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2008 | 18 | 1 | 63-73
Tytuł artykułu

Interpolation-based reconstruction methods for tomographic imaging in 3D Positron Emission Tomography

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Positron Emission Tomography (PET) is considered a key diagnostic tool in neuroscience, by means of which valuable insight into the metabolism function in vivo may be gained. Due to the underlying physical nature of PET, 3D imaging techniques in terms of a 3D measuring mode are intrinsically demanded to assure satisfying resolutions of the reconstructed images. However, incorporating additional cross-plane measurements, which are specific for the 3D measuring mode, usually imposes an excessive amount of projection data and significantly complicates the reconstruction procedure. For this reason, interpolation-based reconstruction methods deserve a thorough investigation, whose crucial parts are the interpolating processes in the 3D frequency domain. The benefit of such approaches is apparently short reconstruction duration, which can, however, only be achieved at the expense of accepting the inaccuracies associated with the interpolating process. In the present paper, two distinct approaches to the realization of the interpolating procedure are proposed and analyzed. The first one refers to a direct approach based on linear averaging (inverse distance weighting), and the second one refers to an indirect approach based on two-dimensional convolution (gridding method). In particular, attention is paid to two aspects of the gridding method. The first aspect is the choice of the two-dimensional convolution function applied, and the second one is the correct discretization of the underlying continuous convolution. In this respect, the geometrical structure named the Voronoi diagram and its computational construction are considered. At the end, results of performed simulation studies are presented and discussed.
Rocznik
Tom
18
Numer
1
Strony
63-73
Opis fizyczny
Daty
wydano
2008
Twórcy
autor
  • Faculty of Electrical, Information and Media Engineering, University of Wuppertal, Rainer-Gruenter-Street 21, 42119 Wuppertal, Germany
  • Faculty of Electrical, Information and Media Engineering, University of Wuppertal, Rainer-Gruenter-Street 21, 42119 Wuppertal, Germany
  • Faculty of Electrical, Information and Media Engineering, University of Wuppertal, Rainer-Gruenter-Street 21, 42119 Wuppertal, Germany
autor
  • Institute of Medicine, Research Centre Juelich, 52428 Juelich, Germany
Bibliografia
  • Beutel J., Kundel H. L. and Van Metter R. L. (2000). Handbook of Medical Imaging, SPIE Press, Bellingham, Washington.
  • Bendriem B. and Townsend D. W. (1998). The Theory and Practice of 3D PET, Kluwer Academic Publishers, Dordrecht.
  • De Berg M., Van Kreveld M., Overmars M. and Schwarzkopf O. (1997). Computational Geometry, Springer-Verlag, Berlin.
  • Fisher N. I. and Embleton B.J. (1987). Statistical Analysis of Spherical Data, Cambridge University Press, Cambridge.
  • Fortune S. (1987). A SWEEPLINE algorithm for Voronoi diagrams, Algorithmica 2(2): 153-174.
  • Jackson J. I., Meyer C. H., Nishimura D.G. and Macovski A. (1991). Selection of a convolution function for Fourier inversion using gridding, IEEE Transactions on Medical Imaging 10(3): 473-478.
  • Kak A. C. and Slaney M. (1988). Principles of Computerized Tomographic Imaging, New York, IEEE Press.
  • Li Y., Kummert A., Boschen F. and H. Herzog (2005). Investigation on projection signals in 3D PET systems, Proceedings of the 12th International Conference on Biomedical Engineering, Singapore.
  • Li Y., Kummert A., Boschen F. and H. Herzog (2005). Spectral properties of projection signals in 3-D tomography, Proceedings of the 16th Triennial World Congress of the International Federation of Automatic Control, Prague, Czech Republic.
  • Li Y., Kummert A. and Herzog H. (2006). Direct Fourier method in 3D PET using accurately determined frequency sample distribution, Proceedings of the 28th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, New York, USA.
  • Li Y., Kummert A., Li H. and Herzog H. (2006). Evaluation of the direct Fourier method for 3D-PET in the case of accurately determined projection data, Proceedings of the 11th IASTED International Conference on Signal and Image Processing, Honolulu, USA.
  • Matej S. and Lewitt R. M. (2001). 3D-FRP: Direct Fourier reconstruction with Fourier reprojection for fully 3-D PET, IEEE Transactions on Medical Imaging 48(4): 1378-1385.
  • Moon T.K. (1996). The expectation-maximization algorithm, IEEE Signal Processing Magazine 13(6): 47-60.
  • Schomberg H. and Timmer J. (1995). The gridding method for image reconstruction by Fourier transformation, IEEE Transactions on Medical Imaging 14(3): 596-607.
  • Thevenaz P., Blu T. and Unser M. (2000). Interpolation revisited, IEEE Transactions on Medical Imaging 19(7): 739-758.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-amcv18i1p63bwm
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