Skip to main content
SpringerLink
Log in

Quantitative Reconstruction of Complex Permittivity Distributions by Means of Microwave Tomography

  • Conference paper
Inverse Methods in Action

Part of the book series: Inverse Problems and Theoretical Imaging ((IPTI))

Abstract

This paper concerns an iterative method for solving an inverse electromagnetic scattering problem: the quantitative reconstruction of complex permittivity distribution of inhomogeneous objects. During the last decade, intensive research and interest have been focussed on reconstruction algorithms based on the so-called Diffraction Tomography with applications in microwaves or ultrasound [1–16]. The main motivations for using such approaches are to obtain explicit formulas for solving the imaging problem, to take advantage of existing numerical algorithms (Fast Fourier Transform) and to implement the algorithms on PC’s or minicomputers for imaging system purposes (planar microwave camera [5], experiments with ultrasounds and microwaves [11][13][14][16], cylindrical microwave system [15]). However, Diffraction Tomography is subjected to various limitations which include artefacts due to diffraction effects in strongly inhomogeneous media [7][10][16][17][18].The final objective of microwave imagery is to determine the complex permittivity profile (permittivity and conductivity profiles) of the object under investigation. An increasing number of papers [17–25] have been devoted to a such non-linear inverse problem. Different solutions based on Moment Methods [19–25] have been explored, but, convergence depends on contrasting objects. Furthermore, stability is very sensitive to the observation point locations and measurement accuracy (due to the ill-conditioning of the matrix which has to be inverted). Stability and sensivity are why the use of an iterative scheme is important: effects of ill-conditioning can be significantly reduced by enforcing the convergence with “a priori” information (object external shape, upper and lower bounds of complex permittivity, presence of different media,…). Concerning the uniqueness of object reconstruction, it has been proved [24] that if the background medium is dissipative, then the inverse scattering problem has a unique solution.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R.K. Mueller, M. Kaveh, G. Wade, “Reconstructive tomography and applications to ultrasonics,” Proc. IEEE, 67 (4), pp. 567–587, 1979.

    Article  ADS  Google Scholar 

  2. F.M. Adams, A.P. Anderson, “Synthetic aperture tomography (SAT) imaging for microwave diagnostics,” IEE Proc.-H, Micr.,Opt and Ant., 129 (2), pp. 83–88, 1982.

    Google Scholar 

  3. J.Ch. Bolomey, A. Izadnegahdar, L. Jofre, Ch.Pichot, G. Peronnet, M. Solaimani, “Microwave diffraction tomography for biomedical applications,” IEEE Trans. Microwave Theory Tech., MTT-30, pp. 1998–2000, 1982.

    Google Scholar 

  4. M. Baribaud, F. Dubois, R. Floyrac, M. Kom, S. Wong, “Tomographic image reconstruction of biological objects from coherent microwave diffraction data,” BEE Proc.-H, Micr., Opt and Ant., 129 (2), pp. 356–359, 1982.

    Google Scholar 

  5. G. Peronnet, Ch. Pichot, J. Ch Bolomey, L. Joffre, A. Izadnegahdar, C. Szeles, Y. Michel, “A microwave diffraction tomography system for biomedical applications,” Proc. Xlllth European Microwave Conference (Nuremberg, FRG), pp. 529–533, 1983.

    Google Scholar 

  6. A.J. Devaney, “A computer simulation study of diffraction tomography,” IEEE Trans. Biomed. Eng., BME-30, pp 377–386, 1983.

    Article  Google Scholar 

  7. M. Slaney, A. Kak, L. Larsen, “Limitations of imaging with first order diffraction tomography,” IEEE Trans. Microwave Theory Tech., MTT-32, pp. 860–873, 1984.

    Article  ADS  Google Scholar 

  8. Ch. Pichot, L. Joffre, J. Ch Bolomey, G. Peronnet, “Active Microwave Imaging of Inhomogenous bodies,” IEEE Trans. Ant. Propagat., AP-33, pp. 416–425, 1985.

