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IEEE Transactions on Microwave Theory and Techniques
Volume 48 Number 11, November 2000

Table of Contents for this issue

Complete paper in PDF format

Two-Dimensional Dielectric Profile Reconstruction Based on Spectral-Domain Moment Method and Nonlinear Optimization

Theofanis A. Maniatis, Member, IEEE Konstantina S. Nikita, Senior Member, IEEE and Nikolaos K. Uzunoglu Senior Member, IEEE

Page 1831.

Abstract:

A novel method for two-dimensional (2-D) profile reconstruction of dielectric objects, based on nonlinear optimization, is presented in this paper. The unknown dielectric profile is expressed in terms of Gaussian basis functions. The scattering integral equation (SIE) is discretized using a spectral-domain moment technique, where the unknown internal field is described as a superposition of a limited number of plane waves, resulting in a significant reduction of the associated computational cost. The inverse-scattering problem is solved by minimizing a cost function consisting of two terms: the first term represents the error between measured and predicted values of the scattered field, while the second term corresponds to the error in satisfying the SIE for the field in the interior of the scatterer. Accurate and efficient dielectric profile reconstructions of 2-D lossy scatterers of circular and square cross sections using synthetic scattered field data are presented, while the effect of various discretization parameters on the convergence of the method is studied in detail.

