Inverse Scattering Algorithms Based on Contrast Source Integral Representations

This article reviews a number of algorithms to solve the nonlinear inverse scattering problem, where the discrepancy between the measured data and the predicted data is minimized. These algorithms are all based on a source type of integral representation of the scattered field, where the integral operator acts on a contrast source, being the product of the interior field and the contrast of the scattering object. Special attention is paid to the development of the contrast-source-inversion method, where the contrast sources are updated iteratively, and where, in each iteration, an explicit minimizer for the contrast is obtained. In particular, we discuss the effective implementation of a multiplicative constraint that minimizes the spatial variations of the contrast. We present actual reconstructions from both synthetic and experimental scattered field data.

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

[2]  P. M. Berg,et al.  A modified gradient method for two-dimensional problems in tomography , 1992 .

[3]  P. M. Berg,et al.  A contrast source inversion method , 1997 .

[4]  Vito Pascazio,et al.  On the local minima in a tomographic imaging technique , 2001, IEEE Trans. Geosci. Remote. Sens..

[5]  Anton G. Tijhuis,et al.  Born-type reconstruction of material parameters of an inhomogeneous, lossy dielectric slab from reflected-field data , 1989 .

[6]  M. Saillard,et al.  Special section: Testing inversion algorithms against experimental data , 2001 .

[7]  A. T. Hoop.  Handbook of radiation and scattering of waves , 1995 .

[8]  Aria Abubakar,et al.  Three-dimensional inverse scattering applied to cross-well induction sensors , 2000, IEEE Trans. Geosci. Remote. Sens..

[9]  A. Roger,et al.  Newton-Kantorovitch algorithm applied to an electromagnetic inverse problem , 1981 .

[10]  Aria Abubakar,et al.  A Conjugate Gradient Contrast Source Technique for 3D Profile Inversion , 2000 .

[11]  A. Abubakar,et al.  Multiplicative regularization for contrast profile inversion , 2003 .

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

[13]  T. Habashy,et al.  Simultaneous nonlinear reconstruction of two‐dimensional permittivity and conductivity , 1994 .

[14]  P. M. Berg,et al.  A total variation enhanced modified gradient algorithm for profile reconstruction , 1995 .

[15]  P. M. van den Berg,et al.  "Blind" shape reconstruction from experimental data , 1995 .

[16]  P. M. Berg,et al.  Contrast Source Inversion Method: State of Art , 2001 .

[17]  Jack K. Cohen,et al.  Nonuniqueness in the inverse source problem in acoustics and electromagnetics , 1975 .

[18]  Michael S. Zhdanov,et al.  3D electromagnetic inversion based on quasi-analytical approximation , 2000 .

[19]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[20]  T. Habashy,et al.  Beyond the Born and Rytov approximations: A nonlinear approach to electromagnetic scattering , 1993 .

[21]  P. M. Berg,et al.  Extended contrast source inversion , 1999 .

[22]  Aria Abubakar,et al.  Inversion of experimental multi-frequency data using the contrast source inversion method , 2001 .

[23]  C. Pichot,et al.  Diffraction tomography: contribution to the analysis of some applications in microwaves and ultrasonics , 1988 .

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

[25]  L. Blanc-Féraud,et al.  A new regularization scheme for inverse scattering , 1997 .

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

[27]  P. M. van den Berg,et al.  Two‐dimensional location and shape reconstruction , 1994 .

[28]  Michel Barlaud,et al.  Deterministic edge-preserving regularization in computed imaging , 1997, IEEE Trans. Image Process..

[29]  Edward Roy Pike,et al.  Scattering: Scattering and Inverse Scattering in Pure and Applied Science , 2002 .

[30]  P. M. van den Berg,et al.  On the equivalence of the Newton-Kantorovich and distorted Born methods , 2000 .