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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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Main Authors: Erb, Wolfgang (Author) , Weinmann, A. (Author) , Ahlborg, M. (Author) , Brandt, C. (Author) , Bringout, G. (Author) , Buzug, T. M. (Author) , Frikel, J. (Author) , Kaethner, C. (Author) , Knopp, T. (Author) , März, T. (Author) , Möddel, M. (Author) , Storath, Martin (Author) , Weber, A. (Author)
Format: Article (Journal)
Language:English
Published: 20 April 2018
In: Inverse problems
Year: 2018, Volume: 34, Issue: 5
ISSN:1361-6420
DOI:10.1088/1361-6420/aab8d1
Online Access:Verlag, Volltext: https://doi.org/10.1088/1361-6420/aab8d1
Verlag, Volltext: https://doi.org/10.1088%2F1361-6420%2Faab8d1
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Author Notes: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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Summary: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.
Item Description:Gesehen am 18.06.2019
Physical Description:Online Resource
ISSN:1361-6420
DOI:10.1088/1361-6420/aab8d1

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