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 JF - 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 U6 - https://doi.org/10.1088/1361-6420/aab8d1 VL - 34 IS - 5 PB - IOP Publishing ER - TY - JOUR A1 - Broser, Christian A1 - Falter, Thomas A1 - Ławrowski, Robert Damian A1 - Altenbuchner, Amelie A1 - Vögele, Daniel A1 - Koss, Claus A1 - Schlamp, Matthias A1 - Dunnweber, Jan A1 - Steffens, Oliver A1 - Heckner, Markus A1 - Jaritz, Sabine A1 - Schiegl, Thomas A1 - Corsten, Sabine A1 - Lauer, Norina A1 - Guertler, Katherine A1 - Koenig, Eric A1 - Haug, Sonja A1 - Huber, Dominik A1 - Birkenmaier, Clemens A1 - Krenkel, Lars A1 - Wagner, Thomas A1 - Justus, Xenia A1 - Saßmannshausen, Sean Patrick A1 - Kleine, Nadine A1 - Weber, Karsten A1 - Braun, Carina N. A1 - Giacoppo, Giuliano A1 - Heinrich, Michael A1 - Just, Tobias A1 - Schreck, Thomas A1 - Schnabl, Andreas A1 - Gilmore, Amador Téran A1 - Roeslin, Samuel A1 - Schmid, Sandra A1 - Wellnitz, Felix A1 - Malz, Sebastian A1 - Maurial, Andreas A1 - Hauser, Florian A1 - Mottok, Jürgen A1 - Klettke, Meike A1 - Scherzinger, Stefanie A1 - Störl, Uta A1 - Heckner, Markus A1 - Bazo, Alexander A1 - Wolff, Christian A1 - Kopper, Andreas A1 - Westner, Markus A1 - Pongratz, Christian A1 - Ehrlich, Ingo A1 - Briem, Ulrich A1 - Hederer, Sebastian A1 - Wagner, Marcus A1 - Schillinger, Moritz A1 - Görlach, Julien A1 - Hierl, Stefan A1 - Siegl, Marco A1 - Langer, Christoph A1 - Hausladen, Matthias A1 - Schreiner, Rupert A1 - Haslbeck, Matthias A1 - Kreuzer, Reinhard A1 - Brückl, Oliver A1 - Dawoud, Belal A1 - Rabl, Hans-Peter A1 - Gamisch, Bernd A1 - Schmidt, Ottfried A1 - Heberl, Michael A1 - Gänsbauer, Bianca A1 - Bick, Werner A1 - Ellermeier, Andreas A1 - Monkman, Gareth J. A1 - Prem, Nina A1 - Sindersberger, Dirk A1 - Tschurtschenthaler, Karl A1 - Aurbach, Maximilian A1 - Dendorfer, Sebastian A1 - Betz, Michael A. A1 - Szecsey, Tamara A1 - Mauerer, Wolfgang A1 - Murr, Florian ED - Baier, Wolfgang T1 - Forschung 2018 T3 - Forschungsberichte der OTH Regensburg - 2018 KW - Forschung KW - Forschungsbericht Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:898-opus4-13826 SN - 978-3-9818209-5-9 CY - Regensburg ER -