@article{ErbWeinmannAhlborgetal., author = {Erb, Wolfgang and Weinmann, Andreas and Ahlborg, Mandy and Brandt, Christina and Bringout, Gael and Buzug, Thorsten M. and Frikel, J{\"u}rgen and Kaethner, C. and Knopp, Tobias and M{\"a}rz, T. and Moddel, Martin and Storath, Martin and Weber, A.}, title = {Mathematical analysis of the 1D model and reconstruction schemes for magnetic particle imaging}, series = {Inverse Problems}, volume = {34}, journal = {Inverse Problems}, number = {5}, publisher = {IOP Publishing}, doi = {10.1088/1361-6420/aab8d1}, abstract = {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.}, language = {en} } @misc{BroserFalterŁawrowskietal., author = {Broser, Christian and Falter, Thomas and Ławrowski, Robert Damian and Altenbuchner, Amelie and V{\"o}gele, Daniel and Koss, Claus and Schlamp, Matthias and Dunnweber, Jan and Steffens, Oliver and Heckner, Markus and Jaritz, Sabine and Schiegl, Thomas and Corsten, Sabine and Lauer, Norina and Guertler, Katherine and Koenig, Eric and Haug, Sonja and Huber, Dominik and Birkenmaier, Clemens and Krenkel, Lars and Wagner, Thomas and Justus, Xenia and Saßmannshausen, Sean Patrick and Kleine, Nadine and Weber, Karsten and Braun, Carina N. and Giacoppo, Giuliano and Heinrich, Michael and Just, Tobias and Schreck, Thomas and Schnabl, Andreas and Gilmore, Amador T{\´e}ran and Roeslin, Samuel and Schmid, Sandra and Wellnitz, Felix and Malz, Sebastian and Maurial, Andreas and Hauser, Florian and Mottok, J{\"u}rgen and Klettke, Meike and Scherzinger, Stefanie and St{\"o}rl, Uta and Heckner, Markus and Bazo, Alexander and Wolff, Christian and Kopper, Andreas and Westner, Markus and Pongratz, Christian and Ehrlich, Ingo and Briem, Ulrich and Hederer, Sebastian and Wagner, Marcus and Schillinger, Moritz and G{\"o}rlach, Julien and Hierl, Stefan and Siegl, Marco and Langer, Christoph and Hausladen, Matthias and Schreiner, Rupert and Haslbeck, Matthias and Kreuzer, Reinhard and Br{\"u}ckl, Oliver and Dawoud, Belal and Rabl, Hans-Peter and Gamisch, Bernd and Schmidt, Ottfried and Heberl, Michael and G{\"a}nsbauer, Bianca and Bick, Werner and Ellermeier, Andreas and Monkman, Gareth J. and Prem, Nina and Sindersberger, Dirk and Tschurtschenthaler, Karl and Aurbach, Maximilian and Dendorfer, Sebastian and Betz, Michael A. and Szecsey, Tamara and Mauerer, Wolfgang and Murr, Florian}, title = {Forschung 2018}, editor = {Baier, Wolfgang}, address = {Regensburg}, organization = {Ostbayerische Technische Hochschule Regensburg}, isbn = {978-3-9818209-5-9}, doi = {10.35096/othr/pub-1382}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:898-opus4-13826}, pages = {98}, subject = {Forschung}, language = {de} }