Evaluation of the Interpolation Errors of Tomographic Projection Models

  • Csaba OlaszEmail author
  • László G. Varga
  • Antal Nagy
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11845)


Tomographic reconstruction algorithms perform reconstruction on a discrete grid, assuming a discrete projection model. However, such discrete assumptions bring artifacts into the reconstructed results, we call interpolation error. We compared eight projection models including the Joseph, Siddon or box-beam-integrated methods for analyzing their interpolation errors. We found that by selecting the proper projection model, one can gain significantly better reconstruction quality.


Tomography Projection Reconstruction Interpolation error 


  1. 1.
  2. 2.
    Matlab r2017b. The MathWorks Inc, Natick, Massachusetts, United StatesGoogle Scholar
  3. 3.
    van Aarle, W., et al.: Fast and flexible x-ray tomography using the astra toolbox. Opt. Express 24(22), 25129–25147 (2016)CrossRefGoogle Scholar
  4. 4.
    Andersen, A., Kak, A.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the art algorithm. Ultrason. Imaging 6(1), 81–94 (1984)CrossRefGoogle Scholar
  5. 5.
    Danielsson, P.E., Magnusson, M., Cvl, S.: Combining fourier and iterative methods in computer tomography: analysis of an iteration scheme. the 2D-case 49 (2004)Google Scholar
  6. 6.
    Flores, L., Vidal, V., Verdu, G.: System matrix analysis for computed tomography imaging. PLoS ONE 10, 1252–1255 (2015)Google Scholar
  7. 7.
    Foi, A., Trimeche, M., Katkovnik, V., Egiazarian, K.: Practical poissonian-gaussian noise modeling and fitting for single-image raw-data. IEEE Trans. Image Process. 17(10), 1737–1754 (2008)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Hahn, K., Schondube, H., Stierstorfer, K., Hornegger, J., Noo, F.: A comparison of linear interpolation models for iterative CT reconstruction. Med. Phys. 43(12), 6455–6473 (2016)CrossRefGoogle Scholar
  9. 9.
    Hanson, K.M., Wecksung, G.W.: Local basis-function approach to computed tomography. Appl. Opt. 24, 4028 (1985)CrossRefGoogle Scholar
  10. 10.
    Haralick, R., Shanmugam, K., Dinstein, I.: Textural features for image classification. IEEE Trans. Syst. Man Cybern. SMC 3(6), 610–621 (1973)CrossRefGoogle Scholar
  11. 11.
    Herman, G.: Fundamentals of Computerized Tomography: Image Reconstruction from Projections, 2nd edn. Springer, London (2009).
  12. 12.
    Joseph, P.: An improved algorithm for reprojecting rays through pixel images. IEEE Trans. Med. Imaging 1(3), 192–196 (1982)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Kak, A., Slaney, M.: Principles of Computerized Tomographic Imaging. IEEE Press, New York (1999)zbMATHGoogle Scholar
  14. 14.
    Shepp, L.A., Logan, B.F.: The fourier reconstruction of a head section. IEEE Trans. Nucl. Sci. 21(3), 21–43 (1974)CrossRefGoogle Scholar
  15. 15.
    Lewitt, R.: Alternatives to voxels for image representation in iterative reconstruction algorithms. Phys. Med. Biol. 37(3), 705–716 (1992)CrossRefGoogle Scholar
  16. 16.
    Man, B.D., Basu, S.: Distance-driven projection and backprojection in three dimensions. Phys. Med. Biol. 49, 2463–2475 (2004)CrossRefGoogle Scholar
  17. 17.
    Siddon, R.: Fast calculation of the exact radiological path for a three-dimensional ct array. Med. Phys. 12, 252–255 (1985)CrossRefGoogle Scholar
  18. 18.
    van der Sluis, A., van der Vorst, H.: SIRT- and CG-type methods for the iterative solution of sparse linear least-squares problems. Linear Algebra Appl. 130, 257–303 (1990)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Wang, Z., Bovik, A., Sheikh, H., Simoncelli, E.: Image quality assessment: from error visibility to structural similarity. IEEE Trans. Image Process. 13(4), 600–612 (2004)CrossRefGoogle Scholar
  20. 20.
    Xu, F., Mueller, K.: A comparative study of popular interpolation and integration methods for use in computed tomography. In: 3rd IEEE International Symposium on Biomedical Imaging: Nano to Macro, vol. 4, pp. 1252–1255 (2006)Google Scholar
  21. 21.
    Yu, Z., Noo, F., Dennerlein, F., Wunderlich, A., Lauritsch, G., Hornegger, J.: Simulation tools for two-dimensional experiments in x-ray computed tomography using the for bild head phantom. Phys. Med. Biol. 57(13), 237–252 (2012)CrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.University of SzegedSzegedHungary

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