  Magnetic particle imaging is an imaging modality of relatively recent origin,
and it exploits the nonlinear magnetization response for reconstructing the
concentration of nanoparticles. Since first invented in 2005, it has received
much interest in the literature. In this work, we study one prototypical
mathematical model in multi-dimension, i.e., the equilibrium model, which
formulates the problem as a linear Fredholm integral equation of the first
kind. We analyze the degree of ill-posedness of the associated linear integral
operator by means of the singular value decay estimate for Sobolev smooth
bivariate functions, and discuss the influence of various experimental
parameters. In particular, applied magnetic fields with a field free point and
a field free line are distinguished. The study is complemented with extensive
numerical experiments.
