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An inverse scattering technique based on the differential E-formulation in the frequency domain is proposed. The inversion is achieved by minimizing a cost functional, taking into account the discrepancy between measured and estimated field values, while the Helmholtz wave equation is set as constraint. The Fre´chet derivatives of the cost functional with respect to the scatterer properties are derived analytically by means of the calculus of variations. Edge elements are used for the numerical treatment of the problem.