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Analysis of Inverse Scattering Solutions from Single Frequency, Combined Transmission and Reflection Data for the Helmholtz and Riccati Exact Wave Equations

  • W. W. Kim
  • S. A. Johnson
  • M. J. Berggren
  • F. Stenger
  • C. H. Wilcox
Part of the Acoustical Imaging book series (ACIM, volume 15)

Abstract

Various numerical methods to solve the exact inverse scattering problem are presented here. These methods consist of the following steps: first, modeling the scattering of acoustic waves by an accurate wave equation; second, discretizing this equation; and third, numerically solving the discretized equations. The fixed-point method and the nonlinear Newton-Raphson method are applied to both the Helmholtz and Riccati exact wave equations after discretizations by the moment method or by the discrete Fourier transform methods. Validity of the proposed methods is verified by computer simulation, using exact scattering data from the analytical solution for scattering from right circular cylindrical objects. (Acoustical Imaging 15, Halifax, Nova Scotia, July, 1986)

Keywords

Wave Equation Discrete Fourier Transform Conjugate Gradient Algorithm Acoustical Image Linear Inversion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Plenum Press, New York 1987

Authors and Affiliations

  • W. W. Kim
    • 1
  • S. A. Johnson
    • 1
    • 2
    • 3
  • M. J. Berggren
    • 2
  • F. Stenger
    • 4
  • C. H. Wilcox
    • 4
  1. 1.Department of Electrical EngineeringUniversity of UtahSalt Lake CityUSA
  2. 2.Department of BioengineeringUniversity of UtahSalt Lake CityUSA
  3. 3.Department of RadiologyUniversity of UtahSalt Lake CityUSA
  4. 4.Department of MathematicsUniversity of UtahSalt Lake CityUSA

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