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Approximate Scattering Models in Inverse Scattering: Past, Present, and Future

  • Anthony J. Devaney

Abstract

There exist a number of applications in industry and the military that involve what is generally known as inverse scattering. Examples include radar target detection and estimation, radar imaging, nondestructive evaluation (NDE), biological and geophysical imaging, and structure determination using X-rays and electron beams. Although the applications appear very different they all involve estimating (reconstructing) the properties of a scatterer from scattered field data and have a common underlying mathematical structure.

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References

  1. 1.
    P.C. Sabatier, “Basic concepts and methods of inverse problems,” in Tomography and Inverse Problems, ed. P.C. Sabatier. Philadelphia: Adam Hilger, 1987.Google Scholar
  2. 2.
    R.G. Newton, “The Marchenko and Gelfand-Levitand methods in the inverse scattering problem in one and three dimensions,” in Conference on Inverse Scattering: Theory and Application Philadelphia: SIAM Press, 1983.Google Scholar
  3. 3.
    J.M. Cowley, Diffraction Physics. New York: North-Holland, 1984.Google Scholar
  4. 4.
    E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Commun. 1, p. 153, 1969.ADSCrossRefGoogle Scholar
  5. 5.
    K.J. Langenberg, “Applied inverse problems for acoustic, electromagnetic and elastic wave scattering,” in Tomography and Inverse Problems, ed. P.C. Sabatier. Philadelphia: Adam Hilger, 1987.Google Scholar
  6. 6.
    A.J. Devaney, “Inverse source and scattering problems in ultrasonics,” IEEE Trans. Sonics and Ultra.SU-30, pp. 355–364, 1983.Google Scholar
  7. 7.
    A.C. Kak, “Computerized tomography with x-ray emission and ultrasound sources,” Proc. IEEE, Vol. 67, pp. 1245–1272, 1979.CrossRefGoogle Scholar
  8. 8.
    A.J. Devaney, Mathematical Topics in Diffraction Tomography, Final Project Report NSF Grant # DMS-8460595, 1985. Available through the U.S. Goverment Printing Office.Google Scholar
  9. 9.
    A.J. Devaney, “Reconstructive tomography with diffracting waveflelds,” Inverse Problems, Vol. 2, pp.161–183, 1986.ADSCrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    A.J. Devaney, “A filtered backpropagation algorithm for diffraction tomography,” Ultrasonic Imaging, Vol. 4, pp. 336–350, 1982.Google Scholar
  11. 11.
    S.X. Pan and A.C. Kak, “A computational study of reconstruction algorithms for diffraction tomography,” IEEE Trans. Acoustics, Speech and Signal Processing, Vol. ASSP-31, pp. 1262–1275, 1982.CrossRefGoogle Scholar
  12. 12.
    R.K. Mueller, M. Kaveh, and G. Wade, “Reconstructive tomography and applications to ultrasonics,” Proc. IEEE, Vol. 67, pp. 567–587, 1979.ADSCrossRefGoogle Scholar
  13. 13.
    A.J. Devaney, “A computer simulation study of diffraction tomography,” IEEE Trans. on Biomed. Eng., Vol. BME-30, pp. 377–386, 1982.MathSciNetGoogle Scholar
  14. 14.
    A. Sommerfeld, Partial Differential Equations in Physics. New York: Academic Press, p. 189, 1967.Google Scholar
  15. 15.
    A.J. Devaney, “Variable density diffraction tomography,” J. Acous. Soc. Am.78, pp. 120–130, 1985.ADSCrossRefzbMATHMathSciNetGoogle Scholar
  16. 16.
    J.R. Taylor, Scattering Theory. New York: Wiley, 1972.Google Scholar
  17. 17.
    A.J. Devaney, “Nonuniqueness in the inverse scattering problem,” J. Math. Phys.19, pp. 1526–1532, 1978.ADSCrossRefGoogle Scholar
  18. 18.
    A.J. Devaney, “Inversion formula for inverse scattering within the Born approximation,” Opt. Commun.7, p. 111, 1982.Google Scholar
  19. 19.
    A.J. Devaney, “Inverse scattering theory within the Rytov approximation,” Opt. Lett.6, pp. 374–376, 1981.ADSCrossRefGoogle Scholar
  20. 20.
    M. Oristaglio, “Accuracy of the Born and Rytov approximations for reflection and refraction at a plane interface,” J. Opt. Soc. Am.2, pp. 1987–1989, 1985.ADSCrossRefGoogle Scholar
  21. 21.
    G. Beylkin and M. Oristaglio, “Distorted wave Born and Rytov approximations,” Opt. Commun.53, pp. 213–216, 1985.ADSCrossRefGoogle Scholar
  22. 22.
    A.J. Devaney and M. Oristaglio, “Inversion procedure for inverse scattering within the distorted wave Born approximation,” Phys. Rev. Letts.51, p.237, 1983.ADSCrossRefGoogle Scholar
  23. 23.
    P.M. Morse and H. Feshbach, Methods of Theoretical Physics. New York, McGraw-Hill, Part I, Chap. 8, 1953.zbMATHGoogle Scholar
  24. 24.
    A.J. Devaney and D.H. Zhang, “Geophysical diffraction tomography in a layered background,” (submitted to Wave Motion). Google Scholar
  25. 25.
    R. Gordon and G.T. Herman, “Three-dimensional reconstruction from projections: A review of algorithms,” Int. Rev. Cytol., Vol. 38, pp. 111–151, 1974.Google Scholar
  26. 26.
    R. Gordon, “A tutorial on ART,” IEEE Trans. Nuclear Science, Vol. NS-21, pp. 78–93, 1974.ADSCrossRefGoogle Scholar
  27. 27.
    F. Natterer, The Mathematics of Computerized Tomography. New York, John Wiley, 1986.zbMATHGoogle Scholar
  28. 28.
    O. Brander and B. DeFacio, “The role of filters and the singular-value decomposition for the inverse Born approximation,” Inverse Problems 2, pp. 375–393, 1986.ADSCrossRefzbMATHMathSciNetGoogle Scholar
  29. 29.
    A.J. Devaney, “The limited view problem in diffraction tomography,” Inverse Problems, Vol.5, p. 501, 1989.ADSCrossRefzbMATHMathSciNetGoogle Scholar
  30. 30.
    A.J. Devaney and A.B. Weglein, “Inverse scattering within the Heitler approximation,” Inverse Problems, Vol. 5, p. L49, 1989.ADSCrossRefGoogle Scholar
  31. 31.
    R.J. Wombell and M. A. Fiddy, “Inverse scattering within the distorted wave Born approximation,” Inverse Problems, Vol. 4, p. L23, 1988.ADSCrossRefGoogle Scholar
  32. 32.
    W.C. Chew and Y.M. Wang, “Reconstruction of two-dimensional permittivity distribution using the distorted Born iterative method,” IEEE Trans. Med. Imag., Vol. 9, p. 218, 1990.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • Anthony J. Devaney
    • 1
    • 2
  1. 1.Department of Electrical and Computer EngineeringNortheastern UniversityBostonUSA
  2. 2.A.J. Devaney AssociatesBostonUSA

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