Skip to main content

Multiple Frequency Distorted Born Iterative Method for Tomographic Imaging

  • Chapter
Acoustical Imaging

Part of the book series: Acoustical Imaging ((ACIM,volume 23))

Abstract

The goal of ultrasound tomography is to produce a two-dimensional (2D) map of the acoustical properties of a region of interest (ROI) from measurements of the acoustic field taken outside the ROL This map or image can prove very useful in medical diagnosis, non-destructive evaluation, and earth sciences [2, 5, 8, 12]. One solution of the tomographic imaging problem is by solving the inverse scattering problem [2, 4, 6, 10]. The inverse scattering problem is dependent on the total field inside the ROI which is unknown and is dependent on medium properties. This makes the inverse scattering problem nonlinear, and difficult to solve. A linearized, Born-approximate wave equation is usually inverted instead [4, 12].

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

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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.

Similar content being viewed by others

References

  1. G. Beylkin and M. Oristaglio, “Distorted-wave Born distorted-wave Rytov approximations,” Optics Comm., vol. 53, pp. 213–215, 1985.

    Article  ADS  Google Scholar 

  2. H. Blok and M. Oristaglio, Wavefield Imaging and Inversion in Electromagnetics and Acoustics, Delft University of Technology, report number Et/EM 1995-21, June 1995.

    Google Scholar 

  3. W. C. Chew and Y. M. Wang, “Reconstruction of two-dimensional permittivity distribution the using the distorted Born iterative method,” IEEE Trans. Medical Imaging, vol. 9, no. 2, pp. 218–225, June 1990.

    Article  Google Scholar 

  4. W. C. Chew, Waves and Fields in Inhomogeneous Media, Van Nostrand Reinhold, 1992.

    Google Scholar 

  5. Z. H. Cho, J. P. Jones, and M. Singh, Foundations of Medical Imaging, John Wiley and Sons, 1993.

    Google Scholar 

  6. D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, Springer-Verlag, 1992.

    Google Scholar 

  7. A. J. Devaney, “Inversion formula for inverse scattering within the Born approximation,” Optical Lett., vol.7, pp. 111–112, 1982.

    Article  ADS  Google Scholar 

  8. A. J. Devaney, “Geophysical diffraction tomography,” IEEE Trans. Geological science, Special Issue on Remote Sensing, vol. 22, pp. 3–13, January 1984.

    Article  ADS  Google Scholar 

  9. A. J. Devaney and M. Oristaglio, “Inversion procedure for inverse scattering within the distorted-wave Born approximation,” Phys. Rev. Lett., vol. 51, pp. 237–240, 1984.

    Article  ADS  Google Scholar 

  10. T. M. Habashy and R. Mittra, “On some inverse methods in electromagnetics,” J. Electromagnetic Waves and Appl., vol. 1, no. 1, pp. 25–58, 1987.

    Article  Google Scholar 

  11. O. S. Haddadin and E. S. Ebbini, “Adaptive Regularizad on of a Distorted Born Iterative Algorithm for Diffraction Tomography,” Int. Conf. Image Processing, pp. 725–728, September 1996.

    Google Scholar 

  12. A. C. Kak and M. Slaney, Principles of Computed Tomographic Imaging, IEEE Press, 1988.

    Google Scholar 

  13. M. Slaney, A. C. Kak, and L. E. Larson, “Limitations of imaging with first order diffraction tomography,” IEEE Trans. Microwave Theory and Tech., vol. 32, no. 8, pp. 860–873, 1984.

    Article  ADS  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer Science+Business Media New York

About this chapter

Cite this chapter

Haddadin, O.S., Ebbini, E.S. (1997). Multiple Frequency Distorted Born Iterative Method for Tomographic Imaging. In: Lees, S., Ferrari, L.A. (eds) Acoustical Imaging. Acoustical Imaging, vol 23. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-8588-0_96

Download citation

  • DOI: https://doi.org/10.1007/978-1-4419-8588-0_96

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-4640-1

  • Online ISBN: 978-1-4419-8588-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics