  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.