    Google Scholar 

  9. Inverse methods in Electromagnetic Imaging, W.-M. Boerner et al. Eds, NATO ASI Series, Reidel Publ. Comp., Dordrecht, 1985.

    Google Scholar 

  10. H. Ermert, M. Dohlus, “Microwave-diffraction-tomography of cylindrical objects using 3-dimensional wave-fields,” ntzArchiv, Bd.8 H. 5, pp. 111–117, 1986.

    Google Scholar 

  11. F.J. Paolini, “Implementation of microwave diffraction tomography for measurement of dielectric constant distribution,” IEE Proc.-H, Micr., Opt and Ant., 134 (1), pp. 25–29, 1987.

    Google Scholar 

  12. J.M. Rius, M.Ferrando, L. Joffre, A. Broquetas, “Microwave tomography: an algorithm for cylindrical geometries,” Electr. Lett., 23 (11), pp. 564–565, 1987.

    Article  Google Scholar 

  13. W. Tabbara, B. Duchêne, Ch. Pichot, D. Lesselier, L. Chommeloux, N. Joachimowicz, “Diffraction tomography: contribution to the analysis of some applications in microwaves and ultrasonics,” Inverse Problems, 4, pp. 305–331, 1988.

    Article  ADS  MathSciNet  Google Scholar 

  14. R. Aitmehdi, A.P. Anderson, S. Sali, M. Ferrando, “The determination of dielectric loss tangent by microwave phase tomography,” Inverse Problems, 4, pp. 333–345, 1988

    Article  ADS  Google Scholar 

  15. L. Joffre, M.S. Hawley, A. Broquetas, E. De Los Reyes, M. Ferrando, “Medical imaging with a microwave tomographic scanner,” Submitted for publication in IEEE Trans. Biomed. Eng.

    Google Scholar 

  16. J.Ch. Bolomey, Ch. Pichot, G. Gaboriaud, “Critical and prospective analysis of reconstruction algorithms devoted to a planar microwave camera for biomedical applications,” URSI Int. Symp. Proc. (Stockholm, Sueden), pp. 144–146, 1989.

    Google Scholar 

  17. B. Duchêne, D. Lesselier, W. Tabbara, “Diffraction tomography approach to accoustical omaging and media characterization,” J. Opt. Soc. Am., 2 (11), pp. 1943–1953, 1985.

    Article  ADS  Google Scholar 

  18. M.A. El Khalifa, “Amélioration de la qualité des images en tomographic microonde. Contribution a une imagerie quantitative,” Thèse de doctorat en Sciences Physiques, Université de Paris-Sud (Orsay ), 1989.

    Google Scholar 

  19. D.K. Ghodgaonkar, O.P. Gandhi, M.J. Hagmann, “Estimation of complex permittivities of three-dimensional biological bodies,” IEEE Trans. Microwave Theory Tech., MTT-31, pp. 442–446, 1983.

    Google Scholar 

  20. S.A. Johnson, M.L. Tracy, “Inverse scattering solutions by a sine basis, multiple source, Moment Method- Part I: Theory, Part II: Numerical Evaluations,” Ultrasonic Imaging, 5, pp. 361–392, 1983.

    Google Scholar 

  21. S.A. Johnson, M.L. Tracy, “Inverse scattering solutions by a sine basis, multiple source, Moment Method- Part HI: Fast Algorithms,” Ultrasonic Imaging, 6, pp. 103–116, 1984.

    Article  Google Scholar 

  22. M.M. Ney, A.M. Smith, S.S. Stuchly, “A solution of electromagnetic imaging using pseudoinverse transformation,” IEEE Trans. Medical Imaging, MI-3, pp. 155–162, 1984.

    Google Scholar 

  23. A.N. Datta, B. Bandyopadhyay, “Nonlinear extension to a moment method iterative reconstruction algorithm for microwave tomography,” Proc. IEEE, 74 (4), pp. 604–606, 1986.

