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Method of Formal Parameter Expansion for Acoustical Inverse Scattering Problems

  • Zhen-Qiu Lu
Part of the Acoustical Imaging book series (ACIM, volume 23)

Abstract

In acoustical diffraction tomography, the inverse scattering perturbation theory, especially the first-order Born perturbation approximation has its advantages: comparatively simple calculations. That is why it has been used in diffraction tomography in many fields, such as in medical and seismic imaging 1−2. But this method has its disadvantages: severe limitations on scatterers, i.e., objects to be imaged3−5. These limitations are impracticable in the most cases, such as in medical imaging and petroleum exploration. The use of high-order, for example, second-order Born perturbation algorithms can reduce these limitations to a certain extent. But they also failed to reconstruct the object with good accuracy in many cases 5. In such cases, the third- or even higher-order Born approximation must be taken into ac- count. This will result in more and more tedious calculations. Can and how do we find a method which needs comparatively simple calculations and has not severe limitations on objects?

Keywords

Fourier Spectrum Helmholtz Equation Severe Limitation Inverse Scattering Scattered Field 
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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Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Zhen-Qiu Lu
    • 1
  1. 1.Department of PhysicsNankai UniversityTianjinPeople’s Republic of China

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