1361-6420%2Faab8d1
Volltext
Verfasserangaben:W. Erb, A. Weinmann, M. Ahlborg, C. Brandt, G. Bringout, T.M. Buzug, J. Frikel, C. Kaethner, T. Knopp, T. März, M. Möddel, M. Storath and A. Weber
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Zusammenfassung:Magnetic particle imaging (MPI) is a promising new in vivo medical imaging modality in which distributions of super-paramagnetic nanoparticles are tracked based on their response in an applied magnetic field. In this paper we provide a mathematical analysis of the modeled MPI operator in the univariate situation. We provide a Hilbert space setup, in which the MPI operator is decomposed into simple building blocks and in which these building blocks are analyzed with respect to their mathematical properties. In turn, we obtain an analysis of the MPI forward operator and, in particular, of its ill-posedness properties. We further get that the singular values of the MPI core operator decrease exponentially. We complement our analytic results by some numerical studies which, in particular, suggest a rapid decay of the singular values of the MPI operator.
Beschreibung:Gesehen am 18.06.2019
Beschreibung:Online Resource
ISSN:1361-6420
DOI:10.1088/1361-6420/aab8d1

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