Skip to main content
SpringerLink
Log in

Location and reconstruction of objects using a modified gradient approach

  • Conference paper
  • First Online:
Book cover Inverse Problems of Wave Propagation and Diffraction

Part of the book series: Lecture Notes in Physics ((LNP,volume 486))

Abstract

A large class of inverse scattering problems involves the attempt to determine the shape, location, and constitutive parameters of a bounded object or objects from a knowledge of the field scattered by the object(s) when illuminated or ensonified by a known time harmonic incident field. The fields may be electromagnetic or acoustic and while the field equations are different in each case, the inverse problem may be cast in a general framework which accommodates both phenomena and in fact may be extended to include time-harmonic inverse scattering of elastic waves. This class of problems has been attacked in a number of ways including Born-based methods [1], Newton-Kantorovich methods [2], diffraction tomography

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Tijhuis A. G.: Born-type reconstruction of material parameters of an inhomogeneous lossy dielectric slab from reflected-field data. Wave Motion 11, 151–173 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  2. Roger A.: A Newton-Kantorovich algorithm applied to an electromagnetic inverse problem. IEEE Trans. Antennas Propagat. AP-29, 232–238 (1981)

    Article  ADS  MathSciNet  Google Scholar 

  3. Tabbara W., Duchêne B., Pichot Ch., Lesselier D., Chommeloux L., Joachimowicz N.: Diffraction tomography: Contribution to the analysis of applications in microwaves and ultrasonics. Inverse Problems 4, 305–331 (1988)

    Article  ADS  MathSciNet  Google Scholar 

  4. Colton D., Kress R.: Inverse Acoustic and Electromagnetic Scattering Theory (Springer, Berlin Heidelberg, 1992)

    MATH  Google Scholar 

  5. Kleinman R. E., van den Berg P. M.: A modified gradient method for two-dimensional problems in tomography. J. Comp. Appl. Math. 42, 17–35 (1992)

    Article  MATH  Google Scholar 

  6. van den Berg P. M., Kleinman R. E.: Gradient Methods in Inverse Acoustic and Electromagnetic Scattering. IMA Proc. Large Scale Global Optimization (Springer, Berlin Heidelberg, to appear)

    Google Scholar 

  7. Wen Lixin, Kleinman R. E., van den Berg P. M.: Modified gradient profile inversion using H-polarized waves. Digest of IEEE-AP Symp., Newport Beach, CA, 1598–1601 (1995)

    Google Scholar 

  8. Charbonnier P., Blanc-Féraud L., Aubert G., Barlaud M.: Deterministic edgepreserving regularization in computed imagery. IEEE Trans. Image Processing (to appear)

    Google Scholar 

  9. Aubert G., Lazavoaia L.: A variational method in image recovery. SIAM J. Num. Anal. (to appear)

    Google Scholar 

  10. Ruden B., Osher S., Fatemi C.: Nonlinear total variation based noise removal algorithm. Physica 60D, 259–268 (1992)

    ADS  Google Scholar 

  11. Dobson D. C., Santosa F.: An image-enhancement technique for electrical impedance tomography. Inverse Problems 10, 317–334 (1994)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  12. Acar R., Vogel C. R.: Analysis of bounded variation penalty methods for ill-posed problems. Inverse Problems 10, 1217–1229 (1994)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  13. van den Berg P. M., Kleinman R. E.: A total variation enhanced modified gradient algorithm for profile reconstruction. Inverse Problems 11, L5–L10 (1995)

    Article  MATH  Google Scholar 

  14. Kleinman R. E., van den Berg P. M.: An extended range modified gradient technique for profile inversion. Radio Sci. 28, 877–884 (1993)

    Article  ADS  Google Scholar 

  15. Kleinman R. E., van den Berg P. M.: Two-dimensional location and shape reconstruction. Radio Sci. 29, 1157–1169 (1994)

    Article  ADS  Google Scholar 

  16. Belkebir K., Kleinman R. E., Pichot Ch.: Microwave imaging-location and shape reconstruction from multifrequency scattering data. IEEE Trans. Microwave Theory (to appear) Tech.

    Google Scholar 

  17. Lesselier D., Duchêne B.: Wavefield inversion of objects in stratified environments; from back propagation schemes to full solutions. Review of Radio Science 1993–1996, W. R. Stone Ed. (Oxford University Press, New York, 1996), 235–268

    Google Scholar 

  18. Souriau L., Duchêne B., Lesselier D., Kleinman R. E.: Modified gradient approach to inverse scattering for binary objects in stratified media. Inverse Problems 12, 463–481 (1996)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  19. van den Berg P. M., Coté M. G., Kleinman R. E.: “Blind” shape reconstruction from experimental data. IEEE Trans. Antennas Propagat. AP-43, 1389–1396 (1995)

    Article  ADS  Google Scholar 

  20. Duchêne B., Lesselier D.: On modified gradient solution methods using the binary aspect of the unknown electromagnetic parameters and their application to the Ipswich data. IEEE Antennas Propagat. Mag. 38, 45–47 (1996)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Center for the Mathematics of Waves, Department of Mathematical Sciences, University of Delaware, 19716, Newark, Delaware, USA

    Ralph E. Kleinman

  2. Centre for Technical Geoscience, Laboratory of Electromagnetic Research, Delft University of Technology, P.O. Box 5031, 2600 GA, Delft, The Netherlands

    Peter M. van den Berg

  3. Laboratoire des Signaux et Systèmes, C.N.R.S.-SUPELEC, Plateau de Moulon, 91192, Gif-sur-Yvette Cedex, France

    Bernard Duchêne & Dominique Lesselier

Authors
  1. Ralph E. Kleinman
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Peter M. van den Berg
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Bernard Duchêne
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Dominique Lesselier
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Guy Chavent Pierre C. Sabatier

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer-Verlag

About this paper

Cite this paper

Kleinman, R.E., van den Berg, P.M., Duchêne, B., Lesselier, D. (1997). Location and reconstruction of objects using a modified gradient approach. In: Chavent, G., Sabatier, P.C. (eds) Inverse Problems of Wave Propagation and Diffraction. Lecture Notes in Physics, vol 486. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0105767

Download citation

  • DOI: https://doi.org/10.1007/BFb0105767

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-62865-1

  • Online ISBN: 978-3-540-68713-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation