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Performance of Fast Inverse Scattering Solutions for the Exact Helmholtz Equation Using Multiple Frequencies and Limited Views

  • M. J. Berggren
  • S. A. Johnson
  • B. L. Carruth
  • W. W. Kim
  • F. Stenger
  • P. L. Kuhn
Part of the Acoustical Imaging book series (ACIM, volume 15)

Abstract

We have previously reported fast algorithms for imaging by acoustical inverse scattering using the exact (not linearized) Helmholtz wave equation [1]. We now report numerical implementations of these algorithms which allow the reconstruction of quantitative images of speed of sound, density, and absorption from either transmission or reflection data. We also demonstrate the application of our results to larger grids (up to 64 × 64 pixels) and compare our results with analytically derived data, which are known to be highly accurate, for scattering from right circular cylindrical objects. We report on the performance of our algorithms for both transmission and reflection data and for the simultaneous solution of scattering components corresponding to speed of sound and absorption. We have further examined the performance of our methods with various amounts of random noise added to the simulated data. We also report on the performance of one technique we have devised to extract quantitative density images from our algorithms.

Keywords

Test Object Inverse Scattering Reflection Data Acoustical Image Pixel Grid 
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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References

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    S. A. Johnson, Y. Zhou, M. L. Tracy, M. J. Berggren, and F. Stenger, “Fast Iterative Algorithms for Inverse Scattering of the Helmholtz and Riccati Wave Equations,” Acoustical Imaging 13, Plenum Press, pp. 75–87 (1984).CrossRefGoogle Scholar
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Copyright information

© Plenum Press, New York 1987

Authors and Affiliations

  • M. J. Berggren
    • 1
  • S. A. Johnson
    • 1
    • 2
    • 3
  • B. L. Carruth
    • 2
  • W. W. Kim
    • 2
  • F. Stenger
    • 4
  • P. L. Kuhn
    • 2
  1. 1.Department of BioengineeringUniversity of UtahSalt Lake CityUSA
  2. 2.Department of Electrical EngineeringUniversity 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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