MPISuperRes-PnP: A Super-Resolution Zero-Shot Plug-and-Play Reconstruction Algorithm for Magnetic Particle Imaging

Magnetic Particle Imaging (MPI) is an emerging medical imaging modality. MPI is based on the non-linear response of magnetic nanoparticles to an applied magnetic field and avoids ionizing radiation. The measured signal is the voltage induced in receive coils by the particles' response. Reconstructing the particle concentration from the signal constitutes the imaging task. Even using state-of-the-art measurement-based reconstruction, the associated spatial grid is very coarse, hence super-resolution (SR) techniques are important. In this work, we propose an approach for SR in MPI inspired by energy minimization. Different methods have been proposed for SR in MPI, ranging from upscaling of the associated system matrix to interpolation of the reconstruction. Here we incorporate SR into the reconstruction task via an energy minimization formulation. Following the plug-and-play approach to energy minimization we derive a splitting scheme and a SR method for MPI where the arising Gaussian denoising task is treated with a pre-trained learned Gaussian denoiser in a zero-shot fashion. This way, we incorporate benefits of deep learning without training and avoid the need of training data. Further, we provide a quantitative and qualitative evaluation of the proposed method. Hyper-parameter are selected via an extended parameter search. The found parameters are applied for reconstruction on real data. We show the applicability of our method on synthetic and on real data (MPIData: EquilibriumModelWithAnisotropy and 2D-OpenMPI Data). The proposed method employs a deep-learning denoiser without training -- thus it does not require presently scarcely available MPI training data. The denoiser behaves conservatively, i.e., no hallucination artifacts were observed. The SR approach is generic such that it can be applied in future MPI contexts involving different regularizers or different imaging tasks.