An iterative solution of the two‐dimensional electromagnetic inverse scattering problem

A new method, based on an iterative procedure, for solving the two‐dimensional inverse scattering problem is presented. This method employs an equivalent Neumann series solution in each iteration step. The purpose of the algorithm is to provide a general method to solve the two‐dimensional imaging problem when the Born and the Rytov approximations break down. Numerical simulations were calculated for several cases where the conditions for the first order Born approximation were not satisfied. The results show that in both high and low frequency cases, good reconstructed profiles and smoothed versions of the original profiles can be obtained for smoothly varying permittivity profiles (lossless) and discontinuous profiles (lossless), respectively. A limited number of measurements around the object at a single frequency with four to eight plane incident waves from different directions are used. The method proposed in this article could easily be applied to the three‐dimensional inverse scattering problem, if computational resources are available.

[1]  S. S. Stuchly,et al.  A Solution of Electromagnetic Imaging Using Pseudoinverse Transformation , 1984, IEEE Transactions on Medical Imaging.

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

[3]  R. Taylor,et al.  The Numerical Treatment of Integral Equations , 1978 .

[4]  A. Devaney.  A Filtered Backpropagation Algorithm for Diffraction Tomography , 1982 .

[5]  A. Devaney,et al.  Nonuniqueness in inverse source and scattering problems , 1982 .

[6]  Joseph B. Keller,et al.  Accuracy and Validity of the Born and Rytov Approximations , 1969 .

[7]  A. Kak,et al.  Distortion in Diffraction Tomography Caused by Multiple Scattering , 1983, IEEE Transactions on Medical Imaging.

[8]  Weng Cho Chew,et al.  Simultaneous reconstruction of permittivity and conductivity profiles in a radially inhomogeneous slab , 1986 .

[9]  E. Wolf.  Three-dimensional structure determination of semi-transparent objects from holographic data , 1969 .

[10]  Roger F. Harrington,et al.  Field computation by moment methods , 1968 .

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

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

[13]  A. Tijhuis.  Iterative determination of permittivity and conductivity profiles of a dielectric slab in the time domain , 1981 .

[14]  F. Agterberg.  Introduction to Mathematics of Inversion in Remote Sensing and Indirect Measurements , 1979 .

[15]  Weng Cho Chew,et al.  PROFILE INVERSION OF A PLANAR MEDIUM WITH A LINE SOURCE OR A POINT SOURCE. , 1984 .

[16]  S. Johnson,et al.  Inverse Scattering Solutions by a Sinc Basis, Multiple Source, Moment Method -- Part I: Theory , 1983, Ultrasonic imaging.

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

[18]  J. Richmond.  Scattering by a dielectric cylinder of arbitrary cross section shape , 1965 .

[19]  S. Johnson,et al.  Inverse Scattering Solutions by a Sinc Basis, Multiple Source, Moment Method -- Part II: Numerical Evaluations , 1983, Ultrasonic imaging.

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

[21]  A. J. Devaney,et al.  Radiating and nonradiating classical current distributions and the fields they generate , 1973 .