References

  1. J. R. Shewell and E. Wolf, "Inverse diffraction and a new reciprocity theorem", J. Opt. Soc. Amer., vol. 58, pp.  1596-1603, 1968.
  2. A. J. Devaney, "A filtered backpropagation algorithm for diffraction tomography", Ultrason. Imaging, vol. 4, pp.  336-350, 1982.
  3. M. Slaney, A. C. Kak and L. E. Larsen, "Limitations of imaging with first order diffraction tomography", IEEE Trans. Microwave Theory Tech., vol. MTT-32, pp.  860-873, Aug.  1984.
  4. K. T. Ladas, T. A. Maniatis and N. K. Uzunoglu, "Inverse scattering using a variational principle", J. Electromag. Waves Applicat., vol. 10, pp.  3-17, 1996.
  5. K. T. Ladas, T. A. Maniatis and N. K. Uzunoglu, "On the reconstruction of dielectric objects from scattered field data using the Heitler equation", Electromag. , vol. 16, pp.  17-34, 1996.
  6. D. K. Ghodgaonkar, O. P. Gandhi and M. J. Hagmann, "Estimation of complex permittivities of three-dimensional inhomogeneous biological bodies", IEEE Trans. Microwave Theory Tech., vol. MTT-31, pp.  442-446, June  1983.
  7. S. Caorsi, G. L. Gragnani and M. Pastorino, "Reconstruction of dielectric permittivity distributions in arbitrary 2-D inhomogeneous biological bodies by a multiview microwave numerical method", IEEE Trans. Med. Imag., vol. 12, pp.  232-239, June  1993.
  8. S. Caorsi, G. L. Gragnani and M. Pastorino, "Redundant electromagnetic data for microwave imaging of three-dimensional dielectric objects", IEEE Trans. Antennas Propagat., vol. 42, pp.  581-589, May  1994.
  9. W. C. Chew and Y. M. Wang, "Reconstruction of the two-dimensional permittivity using the distorted Born iterative method", IEEE Trans. Med. Imag., vol. 9, pp.  218-255, June  1990.
  10. N. Joachimowicz, C. Pichot and J. Hugonin, "Inverse scattering: An iterative numerical method for electromagnetic imaging", IEEE Trans. Antennas Propagat., vol. 39, pp.  1742-1752, Dec.  1991.
  11. D. T. Borup, S. A. Johnson, W. W. Kim and M. J. Berggren, "Nonperturbative diffraction tomography via Gauss-Newton iteration applied to the scattering integral equation", Ultrason. Imag., vol. 14, pp.  69-85, 1992.
  12. A. Franchois and C. Pichot, "Microwave imaging-Complex permittivity reconstruction with a Levenberg-Marquardt method", IEEE Trans. Antennas Propagat., vol. 45, pp.  203-215, Feb.  1997.
  13. N. Joachimowicz, J. J. Mallorqui, J. C. Bolomey and A. Broquetas, "Convergence and stability assessment of Newton-Kantorovich reconstruction algorithms for microwave tomography", IEEE Trans. Med. Imag., vol. 17, pp.  562-570, Aug.  1998 .
  14. A. E. Souvorov, A. E. Bulyshev, S. Y. Semenov, R. H. Svenson, A. G. Nazarov, Y. E. Sizov and G. P. Tatsis, "Microwave tomography: A two-dimensional Newton iterative scheme", IEEE Trans. Microwave Theory Tech., vol. 46, pp.  1564-1659, Nov.  1998.
  15. A. Roger, "A Newton-Kantorovich algorithm applied to an electromagnetic inverse problem", IEEE Trans. Antennas Propagat., vol. AP-29, pp.  232-238, Mar.  1981.
  16. H. T. Lin and Y. W. Kiang, "Microwave imaging for a dielectric cylinder", IEEE Trans. Microwave Theory Tech., vol. 42, pp.  1572-1579, Aug.  1994.
  17. R. Kleinman and P. M. van den Berg, "An extended range-modified gradient technique for profile inversion", Radio Sci., vol. 29, pp.  877-884,  1993.
  18. B. J. Kooij and P. M. van den Berg, "Nonlinear inversion in TE scattering", IEEE Trans. Microwave Theory Tech., vol. 46, pp.  1704-1712, Nov.  1998.
  19. T. M. Habashy, M. L. Oristaglio and A. De Hoop, "Simultaneous nonlinear reconstruction of two-dimensional permittivity and conductivity", Radio Sci., vol. 29, pp.  1101-1118, 1994.
  20. P. van den Berg and R. E. Kleinman, "A contrast source inversion method", Inverse Problems, vol. 13, pp.  1607-1620, 1997.
  21. S. Caorsi, G. L. Gragnani, M. Pastorino and M. Rebagliati, "A model-driven approach to microwave diagnostics in biomedical applications", IEEE Trans. Microwave Theory Tech., vol. 44, pp.  1910-1920, Oct.  1996.
  22. I. T. Rekanos, T. V. Yioultsis and T. D. Tsiboukis, "Inverse scattering using the finite-element method and a nonlinear optimization technique", IEEE Trans. Microwave Theory Tech., vol. 47, pp.  336-344, Mar.  1999.
  23. K. D. Paulsen, P. M. Meaney, M. J. Moskowitz and J. M. Sullivan Jr., "A dual mesh scheme for finite element based reconstruction algorithms", IEEE Trans. Med. Imag. , vol. 14, pp.  504-514, Sept.  1995.
  24. L. E. Larsen and J. H. Jacobi, "Microwave scattering parameter imagery of an isolated canine kidney", Med. Phys., vol. 6, pp.  394-403, 1979.
  25. A. Franchois, A. Joisel, C. Pichot and J. C. Bolomey, "Quantitative microwave imaging with a 2.45-GHz planar microwave camera", IEEE Trans. Medical Imaging, vol. 17, pp.  550-561,  Aug.  1998.
  26. A. Broquetas, J. Romeu, J. M. Rius, A. R. Elias-Fuste, A. Cardama and L. Jofre, "Cylindrical geometry: A further step in active microwave tomography", IEEE Trans. Microwave Theory Tech., vol. 39, pp.  836-844, May  1991.
  27. S. Y. Semenov, R. H. Svenson, A. E. Boulyshev, A. E. Souvorov, V. Y. Borisov, Y. Sizov, A. N. Starostin, K. R. Dezern, G. P. Tatsis and V. Y. Baranov, "Microwave tomography: Two-dimensional system for biological imaging", IEEE Trans. Biomed Eng., vol. 43, pp.  869-877, Sept.  1996.
  28. S. Y. Semenov, A. E. Boulyshev, A. E. Souvorov, R. H. Svenson, Y. E. Sizov, V. Y. Borisov, V. G. Posukh, I. M. Kozlov, A. G. Nazarov and G. P. Tatsis, "Microwave tomography: Theoretical and experimental investigation of the iteration reconstruction algorithm", IEEE Trans. Microwave Theory Tech., vol. 46, pp.  133 -141, Jan.  1998.
  29. P. M. Meaney, K. D. Paulsen and J. T. Chang, "Near-field microwave imaging of biologically based materials using a monopole transceiver system", IEEE Trans. Microwave Theory Tech., vol. 46, pp.  31-45, Jan.  1998.
  30. A. J. Devaney and G. Beylkin, "Diffraction tomography using arbitrary transmitter and receiver surfaces", Ultrason. Imag., vol. 6, pp.  181-193, 1984.
  31. H. P. Schwan and K. R. Foster, "RF field interactions with biological systems: Electrical properties and biophysical mechanism", Proc. IEEE, vol. 68, pp.  104-113, Jan.  1980.
  32. C. Gabriel, S. Gabriel and E. Corthout, "The dielectric properties of biological tissues", Med. Phys., vol. 41, pp.  2231-2293, 1996.
  33. D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, Berlin: Germany: Springer-Verlag, 1998.
  34. J. H. Richmond, "Scattering by a dielectric cylinder of arbitrary cross-section shape", IEEE Trans. Antennas Propagat., vol. AP-13, pp.  334-341,  May  1965.
  35. B. S. Robinson and J. F. Greenleaf, "The scattering of ultrasound by cylinders: Implications for diffraction tomography", J. Acoust. Soc. Amer. , vol. 80, pp.  40-49, 1986.