Inverse scattering of two-dimensional dielectric objects buried in a lossy earth using the distorted Born iterative method

An efficient inverse-scattering algorithm is developed to reconstruct both the permittivity and conductivity profiles of two-dimensional (2D) dielectric objects buried in a lossy earth using the distorted Born iterative method (DBIM). In this algorithm, the measurement data are collected on (or over) the air-earth interface for multiple transmitter and receiver locations at single frequency. The nonlinearity due to the multiple scattering of pixels to pixels, and pixels to the air-earth interface has been taken into account in the iterative minimization scheme. At each iteration, a conjugate gradient (CG) method is chosen to solve the linearized problem, which takes the calling number of the forward solver to a minimum. To reduce the CPU time, the forward solver for buried dielectric objects is implemented by the CG method and fast Fourier transform (FFT). Numerous numerical examples are given to show the convergence, stability, and error tolerance of the algorithm.

[1]  Rocco Pierri,et al.  Inverse scattering of dielectric cylinders by a second-order Born approximation , 1999, IEEE Trans. Geosci. Remote. Sens..

[2]  W. Chew,et al.  Reconstruction of two-dimensional permittivity distribution using the distorted Born iterative method. , 1990, IEEE transactions on medical imaging.

[3]  Kenneth P. Bube,et al.  The One-Dimensional Inverse Problem of Reflection Seismology , 1983 .

[4]  Tie Jun Cui,et al.  Inverse scattering method for one-dimensional inhomogeneous lossy medium by using a microwave networking technique , 1995 .

[5]  Jonathan E. Nyquist,et al.  Ground penetrating radar tomography: algorithms and case studies , 1994, IEEE Trans. Geosci. Remote. Sens..

[6]  Richard G. Plumb,et al.  Electromagnetic imaging of underground targets using constrained optimization , 1995, IEEE Trans. Geosci. Remote. Sens..

[7]  Qing Huo Liu,et al.  Reconstruction of two-dimensional axisymmetric inhomogeneous media , 1993, IEEE Trans. Geosci. Remote. Sens..

[8]  David Colton,et al.  The inverse electromagnetic scattering problem for a perfectly conducting cylinder , 1980 .

[9]  D. Lesselier,et al.  The retrieval of a buried cylindrical obstacle by a constrained modified gradient method in the H-polarization case and for Maxwellian materials , 1998 .

[10]  Thorkild B. Hansen,et al.  Inversion scheme for ground penetrating radar that takes into account the planar air-soil interface , 2000, IEEE Trans. Geosci. Remote. Sens..

[11]  Vito Pascazio,et al.  A bilinear approach for subsurface sensing: numerical results , 1998 .

[12]  Vito Pascazio,et al.  A nonlinear estimation method in tomographic imaging , 1997, IEEE Trans. Geosci. Remote. Sens..

[13]  Qing Huo Liu,et al.  Inversion of induction tool measurements using the distorted Born iterative method and CG-FFHT , 1994, IEEE Trans. Geosci. Remote. Sens..

[14]  S. Twomey.  Introduction to the Mathematics of Inversion in Remote Sensing and Indirect Measurements , 1997 .

[15]  S. Barkeshli,et al.  An iterative method for inverse scattering problems based on an exact gradient search , 1994 .

[16]  Ying Wang,et al.  Nonlinear diffraction tomography: The use of inverse scattering for imaging , 1996 .

[17]  A. J. Devaney,et al.  A Computer Simulation Study of Diffraction Tomography , 1983, IEEE Transactions on Biomedical Engineering.

[18]  Weng Cho Chew,et al.  Solution of the three-dimensional electromagnetic inverse problem by the local shape function and the conjugate gradient fast Fourier transform methods , 1997 .

[19]  L. E. Larsen,et al.  Limitations of Imaging with First-Order Diffraction Tomography , 1984 .

[20]  A. Devaney,et al.  Diffraction tomography for multi-monostatic ground penetrating radar imaging , 1997 .

[21]  C. Pichot,et al.  Microwave imaging-complex permittivity reconstruction with a Levenberg-Marquardt method , 1997 .

[22]  P. M. van den Berg,et al.  An extended range‐modified gradient technique for profile inversion , 1993 .

[23]  R. Kleinman,et al.  Modified gradient approach to inverse scattering for binary objects in stratified media , 1996 .

[24]  Mark J. Hagmann,et al.  Estimation of Complex Permittivities of Three-Dimensional Inhomogeneous Biological Bodies , 1983 .

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

[26]  Weng Cho Chew,et al.  Fast algorithm for electromagnetic scattering by buried 3-D dielectric objects of large size , 1999, IEEE Trans. Geosci. Remote. Sens..

[27]  M. Kaveh,et al.  Reconstructive tomography and applications to ultrasonics , 1979, Proceedings of the IEEE.