Fast trajectory-independent model-based reconstruction algorithm for multi-dimensional magnetic particle imaging

Objective. Magnetic Particle Imaging (MPI) is a tomographic technique for visualizing the spatio-temporal distribution of superparamagnetic nanoparticles, with applications ranging from cancer detection to real-time cardiovascular monitoring. Traditional MPI reconstruction relies on either time-consuming calibration (measured system matrix) or model-based simulation of the forward operator. Recent developments have shown the applicability of a Chebyshev-polynomial-based method to multi-dimensional Lissajous Field-Free Point (FFP) scans. This method is bound to the particular choice of sinusoidal scanning trajectories. In this paper, we present a working reconstruction pipeline -- the MoBiT-2S -- that achieves reconstruction on real 2D MPI data, performed with a trajectory-independent model-based reconstruction algorithm based on a reconstruction formula. Approach. We employ a model-based two-stage algorithm to reconstruct the particle concentration from the scanning data, thereby realizing a reconstruction formula. In the first (core) stage the MPI core response is reconstructed from the signal using a variational formulation; in the second (deconvolution) stage, the trace of the core response is deconvolved to obtain the final reconstruction. Main results. We further develop our methodological approach to make the reconstruction-formula-based algorithm work on real 2D MPI data. In particular, we further develop a zero-shot Plug-and-Play (PnP) algorithm to address the deconvolution problem represented by the reconstruction formula. Further contributions of MoBiT-2S include channel-specific thresholding of the input data and per-iteration percentile trimming for artifact reduction. We evaluate MoBiT-2S on the ``MPIData: Equilibrium Model with Anisotropy'' dataset, featuring 2D FFP scans acquired using a Bruker preclinical scanner. We quantitatively and qualitatively compare our reconstructions with state-of-the-art approaches. In addition, we perform reconstructions on data from a 2D MPI scanner which does not employ a Lissajous scanning sequence. Significance. MoBiT-2S exhibits competitive reconstruction capabilities across different scanning scenarios on real MPI data, with Lissajous and non-Lissajous scans, and partial data, showing the potential of the proposed method for general-purpose, flexible model-based MPI reconstruction.