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The electromagnetic probing of an inhomogeneous slab is investigated in the time domain by means of optimization techniques. The iterative search of a minimum of a cost function allows us to determine a best approximated conductivity or permittivity profile of such a slab. The principles of this approach and some numerical results are briefly presented. This approach appears particularly suitable in the case of noisy data. However, it does not allow us to overcome the ill-posed nature of the simultaneous probing of conductivity and permittivity profiles.