Advertisement

Model-Based Approach to Tomographic Reconstruction Including Projection Deblurring. Sensitivity of Parameter Model to Noise on Data

  • Jean Michel Lagrange
  • Isabelle Abraham
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3024)

Abstract

Classical techniques for the reconstruction of axisymmetrical objects are all creating artefacts (smooth or unstable solutions). Moreover, the extraction of very precise features related to big density transitions remains quite delicate. In this paper, we develop a new approach -in one dimension for the moment- that allows us both to reconstruct and to extract characteristics: an a priori is provided thanks to a density model. We show the interest of this method in regard to noise effects quantification ; we also explain how to take into account some physical perturbations occuring with real data acquisition.

Keywords

tomography flexible models regularization deblurring 

References

  1. 1.
    Abel, N.H.: Résolution d’un probième de mécanique. J. Reine u. Angew. Math. 1, 153–157 (1826)Google Scholar
  2. 2.
    Besag, J.: On the statistical analysis of dirty pictures. J.R. Static. Soc. Ser. B 48(3), 259–279 (1986)zbMATHMathSciNetGoogle Scholar
  3. 3.
    Bracewell, R.: The fourier transform and its applications. deuxième. Mc Graw-Hill, New York (1978)zbMATHGoogle Scholar
  4. 4.
    Culioli, J.C., Charpentier, P.: cours de l’école nationale des Mines de Paris. optimisation libre en dimension finie, vol. II (1990)Google Scholar
  5. 5.
    Deutsch, M., Beniaminy, I.: Derivative free inversion of abel’s integral equation. Applied Physics Letters 41(1) (July 1982)Google Scholar
  6. 6.
    Dieudonne, J.: Eléments d’analyse, vol. 3. Gauthier-Villars (1982)Google Scholar
  7. 7.
    Dinten, J.M.: Tomographic à partir d’un nombré limite de projections: régularisation par des champs markoviens. PhD thesis, Université de Paris Sud, centre d’Orsay (1990)Google Scholar
  8. 8.
    Djafari, A.M.: Image reconstruction of a compact object from a few number of projections. In: IASTED SIP 1996, Floride (November 1996)Google Scholar
  9. 9.
    Djafari, A.M.: Slope reconstruction in X-ray tomography. In: Processing of SPIE 1997, San Diego (July 1997)Google Scholar
  10. 10.
    Dusaussoy, N.J.: Image reconstruction from projections. In: SPIE’s international symposium on optics, imaging and instrumentation, San Diego (July 1994)Google Scholar
  11. 11.
    Fugelso, E.: Material density measurement from dynamic flash X-ray photographs using axisymmetric tomography, March 1981. Los Alamos Publication (1981)Google Scholar
  12. 12.
    Geman, S., Geman, D.: Stochastic relaxation, Gibbs distribution, and the bayesian restoration of images. Transactions on pattern analysis and machine intelligence PAMI 6(6), 721–741 (1994)CrossRefGoogle Scholar
  13. 13.
    Hadamard, J.: Sur les problèmes aux dérivées partielles et leur signification physique. Princetown University, Bulletin (1902)Google Scholar
  14. 14.
    Hanson, K.M.: Tomographic reconstruction of axially symmetric objects from a single radiograph. In: Proceedings of the 16th International congress on high speed photography and photonics, Strasbourg, Août (1984)Google Scholar
  15. 15.
    Hanson, K.M., Cunningham, G.S., Jennings, G.R., Wolf, D.R.: Tomographic reconstruction based on flexible geometric models. In: Proceedings of the IEEE international conference on image processing, Austin, Texas (November 1994)Google Scholar
  16. 16.
    Herman, G.T.: Image reconstruction from projections, the fundamentals of computerized tomography. Academic Press, London (1980)zbMATHGoogle Scholar
  17. 17.
    Kain, A.J.: Fundamentals of digital signal processing. International edn. Prentice Hall, Englewood CliffsGoogle Scholar
  18. 18.
    Lagrange, J.M.: Reconstruction tomographique à partir d’un petit nombre de vues. PhD thesis, Ecole Normale Superieure de Cachan (1998)Google Scholar
  19. 19.
    Maître, H., Pellot, C., Herment, A., Sigelle, M., Horain, P., Peronneau, P.: A 3D reconstruction of vascular structures from two X-rays angiograms using an adapted simulated annealing algorithm. IEEE transactions on medical imaging 13(1) (March 1994)Google Scholar
  20. 20.
    Pellot, C., Herment, A., Sigelle, M., Horain, P., Peronneau, P.: Segmentation, modelling and reconstruction of arterial bifurcations in digital angiography. Medical and biological engeeneering and computing (November 1992)Google Scholar
  21. 21.
    Powell, M.J.D., Yuan, Y.: A recursive quadratic programming algorithm that uses differentiable exact penalty functions. Mathematical programming 35, 265–278 (1986)zbMATHCrossRefMathSciNetGoogle Scholar
  22. 22.
    Schittkowski, K.: Solving non linear problems with very many constraints. Optimization 25, 179–196 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  23. 23.
    Senasli, M., Garnero, L., Herment, A., Pellot, C.: Stochastic active contour model for 3D reconstruction from two X-ray projections. In: 1995 international meeting on fully 3D image reconstruction in radiology and nuclear medecine, Grenoble (July 1995)Google Scholar
  24. 24.
    Tikhonov, A., Arsenin, V.: Solutions off il-posed problems. Winston, Washington (1977)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Jean Michel Lagrange
    • 1
  • Isabelle Abraham
    • 1
  1. 1.Commissariat à l’Energie Atomique, B.P. 12Bruyères le ChatelFrance

Personalised recommendations