Variational model-based reconstruction techniques for multi-patch data in Magnetic Particle Imaging

Magnetic Particle Imaging is an emerging imaging modality through which it is possible to detect tracers containing superparamagnetic nanoparticles. The exposure of the particles to dynamic magnetic fields generates a non-linear response that is used to locate the particles and produce an image of their distribution. The bounding box that can be covered by a single scan curve depends on the strength of the gradients of the magnetic fields applied, which is limited due to the risk of causing peripheral nerve stimulation (PNS) in the patients. To address this issue, multiple scans are performed. The scan data must be merged together to produce reconstructions of larger regions of interest. In this paper we propose a mathematical framework which can deal with rather general multi-patching scenarios including rigid transformations of the field of view (FoV), the specimen and of the scanner. We show the flexibility of this framework in a variety of different scanning scenarios. Moreover, we describe an iterative reconstruction algorithm that yields a reconstruction of the target distribution by minimizing a convex functional which includes positivity constraints and sparsity enforcing priors. We show its convergence to a minimizer and perform numerical experiments on simulated data.