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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 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.

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Metadaten
Author:Wolfgang ErbORCiD, Andreas Weinmann, Mandy AhlborgORCiD, Christina BrandtORCiD, Gael BringoutORCiD, Thorsten M. BuzugORCiD, Jürgen FrikelORCiD, C. Kaethner, Tobias KnoppORCiD, T. März, Martin ModdelORCiD, Martin StorathORCiD, A. Weber
DOI:https://doi.org/10.1088/1361-6420/aab8d1
Parent Title (English):Inverse Problems
Publisher:IOP Publishing
Document Type:Article
Language:English
Year of first Publication:2018
Release Date:2022/03/29
Tag:FORMULATION; INTERPOLATION; MPI; NODES; RELAXATION; RESOLUTION; ill-posedness; inverse problems; magnetic particle imaging; model-based reconstruction; reconstruction operator
Volume:34
Issue:5
Article Number:055012
Institutes:Fakultät Informatik und Mathematik
Begutachtungsstatus:peer-reviewed
research focus:Lebenswissenschaften und Ethik
Licence (German):Keine Lizenz - Es gilt das deutsche Urheberrecht: § 53 UrhG