On the formulation of the image reconstruction problem in magnetic particle imaging

In magnetic particle imaging (MPI), the spatial distribution of magnetic nanoparticles is determined by applying various static and dynamic magnetic fields. Due to the complex physical behavior of the nanoparticles, it is challenging to determine the MPI system matrix in practice. Since the first publication on MPI in 2005, different methods that rely on measurements or simulations for the determination of the MPI system matrix have been proposed. Some methods restrict the simulation to an idealized model to speed up data reconstruction by exploiting the structure of an idealized MPI system matrix. Recently, a method that processes the measurement data in x-space rather than frequency space has been proposed. In this work, we compare the different approaches for image reconstruction in MPI and show that the x-space and the frequency space reconstruction techniques are equivalent.