Advertisement

Algorithms for Image Reconstruction

  • Christoph Hoeschen
  • Magdalena Rafecas
  • Timo Aspelmeier
Chapter
  • 1.7k Downloads

Abstract

Three-dimensional (3D) imaging is becoming one of the most important applications of radioactive materials in medicine. It offers good spatial resolution, a 3D insight into the human body, and a high sensitivity in the picomolar range because markers for biological processes can be detected well when labeled with radioactive materials. In addition, the technical equipment has undergone many technological achievements. This is true for single-photon emission computed tomography (SPECT), positron emission tomography (PET), and X-ray computed tomography (CT), which is often used in connection with the nuclear medical imaging systems, as also described in chapter 5 about sources in nuclear medicine. As can be realized by the names of the systems, the imaging methodologies all generate the images using a computational process. This is necessary since in all types of CT the purpose is to generate a stack of two-dimensional slices (a 3D data set) that are reconstructed from various “projections” along certain lines. This reconstruction process can be achieved by various different methods, which can be divided into so-called algebraic or iterative reconstruction methods and analytical methods. After a brief introduction to give an approach to the reconstruction task in general, we describe both kinds of algorithms.

Keywords

Positron Emission Tomography Iterative Reconstruction Technique Unknown Image Iterative Reconstruction Method Exact Inversion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Radon J.H. Über die Bestimmung von Funktionen durch ihre Integralwerte längs gewisser Mannigfaltigkeiten. Akad. Wiss. 69, 262–277 (1917).Google Scholar
  2. 2.
    Gaskill, J.D. Linear Systems, Fourier Transforms, and Optics. Wiley, New York. ISBN 0-471-29288-5 (1978).Google Scholar
  3. 3.
    Hsieh, J. Computed Tomography: Principles, Design, Artifacts and Recent Advances. SPIE Press, Bellingham. ISBN 0-8194-4425-1 (2003).Google Scholar
  4. 4.
    Natterer, F. and Wübbeling, F. Mathematical Methods in Image Reconstruction. Society for Industrial and Applied Mathematics, Philadelphia, PA. ISBN 0-89871-472-9 (2001).Google Scholar
  5. 5.
    Xu, Y., Tischenko, O. and Hoeschen, C. Approximation and reconstruction from attenuated Radon projections. SIAM J. Numer. Anal. 45 (1), 108–132 (2007).CrossRefGoogle Scholar
  6. 6.
    Barret, H.H. and Myers, K.J. Foundations of Image Science. Wiley, Hoboken. ISBN 0 471 15300 1 (2004)Google Scholar
  7. 7.
    Bruyant, Ph.P. Analytic and iterative reconstruction algorithms in SPECT. J. Nucl. Med. 43, 1343–1358 (2002).PubMedGoogle Scholar
  8. 8.
    Defrise, M., Kinahan, P.E. and Michel, Ch. J. Image reconstruction algorithms in PET. In: Bailey, D.L., Townsend, D.W., Valk, P.E., and Maisey, M.N., editors. Positron Emission Tomography: Basic Sciences. Springer, London. ISBN 1 852337982 (2005).Google Scholar
  9. 9.
    Hutton, B.F., Nuyts, J. and Zaidi, H. Iterative reconstruction methods. In: Zaidi, H., editor. Quantitative Analysis in Nuclear Medicine. Springer Science + Business Media, New York. ISBN 0 38 238549 (2006).Google Scholar
  10. 10.
    Leahy, R.M. and Qi, J. Statistical approaches in quantitative positron emission tomography. Statis. Comput. 10, 147–165 (2000)CrossRefGoogle Scholar
  11. 11.
    Lewitt, R.M. and Matej, S. Overview of methods for image reconstruction from projections in emission computed tomography. Proc. IEEE 91, 1588–1611 (2003).CrossRefGoogle Scholar
