Publisher URL: http://arxiv.org/abs/1711.08074v1
Publisher DOI: 10.1088/1361-6420/aab8d1
Title: Mathematical Analysis of the 1D Model and Reconstruction Schemes for Magnetic Particle Imaging
Language: English
Authors: Erb, Wolfgang 
Weinmann, Andreas 
Ahlborg, Mandy 
Brandt, Christina 
Bringout, Gael 
Buzug, Thorsten M. 
Frikel, Jürgen 
Kaethner, Christian 
Knopp, Tobias 
März, Thomas 
Hofmann, Martin 
Möddel, Martin 
Storath, Martin 
Weber, Alexander 
Keywords: Mathematics - Numerical Analysis;Mathematics - Numerical Analysis;Primary: 94A12, 92C55, 65R32, Secondary: 44A35, 94A08
Issue Date: 20-Apr-2018
Source: Inverse Problems 5 (34): 055012 (2018-04-20)
Journal or Series Name: Inverse problems 
Abstract (english): 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.
URI: http://hdl.handle.net/11420/2513
ISSN: 0266-5611
Institute: Biomedizinische Bildgebung E-5 
Type: (wissenschaftlicher) Artikel
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