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Erb, W.* ; Weinmann, A. ; Ahlborg, M.* ; Brandt, C.* ; Bringout, G.* ; Buzug, T.M.* ; Frikel, J.* ; Kaethner, C.* ; Knopp, T.* ; Maerz, T.* ; Moeddel, M.* ; Storath, M.* ; Weber, A.*

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

Inverse Probl. 34:055012 (2018)
Verlagsversion Postprint DOI
Open Access Green
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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Publikationstyp Artikel: Journalartikel
Dokumenttyp Wissenschaftlicher Artikel
Schlagwörter Ill-posedness ; Inverse Problems ; Magnetic Particle Imaging ; Model-based Reconstruction ; Reconstruction Operator
ISSN (print) / ISBN 0266-5611
e-ISSN 1361-6420
Zeitschrift Inverse Problems
Quellenangaben Band: 34, Heft: 5, Seiten: , Artikelnummer: 055012 Supplement: ,
Verlag Institute of Physics Publishing (IOP)