Analysis of stability of tomographic reconstruction of x-ray medical images

  • L. A. Bulavin Taras Shevchenko National University of Kyiv, 2 A Glushkova Ave., Kyiv, Ukraine
  • Y. F. Zabashta Taras Shevchenko National University of Kyiv, 2 A Glushkova Ave., Kyiv, Ukraine
  • O. V. Motolyha Taras Shevchenko National University of Kyiv, 2 A Glushkova Ave., Kyiv, Ukraine https://orcid.org/0000-0001-5386-2737
  • S. P. Senchurov Taras Shevchenko National University of Kyiv, 2 A Glushkova Ave., Kyiv, Ukraine https://orcid.org/0000-0001-7404-862X
Keywords: X-ray computed tomography, inverse projection method, variational method

Abstract

Slice reconstruction in X-ray computed tomography is reduced to the solution of integral equations, or a system of algebraic equations in discrete case. It is considered to be an ill-posed problem due to the inconsistencies in the number of equations and variables and due to errors in the experimental data. Therefore, determination of the best method of the slice reconstruction is of great interest. Furthermore, all available methods give approximate results. The aim of this article was two-fold: i) to compare two methods of image reconstruction, viz. inverse projection and variation, using the numerical experiment; ii) to obtain the relationship between image accuracy and experimental error. It appeared that the image obtained by inverse projection is unstable: there was no convergence of the approximate image to the accurate one, when the experimental error reached zero. In turn, the image obtained by variational method was accurate at zero experimental error. Finally, the latter showed better slice reconstruction, despite the low number of projections and the experimental errors.

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Author Biographies

L. A. Bulavin, Taras Shevchenko National University of Kyiv, 2 A Glushkova Ave., Kyiv, Ukraine

Доктор фізико-математичних наук, професор. Академік НАН України. Академік АН ВШ України

Y. F. Zabashta, Taras Shevchenko National University of Kyiv, 2 A Glushkova Ave., Kyiv, Ukraine

Доктор фізико-математичних наук, професор кафедри молекулярної фізики, фізичного факультету

O. V. Motolyha, Taras Shevchenko National University of Kyiv, 2 A Glushkova Ave., Kyiv, Ukraine

аспірант кафедри молекулярної фізики, фізичного факультету

S. P. Senchurov, Taras Shevchenko National University of Kyiv, 2 A Glushkova Ave., Kyiv, Ukraine

Кандидат фізико-математичних наук, доцент кафедри молекулярної фізики фізичного факультету

References

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4. Herman GT. Fundamentals of computerized tomography: Image reconstruction from projection, 2nd edition. London : Springer; 2009. 300 p.

5. Shepp L, Logan B. The Fourier Reconstruction of a Head Section. IEEE Transactions on Nuclear Science. 1974;NS-21:21-43
Published
2017-09-11
Cited
How to Cite
Bulavin, L. A., Zabashta, Y. F., Motolyha, O. V., & Senchurov, S. P. (2017). Analysis of stability of tomographic reconstruction of x-ray medical images. Biophysical Bulletin, 1(37), 9-15. https://doi.org/10.26565/2075-3810-2017-37-02
Section
Medical physics