In this article, we present a new hybrid method to reconstruct one-dimensional lossy profile in order to get effective and stable solutions that can be used for both acoustic and electromagnetic cases. Unlike classical integral equation methods for the solution of the inverse medium problems, the neural network approach is applied to avoid the nonlinear and ill-posed nature of the integral equation of the first kind. The applicability and the effectiveness of the method is tested by selecting an inverse problem, namely, to determine nonsmooth one-dimensional profile of an inhomogeneous layer located over an inhomogeneous impedance ground. To reveal the advantage and the accuracy of the method, noisy data and rectangular/triangular types of non-smooth profiles are used. Good agreement with exact profiles has been observed. (c) 2007 Wiley Periodicals, Inc.