An $\ell^1$-Plug-and-Play Approach for Magnetic Particle Imaging Using a
  Zero Shot Denoiser with Validation on the 3D Open MPI Dataset
Vladyslav Gapyak Corinna Rentschler Thomas März Andreas Weinmann
Magnetic particle imaging (MPI) is an emerging medical imaging modality which
has gained increasing interest in recent years. Among the benefits of MPI are
its high temporal resolution, and that the technique does not expose the
specimen to any kind of ionizing radiation. It is based on the non-linear
response of magnetic nanoparticles to an applied magnetic field. From the
electric signal measured in receive coils, the particle concentration has to be
reconstructed. Due to the ill-posedness of the reconstruction problem, various
regularization methods have been proposed for reconstruction ranging from early
stopping methods, via classical Tikhonov regularization and iterative methods
to modern machine learning approaches. In this work, we contribute to the
latter class: we propose a plug-and-play approach based on a generic zero-shot
denoiser with an $\ell^1$-prior. Moreover, we develop parameter selection
strategies. Finally, we quantitatively and qualitatively evaluate the proposed
algorithmic scheme on the 3D Open MPI data set with different levels of
preprocessing.