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doi:10.22028/D291-39414
Title: | Parameter Identification for the Landau–Lifshitz–Gilbert Equation in Magnetic Particle Imaging |
Author(s): | Kaltenbacher, Barbara Nguyen, Tram Thi Ngoc Wald, Anne Schuster, Thomas |
Editor(s): | Kaltenbacher, Barbara Schuster, Thomas Wald, Anne |
Language: | English |
Title: | Time-dependent Problems in Imaging and Parameter Identification |
Pages: | 377-412 |
Publisher/Platform: | Springer Nature |
Year of Publication: | 2021 |
DDC notations: | 510 Mathematics |
Publikation type: | Book Chapter |
Abstract: | Magnetic particle imaging (MPI) is a tracer-based technique for medical imaging where the tracer consists of ironoxide nanoparticles. The key idea is to measure the particle response to a temporally changing external magnetic field to compute the spatial concentration of the tracer inside the object. A decent mathematical model demands for a data-driven computation of the system function which does not only describe the measurement geometry but also encodes the interaction of the particles with the external magnetic field. The physical model of this interaction is given by the Landau–Lifshitz–Gilbert (LLG) equation. The determination of the system function can be seen as an inverse problem of its own which can be interpreted as a calibration problem for MPI. In this contribution the calibration problem is formulated as an inverse parameter identification problem for the LLG equation. We give a detailed analysis of the direct as well as the inverse problem in an all-at-once as well as in a reduced setting. The analytical results yield a deeper understanding of inverse problems connected to the LLG equation and provide a starting point for the development of robust numerical solution methods in MPI. |
DOI of the first publication: | 10.1007/978-3-030-57784-1_13 |
URL of the first publication: | https://link.springer.com/chapter/10.1007/978-3-030-57784-1_13 |
Link to this record: | urn:nbn:de:bsz:291--ds-394143 hdl:20.500.11880/35535 http://dx.doi.org/10.22028/D291-39414 |
ISBN: | 978-3-030-57784-1 978-3-030-57783-4 |
Date of registration: | 30-Mar-2023 |
Faculty: | MI - Fakultät für Mathematik und Informatik |
Department: | MI - Mathematik |
Professorship: | MI - Prof. Dr. Thomas Schuster |
Collections: | SciDok - Der Wissenschaftsserver der Universität des Saarlandes |
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