TY - JOUR A1 - Erb, Wolfgang A1 - Weinmann, Andreas A1 - Ahlborg, Mandy A1 - Brandt, Christina A1 - Bringout, Gael A1 - Buzug, Thorsten M. A1 - Frikel, Jürgen A1 - Kaethner, C. A1 - Knopp, Tobias A1 - März, T. A1 - Moddel, Martin A1 - Storath, Martin A1 - Weber, A. T1 - Mathematical analysis of the 1D model and reconstruction schemes for magnetic particle imaging T2 - Inverse Problems N2 - 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. KW - FORMULATION KW - ill-posedness KW - INTERPOLATION KW - inverse problems KW - magnetic particle imaging KW - model-based reconstruction KW - MPI KW - NODES KW - reconstruction operator KW - RELAXATION KW - RESOLUTION Y1 - 2018 UR - https://opus4.kobv.de/opus4-oth-regensburg/frontdoor/index/index/docId/3171 VL - 34 IS - 5 PB - IOP Publishing ER -