A regularized theory of the one-dimensional profile inversion connected with inhomogeneous conducting slabs is established through an illumination by Gaussian beams. This kind of illumination does not have the difficulties which occur in forming and measuring plane and cylindrical waves. The explicit expression of the Gaussian beam is obtained by assuming that its amplitude and phase are known on a certain 'aperture plane'. The solution involves the frequency and the regularization constant as two adjustible parameters. By appropriately choosing these parameters one gets the best regularized approximate solution. Some illustrative examples show the accuracy as well as the applicability of the theory.