Method of Formal Parameter Expansion for Acoustical Inverse Scattering Problems

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


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?


Fourier Spectrum Helmholtz Equation Severe Limitation Inverse Scattering Scattered Field 
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  1. [1]
    M. Kaveh, R.K. Mueller and R.D. Inversion, Ultrasonic tomography based on perturbation solution of the wave equation, Computer graphics and image processing, 9:105(1979).CrossRefGoogle Scholar
  2. [2]
    N. Bleistein, J.K. Cohen, and F.G. Hagin, ”Two and one-half dimensional Born inversion with an arbitrary reference,” Geophysics, 52(1):26(1987).ADSCrossRefGoogle Scholar
  3. [3]
    M. Kaveh, M. Soumekh, and R.K. Mueller, A comparison of Born and Rytov approximations in acoustic tomography, in:” Acoustical Imaging, vol.11,” J. Powers, ed. Plenum, New York(1981).Google Scholar
  4. [4]
    M. Slaney, A.C. Kak, and L.E. Larsen, Limitations of imaging with first-order approximations in acoustic tomography, IEEE Trans. Microwave Theory Tech., 32(8):860(1984).ADSCrossRefGoogle Scholar
  5. [5]
    Zhen-Qiu Lu and Yan-Yun Zhang, Acoustical tomograpy based on the second-order Born transform perturbation approximation, IEEE Trans. Ultrason. Fer-roelectrics, Freq. Contr., 43(2):296(1996).CrossRefGoogle Scholar
  6. [6]
    M. Kaveh, M. Soumekh, Zhen-Qiu Lu, R.K. Mueller, and J.F. Greenleaf, Further results on diffraction tomography using Rytov approximation, in: ”Acoustical Imaging, vol.12,” E.A. Ash and K. Hill, eds. Plenum, New York(1982).Google Scholar
  7. [7]
    Zhen-Qiu Lu, JKM perturbation theory, relaxation perturbation theory and their applications to inverse scattering: theory and reconstruction algorithms, IEEE Trans. Ultrason. Ferroelectrics, Freq. Contr., 33(6):722(1986).ADSCrossRefGoogle Scholar
  8. [8]
    I.M. Gel’fand and G.E. Shilov, ”Generalized Functions (Vol.1),” Academic, New York(1964).Google Scholar

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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