We contribute to the mathematical modeling and analysis of magnetic particleimaging which is a promising new in-vivo imaging modality. Concerning modeling,we develop a structured decomposition of the imaging process and extract itscore part which we reveal to be common to all previous contributions in thiscontext. The central contribution of this paper is the development ofreconstruction formulae for MPI in 2D and 3D. Until now, in the multivariatesetup, only time consuming measurement approaches are available, whereasreconstruction formulae are only available in 1D. The 2D and the 3D (describingthe real world) reconstruction formulae which we derive here are significantlydifferent from the 1D situation -- in particular there is no Dirac property indimensions greater than one when the particle sizes approach zero. As a furtherresult of our analysis, we conclude that the reconstruction problem in MPI isseverely ill-posed. Finally, we obtain a model-based reconstruction algorithm.
展开▼
