Skip to main content
Log in

Projection data replenishment algorithm for limited angle tomography

  • Analysis and Synthesis of Signals and Images
  • Published:
Optoelectronics, Instrumentation and Data Processing Aims and scope

Abstract

A new iterative algorithm of tomographic reconstruction of objects on the basis of projection data available in a limited range of angles only is proposed. The algorithm is based on calculating artificial projections in those directions where projection data are unavailable. By means of numerical simulations, it is verified that the algorithm developed ensured high quality of reconstruction up to the angular interval of 45–60°.

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

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. G. T. Hermen, Image Reconstruction from Projections. The Fundamentals of Computerized Tomography (Academic Press, New York, 1980).

    Google Scholar 

  2. H. H. Barrett and W. Swindell, Radiological Imaging: The Theory of Image Formation, Detection and Processing (Academic Press, New York, 1981).

    Google Scholar 

  3. F. Natterer, The Mathematics of Computerized Tomography (John Wiley and Sons, Chichester, 1986).

    MATH  Google Scholar 

  4. M. M. Lavrent’ev, S. M. Zerkal, and O. E. Trofimov, Computer Modeling in Tomography and Ill-Posed Problems (IDMI NGU, Novosibirsk, 1999; VSP, Utrecht, the Netherlands, 2001).

    Google Scholar 

  5. L. A. Shepp and B. F. Logan, “The Fourier Reconstruction of a Head Section,” IEEE Trans. Nucl. Sci. 21(3), 21–43 (1974).

    Google Scholar 

  6. A. V. Likhachov, “Investigating of 1/z 2 Filtering in Tomography Algorithms,” Avtometriya 43(3), 57–64 (2007) [Optoelectr., Instrum. Data Process. 43 (3), 239–245 (2007)].

    Google Scholar 

  7. A. V. Likhachov, “Regularizing Filtration of Projections in Algorithms of Two-Dimensional Tomography,” Sib. Zh. Vychisl. Mat. 11(2), 187–200 (2008).

    Google Scholar 

  8. B. Redmer, F. Weise, U. Ewert, and A. Likhatchev, “Location of Reinforcement in Structures by Different Methods of Gamma-Radiography,” in Proc. of the Int. Symp. Non-Destructive Testing in Civil Engineering (BAM, Berlin, 2003), Vol. 020, pp. 1–6.

    Google Scholar 

  9. B. Redmer, U. Ewert, Ch. Radel, et al., “Planar Tomography under Limited View Conditions for Crack Detection in Austenitic Welds,” in Proc. of the 2nd Workshop “NDT in Progress,” Int. Meeting of NDT Experts (Brno Univ. Technol, Brno, 2003), p. 321.

    Google Scholar 

  10. A. V. Likhachov and V. V. Pickalov, “New Method of Determining Unknown Additive Background in Projection Data in the Problem of Three-Dimensional Tomography,” Zh. Vychisl. Mat. Mat. Fiz. 42(3), 85–97 (2002).

    Google Scholar 

  11. V. V. Pickalov and N. G. Preobrazhenskii, Reconstructive Tomography in Gas Dynamics and Plasma Physics (Nauka, Novosibirsk, 1987) [in Russian].

    Google Scholar 

  12. A. V. Likhachov and V. V. Pickalov, “Three-Dimensional Tomography in Gas Flow Diagnostics in the Presence of an Opaque Body,” J. Appl. Mech. Tech. Phys. 39(1), 152–158 (1998).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. V. Likhachov.

Additional information

Original Russian Text © A.V. Likhachov, 2009, published in Avtometriya, 2009, Vol. 45, No. 1, pp. 83–91.

About this article

Cite this article

Likhachov, A.V. Projection data replenishment algorithm for limited angle tomography. Optoelectron.Instrument.Proc. 45, 55–61 (2009). https://doi.org/10.1134/S8756699009010099

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S8756699009010099

Key words

Navigation