Directions in Electromagnetic Wave Modeling pp 507-515 | Cite as

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

Chapter

## 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.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.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.J.M. Cowley,
*Diffraction Physics*. New York: North-Holland, 1984.Google Scholar - 4.E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,”
*Opt. Commun.*1, p. 153, 1969.ADSCrossRefGoogle Scholar - 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.A.J. Devaney, “Inverse source and scattering problems in ultrasonics,”
*IEEE Trans. Sonics and Ultra*.**SU-30**, pp. 355–364, 1983.Google Scholar - 7.A.C. Kak, “Computerized tomography with x-ray emission and ultrasound sources,”
*Proc. IEEE*, Vol. 67, pp. 1245–1272, 1979.CrossRefGoogle Scholar - 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.A.J. Devaney, “Reconstructive tomography with diffracting waveflelds,”
*Inverse Problems*, Vol. 2, pp.161–183, 1986.ADSCrossRefzbMATHMathSciNetGoogle Scholar - 10.A.J. Devaney, “A filtered backpropagation algorithm for diffraction tomography,”
*Ultrasonic Imaging*, Vol. 4, pp. 336–350, 1982.Google Scholar - 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.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.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.A. Sommerfeld,
*Partial Differential Equations in Physics*. New York: Academic Press, p. 189, 1967.Google Scholar - 15.A.J. Devaney, “Variable density diffraction tomography,”
*J. Acous. Soc. Am*.**78**, pp. 120–130, 1985.ADSCrossRefzbMATHMathSciNetGoogle Scholar - 16.J.R. Taylor,
*Scattering Theory*. New York: Wiley, 1972.Google Scholar - 17.A.J. Devaney, “Nonuniqueness in the inverse scattering problem,”
*J. Math. Phys*.**19**, pp. 1526–1532, 1978.ADSCrossRefGoogle Scholar - 18.A.J. Devaney, “Inversion formula for inverse scattering within the Born approximation,”
*Opt. Commun*.**7**, p. 111, 1982.Google Scholar - 19.A.J. Devaney, “Inverse scattering theory within the Rytov approximation,”
*Opt. Lett*.**6**, pp. 374–376, 1981.ADSCrossRefGoogle Scholar - 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.G. Beylkin and M. Oristaglio, “Distorted wave Born and Rytov approximations,”
*Opt. Commun*.**53**, pp. 213–216, 1985.ADSCrossRefGoogle Scholar - 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.P.M. Morse and H. Feshbach,
*Methods of Theoretical Physics*. New York, McGraw-Hill, Part I, Chap. 8, 1953.zbMATHGoogle Scholar - 24.A.J. Devaney and D.H. Zhang, “Geophysical diffraction tomography in a layered background,” (submitted to
*Wave Motion).*Google Scholar - 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.R. Gordon, “A tutorial on ART,”
*IEEE Trans. Nuclear Science*, Vol. NS-21, pp. 78–93, 1974.ADSCrossRefGoogle Scholar - 27.F. Natterer,
*The Mathematics of Computerized Tomography*. New York, John Wiley, 1986.zbMATHGoogle Scholar - 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.A.J. Devaney, “The limited view problem in diffraction tomography,”
*Inverse Problems*, Vol.5, p. 501, 1989.ADSCrossRefzbMATHMathSciNetGoogle Scholar - 30.A.J. Devaney and A.B. Weglein, “Inverse scattering within the Heitler approximation,”
*Inverse Problems*, Vol. 5, p. L49, 1989.ADSCrossRefGoogle Scholar - 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.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

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© Springer Science+Business Media New York 1991