  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.

Numerical Analysis