Reconstruction Formulae for 3D Field-Free Line Magnetic Particle Imaging

.Magnetic particle imaging is a promising noninvasive in vivo imaging modality that makes it possible to map the spatial distribution of superparamagnetic nanoparticles by exposing them to dynamic magnetic fields. In the field-free line (FFL) scanner topology, the spatial encoding of the particle distribution is performed by applying magnetic fields vanishing on straight lines. The voltage induced in the receiving coils by the particles when exposed to the magnetic fields constitutes the signal from which the particle distribution is to be reconstructed. To avoid lengthy calibration, model-based reconstruction formulae have been developed for the two-dimensional (2D) FFL scanning topology. In this work we develop reconstruction formulae for 3D FFL. Moreover, we provide a model-based reconstruction algorithm for 3D FFL and we validate it with a numerical experiment.Keywordsmagnetic particle imagingmodel-based reconstructionreconstruction formulaephase spaceinverse problemsvariational regularizationfield-free lineRadon transformMSC codes94A1292C5594A0844A3565R32