Skip to main content
SpringerLink
Log in

Application of the fractional-rational method to problems in linear three-dimensional tomography

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

Abstract

On the basis of the fractional-rational method of finding the solution of an operator equation of first kind that coincides with the pseudo-solution of minimal norm for this equation we construct an algorithm for solving a problem of linear three-dimensional tomography with limited data.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Literature Cited

  1. G. Baker and P. R. Graves-Morris,Padé Approximants, Addison-Wesley, Reading, MA (1981).

    Google Scholar 

  2. A. B. Goncharov, “Integral geometry and the three-dimensional reconstruction of arbitrarily oriented identical particles from electron microphotographs,”Kristallografiya,32, No. 5, 1131–1136 (1987).

    MathSciNet  Google Scholar 

  3. W. Jones and W. Thron,Continued Fractions, Addison-Wesley, Reading, MA (1980)

    Google Scholar 

  4. F. Natterer,Mathematical Aspects of Computer Tomography [Russian translation], Mir, Moscow (1990).

    Google Scholar 

  5. S. S. Orlov, “Theory of three-dimensional reconstruction. I. Conditions for completeness of the set of projections,”Kristallografiya,20, No. 3, 511–515 (1975).

    MathSciNet  Google Scholar 

  6. M. S. Syavavko, T. V. Pasechnik, and O. M. Rybyts'ka, “The pseudo-inverse operator and rational algorithms for normal solution of Fredholm integral equations of first kind,”Elektron. Model.,17, No. 1, 10–16 (1995).

    Google Scholar 

  7. A. I. Tikhonov and V. Ya. Arsenin,Methods of Solving III-posed Problems [in Russian], Nauka, Moscow (1979).

    Google Scholar 

  8. S. R. Deans,The Radon Transform and Some of its Applications, Wiley, New York (1983).

    MATH  Google Scholar 

  9. R. Gordon,Image Processing for 2-D and 3-D Reconstruction from Projections: Theory and Practice in Medicine and the Physical Sciences. Digest of Technical Papers, Stanford, California (1975).

  10. R. B. Marr, “Techniques for three-dimensional reconstruction,” in:Proceedings of an International Workshop, Brookhaven National Laboratory, Upton, New York (1974).

    Google Scholar 

  11. J. G. Rogers, R. Harrop, and P. E. Kindhan, “The theory of three-dimensional image reconstruction for PET,”IEEE Trans. Med. Imag., No. 6, 239–243 (1987).

    Article  Google Scholar 

Download references

Authors
  1. T. V. Pasichnik
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 39, No. 2, 1996, pp. 123-126.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pasichnik, T.V. Application of the fractional-rational method to problems in linear three-dimensional tomography. J Math Sci 90, 2427–2430 (1998). https://doi.org/10.1007/BF02433978

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02433978

Keywords

Search

Navigation