Development, analysis and application of mathematical methods for Magnetic Particle Imaging (MathMPI)
Final Report Abstract
The central goal of the interdisciplinary DFG-funded young researcher network ”Mathematical methods for Magnetic Particle Imaging (MathMPI)” is the development, analysis and application of mathematical methods to improve the reconstruction quality of the novel imaging modality Magnetic Particle Imaging (MPI). To achieve these goals the scientific network MathMPI attracted researchers from various scientific backgrounds including applied mathematics, medical physics, image processing, modeling, as well as medical engineering. The network organized five interdisciplinary research meetings in the period between 1.8.2014 and 31.07.2016. In particular, a kick-off meeting in Lübeck, two study groups in Munich and Ettlingen, a workshop combined with a Minisymposium in Hamburg, and a final conference in Osnabrück were organized. During the period of this project and based on the meetings of the network a considerable progress in research has been achieved. Tailored to the specific needs of MPI a fast edge preserving and noise reducing reconstruction algorithm for MPI was developed in which the nonnegative fused lasso model is used for regularization. Concerning the analysis and the modeling of the MPI system kernel a structured decomposition of the MPI imaging equation was developed which led to new reconstruction formulae in 2D and 3D. Regarding the discretization of the MPI system function, sampling on the node points of Lissajous curves was studied which led to new reduced system matrices and reconstruction algorithms adapted to the sampling paths of MPI scanners. Although a unified software toolbox for MPI reconstruction could not be finalized, several new reconstruction algorithms were implemented in single subprojects of the network. The performance of these novel algorithms was tested numerically in experimental setups and for some of them an improvement in reconstruction quality over the state of the art methods could be verified. More tests of these methods, in particular on real biomedical data, have still to be conducted in order to improve the quality of the reconstructions even further.
Publications
- Bivariate Lagrange interpolation at the node points of non-degenerate Lissajous curves. Numer. Math. 133(4):409-425, 2016
W. Erb, K. Kaethner, M. Ahlborg, and T. M. Buzug
(See online at https://doi.org/10.1007/s00211-015-0762-1) - Model-Based Reconstruction for Magnetic Particle Imaging in 2D and 3D. Inverse Problems and Imaging
T. März and A. Weinmann
- Non-Equispaced System Matrix Acquisition for Magnetic Particle Imaging based on Lissajous Node Points. IEEE Transactions on Medical Imaging, vol. 35, no. 11, pp. 2476-2485, Nov. 2016
K. Kaethner, W. Erb, M. Ahlborg, P. Szwargulski, T. Knopp and T. M. Buzug
(See online at https://dx.doi.org/10.1109/TMI.2016.2580458) - Edge preserving and noise reducing reconstruction for magnetic particle imaging. IEEE Transactions on Medical Imaging, vol. 36, no. 1, pp. 74-85, Jan. 2017
M. Storath, C. Brandt, M. Hofmann, T. Knopp, J. Salamon, A. Weber, A. Weinmann
(See online at https://dx.doi.org/10.1109/TMI.2016.2593954)