  12. 12.
    Qi, J. and Leahy, R.M. Iterative reconstruction techniques in emission computed tomography. Phys. Med. Biol. 51, R541–R578 (2006)CrossRefPubMedGoogle Scholar
  13. 13.
    Wernick, M.N. and Lalush, D.S. Iterative image reconstruction. In: Wernick, M.N. and Aarsvold, J.N., editors. Emission Tomography: The Fundamentals of PET and SPECT. Elsevier Academic Press, London. ISBN 0 12 744482 3 (2004).Google Scholar
  14. 14.
    Fessler, J. Penalized weighted least-squares image-reconstruction for positron emission tomography. IEEE Trans. Med. Imaging. 13, 209–300 (1994).CrossRefGoogle Scholar
  15. 15.
    Herman, G.T. Image Reconstruction from Projections: The Fundamentals of Computerized Tomography. Springer, New York. ISBN 978-1-85233-617-2 (2009).Google Scholar
  16. 16.
    Matej, S. and Lewitt, R.M. Practical considerations for 3-D image reconstruction using spherically symmetric volume elements. IEEE Trans. Med. Imaging. 15, 68–78 (1996).CrossRefPubMedGoogle Scholar
  17. 17.
    Buonocore, M.H., Brody, W.R. and Macovski, A. A natural pixel decomposition for two-dimensional image reconstruction. IEEE Trans. Biomed. Eng. BME–28, 69–78 (1981).Google Scholar
  18. 18.
    Herbert, T, Leahy, R. and Singh, M. Fast MLE for SPECT using an intermediate polar representation and a stopping criterion. IEEE Trans. Nucl. Sci. 35, 615–619 (1988).Google Scholar
  19. 19.
    Siddon, R.L. Fast calculation of the exact radiological path for a three-dimensional CT array. Med. Phys. 12, 252–255 (1985).CrossRefPubMedGoogle Scholar
  20. 20.
    Rafecas, M., Mosler, B., Dietz, M., Pögl, M., Stamatakis, S., McElroy, D.P. and Ziegler, S.I. Use of a Monte–Carlo based probability matrix for 3D reconstruction of MADPET–II data. IEEE Trans. Nucl. Sci. 51, 2597–2605 (2004).CrossRefGoogle Scholar
  21. 21.
    Panin, V.Y., Kehren, F., Michel, C., and Casey, M. Fully 3-D PET reconstruction with system matrix derived from point source measurements. IEEE Trans. Med. Imaging. 25, 907–921 (2006).CrossRefPubMedGoogle Scholar
  22. 22.
    Lange, K. and Carson, R. EM reconstruction algorithms for emission and transmission tomography. J. Comput. Assist. Tomogr. 8, 306–316 (1984).PubMedGoogle Scholar
  23. 23.
    Shepp, L.A. and Vardi, Y. Maximum likelihood reconstruction for emission tomography. IEEE Trans. Med. Imaging. 1, 113–122 (1982).CrossRefPubMedGoogle Scholar
  24. 24.
    Hudson, H.M. and Larkin, R.S. Accelerated image reconstruction using ordered subsets of projection data. IEEE Trans. Med. Imag. 13, 601–609 (1994).CrossRefGoogle Scholar
  25. 25.
    Yavuz, M. and Fessler, J.A. Statistical image reconstruction methods for randoms-precorrected PET scans. Med. Image Anal. 2, 369–378 (1998).CrossRefPubMedGoogle Scholar
  26. 26.
    Huesman, R.H., Gullberg, G.T., Greenberg, W.L., and Budinger, T.F. Users manual – Donner algorithms for reconstruction tomography. Publication PUB-214, Lawrence Berkeley Laboratory, Berkeley, (1977).Google Scholar

Copyright information

© Springer Berlin Heidelberg 2011

Authors and Affiliations

  • Christoph Hoeschen
    • 1
  • Magdalena Rafecas
    • 2
  • Timo Aspelmeier
    • 3
  1. 1.Helmholtz Zentrum München, German Research Center for Environmental Health GmbHNeuherbergGermany
  2. 2.IFIC Instituto de Física Corpuscula CSIC-Universitat de València, Edificio Institutos, de InvestigaciónValenciaSpain
  3. 3.Scivis wissenschaftliche Bildverarbeitung GmbHGöttingenGermany

Personalised recommendations