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An inverse scattering method for the reconstruction of the permittivity and conductivity profiles of a multilayered medium and for that of the impedance profile of a nonuniform transmission line is proposed. The inversion is based on the global minimization of an objective function by the multilevel single-linkage method. The objective function is defined as the mean-square error between the measured data and the data obtained from the solution of the forward problem. An exact formulation for the gradient of the objective function in closed form is derived. The necessary condition for the unique solution of the inverse problem of a nonuniform transmission line is discussed. Reconstruction examples using both experimental and noisy synthetic data are presented. Index Terms--Inverse scattering, nonhomogeneous media.