  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.