    Article  Google Scholar 

  24. T.C. Guo, W.W. Guo, “Physics of image formation by microwave scattering,” Medical Imaging, SPIE Proc., 767, pp. 1–10, 1987.

    Google Scholar 

  25. S. Caorsi, G.L. Gagnani, M. Pastorino, “Electromagnetic vision-oriented numerical solution to three-dimensional inverse scattering,” Radio Science, 23 (6), pp. 1094–1106, 1988.

    Article  ADS  Google Scholar 

  26. Y.M. Wang, W.C. Chew, “An iterative solution of two-dimensional electromagnetic inverse scattering problem,” Int. J. Imag. Syst., 1, pp. 100–108, 1989.

    Article  Google Scholar 

  27. D.G.H. Tan, R.D. Murch, R.H.T. Bates, “Inverse scattering for penetrable obstacles,” URSI Int. Symp. Proc.(Stockholm, Sueden), pp. 160–162, 1989.

    Google Scholar 

  28. T.M. Habashy, D.G. Dudley, “Simultaneous inversion of permittivity and conductivity profiles using a renormalized source-type integral equation approach,” URSI Int. Symp. Proc.(Stockholm, Sueden), pp. 578–580, 1989.

    Google Scholar 

  29. M.Schueller, H. Chaloupka, “Improve reconstruction in difraction tomography by means of a nonlinear scattering model,” URSI Int. Symp. Proc.(Stockholm, Sueden), pp. 584–586, 1989.

    Google Scholar 

  30. H. Massoudi, C. H. Durney and M. F. Iskander, “Limitations of the cubical block model of man in calculating SAR distributions,” IEEE Trans. Microwave Theory Techn., MTT-32, pp. 746–752, 1984.

    Article  ADS  Google Scholar 

  31. M. J. Hagmann, “Comments on ‘Limitations of the cubical block model of man in calculating SAR distributions’,” IEEE Trans. Microwave Theory Techn., MTT-33, pp. 347–350, 1985.

    Article  ADS  Google Scholar 

  32. D. T. Borup, D. M. Sullivan, and O.P.Ghandhi. Sullivan, and O.P.Ghandhi, “Comparison of the FFT Conjugate Gradient Method and the Finite-Difference Time-Domain Method for the 2-D absorption problem,” IEEE Trans. Microwave Theory Tech., MTT-35, pp. 383–395, 1987.

    Google Scholar 

  33. N.Joachimowicz, Ch. Pichot, “Comparison of Three Integral Formulations for the 2D-TE Scattering Problem’,” to be published in IEEE Trans. Microwave Theory Techn., Feb. 1990.

    Google Scholar 

  34. A. Roger, D. Maystre, M. Cadilhac, “On a problem of inverse scattering in optics: The dielectric inhomogeneous medium,” J. Optics (Paris), 9 (2), pp. 83–90, 1978.

    ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut d’Optique, Bâtiment 503, F-91405, Orsay, France

    J. P. Hugonin

  2. Groupe d’Electromagnétisme, Laboratoire des Signaux et Systèmes, F-91192, Gif-sur-Yvette Cédex, France

    N. Joachimowicz & Ch. Pichot

Authors
  1. J. P. Hugonin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. N. Joachimowicz
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ch. Pichot
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Laboratoire de Physique Mathématique, Université des Sciences et Techniques du Languedoc, Place Eugène Bataillon, F-34060, Montpellier Cedex, France

    Pierre C. Sabatier

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Hugonin, J.P., Joachimowicz, N., Pichot, C. (1990). Quantitative Reconstruction of Complex Permittivity Distributions by Means of Microwave Tomography. In: Sabatier, P.C. (eds) Inverse Methods in Action. Inverse Problems and Theoretical Imaging. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-75298-8_37

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-75298-8_37

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-75300-8

  • Online ISBN: 978-3-642-75298-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation