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 - Mang, Andreas A1 - Schnabel, Julia A. A1 - Crum, William R. A1 - Modat, Marc A1 - Camara-Rey, Oscar A1 - Palm, Christoph A1 - Caseiras, Gisele Brasil A1 - Jäger, H. Rolf A1 - Ourselin, Sébastien A1 - Buzug, Thorsten M. A1 - Hawkes, David J. T1 - Consistency of parametric registration in serial MRI studies of brain tumor progression JF - International Journal of Computer Assisted Radiology and Surgery N2 - Object The consistency of parametric registration in multi-temporal magnetic resonance (MR) imaging studies was evaluated. Materials and methods Serial MRI scans of adult patients with a brain tumor (glioma) were aligned by parametric registration. The performance of low-order spatial alignment (6/9/12 degrees of freedom) of different 3D serial MR-weighted images is evaluated. A registration protocol for the alignment of all images to one reference coordinate system at baseline is presented. Registration results were evaluated for both, multimodal intra-timepoint and mono-modal multi-temporal registration. The latter case might present a challenge to automatic intensity-based registration algorithms due to ill-defined correspondences. The performance of our algorithm was assessed by testing the inverse registration consistency. Four different similarity measures were evaluated to assess consistency. Results Careful visual inspection suggests that images are well aligned, but their consistency may be imperfect. Sub-voxel inconsistency within the brain was found for allsimilarity measures used for parametric multi-temporal registration. T1-weighted images were most reliable for establishing spatial correspondence between different timepoints. Conclusions The parametric registration algorithm is feasible for use in this application. The sub-voxel resolution mean displacement error of registration transformations demonstrates that the algorithm converges to an almost identical solution for forward and reverse registration. KW - Inverse registration consistency KW - Parametric serial MR image registration KW - Tumor disease progression KW - Kernspintomografie KW - Registrierung KW - Hirntumor Y1 - 2008 U6 - https://doi.org/10.1007/s11548-008-0234-5 VL - 3 IS - 3-4 SP - 201 EP - 211 ER -