We are interested in recovering the shape of an object from measures of the scattered electromagnetic field when the incident wave is time-harmonic with fixed frequency in the resonance region. This problem is ill-posed and non-linear. We provide an exact linear method for solving the problem, based on the solution of a linear integral equation of the first kind. It is a regularization method since the integral equation is solved by using Tikhonov regularization algorithm. We apply the method in the case of simulated data from obstacles and inhomogeneous objects.
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