Neural network approach to determine nonsmooth one‐dimensional profiles in inverse scattering theory

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. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 3158–3162, 2007; Published online in Wiley InterScience (www.interscience.wiley.com).DOI 10.1002/mop.22958

[1]  R. Kress,et al.  Inverse Acoustic and Electromagnetic Scattering Theory , 1992 .

[2]  Mohammad Bagher Menhaj,et al.  Training feedforward networks with the Marquardt algorithm , 1994, IEEE Trans. Neural Networks.

[3]  D. Hoppe.  Impedance Boundary Conditions In Electromagnetics , 1995 .

[4]  Krzysztof A. Michalski,et al.  A neural-network approach to the electromagnetic imaging of elliptic conducting cylinders , 2001 .

[5]  Paolo Gamba,et al.  Electromagnetic detection of dielectric cylinders by a neural network approach , 1999, IEEE Trans. Geosci. Remote. Sens..

[6]  A. N. Tikhonov,et al.  Solutions of ill-posed problems , 1977 .

[7]  Reconstruction of the surface impedance of an inhomogeneous planar boundary beyond layered media , 2001 .

[8]  I. Kay,et al.  Introduction to the special issue on inverse methods in electromagnetics , 1981 .

[9]  Ioannis T. Rekanos.  On-line inverse scattering of conducting cylinders using radial basis-function neural networks , 2001 .

[10]  Satish S. Udpa,et al.  Solution of inverse problems in electromagnetics using Hopfield neural networks , 1995 .

[11]  Salvatore Caorsi,et al.  A threshold electromagnetic classification approach for cylinders embedded in a lossy medium by using a neural network technique , 2000 .

[12]  Satish S. Udpa,et al.  Application of neural networks to inverse problems in electromagnetics , 1994 .

[13]  D. Marquardt.  An Algorithm for Least-Squares Estimation of Nonlinear Parameters , 1963 .

[14]  Ioannis T. Rekanos,et al.  Neural-network-based inverse-scattering technique for online microwave medical imaging , 2002 .

[15]  S.R.H. Hoole,et al.  Artificial neural networks in the solution of inverse electromagnetic field problems , 1993 .

[16]  Ibrahim Akduman,et al.  One-dimensional profile inversion of a cylindrical Layer with inhomogeneous impedance boundary: a Newton-type iterative solution , 2005, IEEE Transactions on Geoscience and Remote Sensing.

[17]  I. Kay,et al.  A review of the one dimensional inverse scattering problem for stratified inhomogenous , 1979 .

[18]  Isin Erer,et al.  A wavelet-based radial-basis function neural network approach to the inverse scattering of conducting cylinders , 2004 .

[19]  Salvatore Caorsi,et al.  Microwave detection and dielectric characterization of cylindrical objects from amplitude-only data by means of neural networks , 2002 .

[20]  I. Akduman,et al.  One-dimensional profile inversion of a half-space over a two-part impedance ground , 1996 .