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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 16, Iss. 7 — Jul. 1, 1999
  • pp: 1779–1787

Inverse scattering under the distorted Born approximation for cylindrical geometries

Giovanni Leone, Raffaele Persico, and Rocco Pierri  »View Author Affiliations


JOSA A, Vol. 16, Issue 7, pp. 1779-1787 (1999)
http://dx.doi.org/10.1364/JOSAA.16.001779


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Abstract

The problem of reconstructing dielectric permittivity from scattered field data is dealt with for scalar two-dimensional geometry at a fixed frequency by use of a linearized approximation about a chosen reference permittivity profile. To investigate the capabilities and limits of linear inversion algorithms, we analyze the class of retrievable profiles with reference to some canonical geometries for which either analytical or numerical details can be worked through easily. The tool for such an analysis consists of the singular-value decomposition of the relevant scattering operators. For a constant reference permittivity function, the different behavior of linear inversion algorithms with respect to either radial or angular variations of the permittivity profiles is pointed out. In the last-named case the general situation of a multiview radiation is accounted for, and, unlike for the Born approximation, profiles that cannot be reconstructed by linear inversion comprise slowly varying functions. Moreover, the effect of an angularly varying reference profile is examined for a thin circular shell, permitting the possibility of reconstruction of rapidly varying angular profiles by linear inversion. Numerical results of linear inversions that confirm the predictions are shown.

© 1999 Optical Society of America

OCIS Codes
(100.3010) Image processing : Image reconstruction techniques
(100.3190) Image processing : Inverse problems
(290.3200) Scattering : Inverse scattering

History
Original Manuscript: November 19, 1998
Revised Manuscript: March 1, 1999
Manuscript Accepted: March 1, 1999
Published: July 1, 1999

Citation
Giovanni Leone, Raffaele Persico, and Rocco Pierri, "Inverse scattering under the distorted Born approximation for cylindrical geometries," J. Opt. Soc. Am. A 16, 1779-1787 (1999)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-16-7-1779


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References

  1. J. Ch. Bolomey, Ch. Pichot, “Some applications of diffraction tomography to electromagnetics—the particular case of microwaves,” in Inverse Problems in Scattering and Imaging, M. Bertero, E. R. Pike, eds. (Hilger, London1992), pp. 319–344.
  2. D. Colton, R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory (Springer-Verlag, Berlin, 1992).
  3. D. Lesselier, B. Duchene, “Wavefield inversion of objects in stratified environments: from backpropagation schemes to full solutions,” in Review of Radio Science 1993–1996, R. Stone, ed. (Oxford U. Press, Oxford, UK, 1996), pp. 235–268.
  4. A. Roger, F. Chapel, “Iterative methods for inverse problems,” in Application of Conjugate Gradient Method to Electromagnetics and Signal Analysis, T. K. Sarkar, ed. (Elsevier, Amsterdam, 1991), pp. 423–454.
  5. Y. Chen, “Inverse scattering via Heisenberg’s uncertainty principle,” Inverse Probl. 13, 253–282 (1997). [CrossRef]
  6. R. Pierri, A. Brancaccio, “Imaging of a dielectric cylinder: a quadratic approach in the rotational symmetric case,” J. Opt. Soc. Am. A 14, 2777–2785 (1997). [CrossRef]
  7. R. Pierri, G. Leone, “Inverse scattering of dielectric cylinders by a quadratic model,” IEEE Trans. Geosci. Remote Sens. 37, 374–382 (1999). [CrossRef]
  8. R. Pierri, A. Tamburrino, “On the local minima problem in conductivity imaging via a quadratic approach,” Inverse Probl. 13, 1–22 (1997). [CrossRef]
  9. R. G. Keys, A. B. Weglein, “Generalised linear inversion and the first Born theory for acoustic media,” J. Math. Phys. 24, 1444–1449 (1983). [CrossRef]
  10. M. A. Fiddy, “Linearized and approximate methods for inversion of scattered field data,” in Inverse Problems in Scattering and Imaging, M. Bertero, E. R. Pike, eds. (Hilger, London, 1992), pp. 23–46.
  11. W. C. Chew, Y. M. Wang, “Reconstruction of two-dimensional permittivity distribution using the distorted born iterative method,” IEEE Trans. Med. Imaging 9, 218–225 (1990). [CrossRef] [PubMed]
  12. D. O. Batrakov, N. P. Zhuck, “Solution of a general inverse scattering problem using the distorted Born approximation and iterative technique,” Inverse Probl. 10, 39–54 (1994). [CrossRef]
  13. C. Torres-Verdin, T. M. Habashy, “A two-step linear inversion of two-dimensional electrical conductivity,” IEEE Trans. Antennas Propag. 43, 405–415 (1995). [CrossRef]
  14. M. S. Zhadanov, S. Fang, “Three-dimensional quasi-linear electromagnetic inversion,” Radio Sci. 31, 741–754 (1996). [CrossRef]
  15. S. Gutman, M. Klibanov, “Iterative method for multi-dimensional inverse scattering problems at fixed frequencies,” Inverse Probl. 10, 573–599 (1994). [CrossRef]
  16. P. Chaturvedi, R. G. Plumb, “Electromagnetic imaging of underground targets using constrained optimization,” IEEE Trans. Geosci. Remote Sens. 33, 551–561 (1995). [CrossRef]
  17. H. Gan, R. Ludwig, P. L. Levin, “Nonlinear diffractive inverse scattering for multiple scattering in inhomogeneous acoustic background media,” J. Acoust. Soc. Am. 97, 764–776 (1995). [CrossRef]
  18. N. Joachimowitz, C. Pichot, J. P. Hugonin, “Inverse scattering: an iterative numerical method for electromagnetic imaging,” IEEE Trans. Antennas Propag. 39, 1742–1752 (1991). [CrossRef]
  19. J.-H. Lin, W. C. Chew, “Solution of the three-dimensional electromagnetic inverse problem by the local shape function and the conjugate gradient fast Fourier transform methods,” J. Opt. Soc. Am. A 14, 3037–3045 (1997). [CrossRef]
  20. J. A. Scales, P. Docherty, A. Gersztenkorn, “Regularisation of nonlinear inverse problems: imaging the near-surface weathering layer,” Inverse Probl. 6, 115–131 (1990). [CrossRef]
  21. R. P. Porter, A. J. Devaney, “Generalized holography and computational solutions to inverse source problems,” J. Opt. Soc. Am. 72, 1707–1713 (1982). [CrossRef]
  22. A. Brancaccio, G. Leone, R. Pierri, “Information content of Born scattered fields: results in the circular cylindrical case,” J. Opt. Soc. Am. A 15, 1909–1917 (1998). [CrossRef]
  23. M. Slaney, A. C. Kak, L. E. Larsen, “Limitations of imaging with first order diffraction tomography,” IEEE Trans. Microwave Theory Tech. MTT-32, 860–874 (1984). [CrossRef]
  24. J. B. Morris, F. C. Lin, D. A. Pommet, R. V. McGahan, M. A. Fiddy, “A homomorphic filtering method for imaging strongly scattering penetrable objects,” IEEE Trans. Antennas Propag. 43, 1029–1035 (1995). [CrossRef]
  25. E. Hille, J. D. Tamarkin, “On the characteristic values of linear integral equations,” Acta Math. 57, 1–76 (1931). [CrossRef]
  26. W. C. Chew, Waves and Fields in Inhomogeneous Media (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1995).
  27. R. F. Harrington, Time-Harmonic Electromagnetic Fields (McGraw-Hill, New York, 1961).
  28. M. Abramowitz, I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965).

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