The present paper introduces novel reconstruction methods for electrical properties tomography (EPT), in which conductivity and permittivity are reconstructed from the complex B1 field, and phase-based EPT, in which only conductivity is reconstructed from the B1 phase. The proposed methods reconstruct electrical properties (EPs) by solving a linear integral equation derived from Helmholtz's identity, and does not require calculation of the second-order derivatives of the measured data nor iterative updating of the estimates. Numerical simulations and phantom experiments showed that the proposed method could retrieve EPs more stably than the conventional method that solves a linear partial differential equation.
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