Recently, magnetic-resonance-based electrical properties tomography, by which the electrical properties (EPs), namely conductivity and permittivity, of biological tissues are reconstructed, has been an active area of study. We previously proposed an explicit reconstruction method based on the Dbar equation and its explicit solution given by the generalized Cauchy formula. In this method, as in some other conventional methods, the values of EPs on the boundary of the region of interest must be specified by the Dirichlet boundary condition of the partial differential equation. However, it is difficult to know the precise values in practical situations. In this paper, we propose a novel method that reconstructs EPs without the prior information of boundary EP values by deriving a new representation formula of the solution of the Dbar equation with the complex-derivative boundary condition. Numerical simulations and phantom experiments show that the proposed method can reconstruct EPs without knowledge of the boundary EP values. Therefore, the proposed method greatly enhances the applicability of the current EPT methods to practical situations.
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