This paper presents a novel explicit reconstruction method for magnetic resonance-based electrical properties tomography (EPT). We derive the dbar equation for the electric field that incorporates the variation of the magnetic field along the longitudinal axis. This new dbar equation allows an explicit reconstruction of the electrical properties even when the magnetic field varies along that axis. We also propose an iterative reconstruction procedure that solves the dbar equation by the Cauchy–Pompeiu formula and updates EP values in each step. The proposed method correctly reconstructed EPs even in the case that the magnetic field and EPs vary along the longitudinal direction.
