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In this paper we investigate the simultaneous reconstruction of the electric permittivity and magnetic permeability. The two physical parameters are allowed to be highly discontinuous in the concerned physical domain. The ill-posed inverse problem is formulated into an output least-squares nonlinear minimization with BV-regularization. The regularizing effect and mathematical properties of the regularized system are justified and analysed. A fully discrete Nedelec's edge element method is applied to approximate the regularized nonlinear optimization system, and its convergence is demonstrated.
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Feng et al. (2010) studied this question.
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