A Zero-Shot L1-Plug-and-Play Approach for System-Matrix-Based MPI

Abstract

The MPI reconstruction task in the system-matrix-based approach is an example of a severely ill-posed inverse problem that requires regularization. Part of the ill-posedness arises from the noise present in the MPI measurements and in the calibration data. For this reason, various pre-processing steps are applied to mitigate the effect of the noise, among which are bandpass filtering, whitening and lower rank approximation via randomized SVD of the system matrix. Recently, Plug-and-Play (PnP) approaches for inverse problems have been developed. These approaches are iterative reconstruction schemes that iteratively alternate between a reconstruction step and a Gaussian denoising step. Previous PnP approaches applied to MPI employ a denoiser which has been trained on MPI-friendly data. In this work we propose an L1-PnP approach that employs a zero-shot denoiser (trained on natural images and without further fine-tuning). We validate the approach on the 3D OpenMPI Dataset. Moreover, we compare the approach with reconstructions obtained with the standard Tikhonov reconstruction method and the Deep Image Prior, and show reconstructions with increasingly lower levels of pre-processing of the data, suggesting insensitivity of the L1-PnP method to different pre-processing steps.