Föcke L (2015)
Publication Language: English
Publication Type: Thesis
Publication year: 2015
Novel approaches for medical methods use Magnetic Nanoparticles (MNP) for the treatment process. These nanoparticles with a diameter of about 100nm can also be used for
imaging purposes. In Magnetorelaxometry Imaging (MRXI), magnetic nanoparticles
are exposed to an external magnetic field induced by coils outside the region of interest. This
causes a torque on the magnetization leading to an alignment of the MNPs. The overlay of
the magnetic field induced by each MNP itself can be measured using Superconducting
Quantum Interference Devices (SQUIDs). The corresponding mathematical operator that models the MRXI experiment is severely ill-posed and the corresponding inverse
problem of determining the particle distribution is difficult to solve directly. In the recent
literature only basic regularization techniques like Tikhonov regularization and Truncated Singular Value Decomposition were used to derive a reasonable solution. Using
first-order regularization techniques like the Alternating Direction Method of Multipliers (ADMM), it is possible to include a-priori knowledge about the anticipated solution.
In this work we derive a sophisticated mathematical model of the MRXI operator and compare the impact of different regularization techniques on the solution, in particular in the
case of noisy data, for various simulated settings.
APA:
Föcke, L. (2015). Modeling and Solution of the Inverse Problem of Nanoparticle Magnetorelaxometry (Master thesis).
MLA:
Föcke, Lea. Modeling and Solution of the Inverse Problem of Nanoparticle Magnetorelaxometry. Master thesis, 2015.
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