대한의용생체공학회:의공학회지 (Journal of Biomedical Engineering Research)

  • 제28권4호
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  • Pages.520-529
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  • 2007
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  • 1229-0807(pISSN)
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  • 2288-9396(eISSN)
대한의용생체공학회 (The Korean Society of Medical and Biological Engineering)
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컴프턴 카메라 영상재구성을 위한 타원 누적법

Ellipse-Stacking Methods for Image Reconstruction in Compton Cameras

  • 이미노 (배재대학교 전자공학과) ;
  • 이수진 (배재대학교 전자공학과) ;
  • 김수미 (서울대학교 의과대학 핵의학교실 및 방사선응용생명과학 협동과정) ;
  • 이재성 (서울대학교 의과대학 핵의학교실 및 방사선응용생명과학 협동과정)
  • Lee, Mi-No (Department of Electronic Engineering, Paichai University) ;
  • Lee, Soo-Jin (Department of Electronic Engineering, Paichai University) ;
  • Kim, Soo-Mee (Department of Nuclear Medicine and Interdisciplinary Program in Radiation Applied Life Science Major, Seoul National University College of Medicine) ;
  • Lee, Jae-Sung (Department of Nuclear Medicine and Interdisciplinary Program in Radiation Applied Life Science Major, Seoul National University College of Medicine)
  • 발행 : 2007.08.30
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초록

An efficient method for implementing image reconstruction algorithms for Compton cameras is presented. Since Compton scattering formula establishes a cone surface from which the incident photon must have originated, it is crucial to implement a computationally efficient cone-surface integration method for image reconstruction. In this paper we assume that a cone is made up of a series of ellipses (or circles) stacked up one on top of the other. In order to reduce computational burden for tracing ellipses formed by the intersection of a cone and an image plane, we propose a new method using a series of imaginary planes perpendicular to the cone axis so that each plane contains a circle, not an ellipse. In this case the cone surface integral can be performed by simply accumulating the circles along the cone axis. To reduce the computational cost of tracing circles, only one of the circles in the cone is traced and the rest are determined by using simple trigonometric ratios. For our experiments, we used the three different schemes for tracing ellipses; (i) using the samples generated by the ellipse equation, (ii) using the fixed number of samples along a circle on the imaginary plane, and (iii) using the fixed sampling interval along a circle on the imaginary plane. We then compared performance of the above three methods by applying them to the two reconstruction algorithms - the simple back-projection method and the expectation-maximization algorithm. The experimental results demonstrate that our proposed methods (ii) and (iii) using imaginary planes significantly improve reconstruction accuracy as well as computational efficiency.

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참고문헌

  1. R. J. Jaszczak, 'Tomographic radiopharmaceutical imaging,' in Proc. the IEEE, Sep. 1988, 76, pp. 1079-1094
  2. J. T Bushberg, J. A. Seibert, E. M. Leidholdt, J. M. Boone, The Essential Physics of Medical Imaging, Philadelphia, P A, Lippincott Williams & Wilkins, 2002
  3. S. R. Cherry, J. A. Sorenson, M. Phelps, Physics in nuclear medicine, Philadelphia, PA, Saunders, 2003
  4. Y.F. Yang, Y. Gono, S. Motomura, S. Enomoto, and Y. Yano, 'A compton camera for multi-tracer imaging,' IEEE Trans. Nucl. Sci., vol. 48, pp. 656-661, 2001 https://doi.org/10.1109/23.940142
  5. S. Motomura, H. Takeici, R. Hirunuma, H. Haba, K. Igarashi, S. Enomoto, Y. Gono, Y. Yano, 'Gamma-ray Compton imaging of multitracer in bio-samples by strip germanium telescope,' IEEE Nuclear Science Symposium and Medical Imaging Conference Record, Rome, Italy, Oct. 2004, vol. 4, pp. 2152-2154
  6. R. W. Todd, J. M. Nightingale, and D. B. Everett, 'A proposed Gamma camera,' Nature, 251, pp. 132-134, 1974 https://doi.org/10.1038/251132a0
  7. R. Basko, G. L. Zeng, and G. T. Gullberg, 'Application of spherical harmonics to image reconstruction for the Compton camera,' Phys. Med. Biol, vol. 43, pp. 887-894, 1998 https://doi.org/10.1088/0031-9155/43/4/016
  8. L. C. Parra, 'Reconstruction of cone-beam projections from Compton scattered data,' IEEE Trans. Nucl. Sci., vol. 47, pp. 1543-1550, 2000 https://doi.org/10.1109/23.873014
  9. T. Tomitani and M. Hirasawa, 'Image reconstruction from limited angle Compton camera data,' Phys, Med. Biol., vol. 47, pp.1009-1026, 2002
  10. M. Hirasawa and T. Tomitani, 'An analytical image reconstruction algorithm to compensate for scattering angle broadening in Compton cameras,' Phys. Med. biol., vol. 48, pp. 1009-1026, 2003 https://doi.org/10.1088/0031-9155/48/8/304
  11. B. Smith, 'Reconstruction methods and completeness conditions for two Compton data models,' J. Opt. Soc. Am. A, vol. 22, no. 3, pp. 445-459, 2005 https://doi.org/10.1364/JOSAA.22.000445
  12. D. Xu, Z. He, 'Filtered back-projection in $4{\pi}$ Compton imaging with a single 3D position sensitive CdZnTe detector,' IEEE Trans. Nucl. Sci., vol 53, no. 5, pp. 2787-2793, 2006 https://doi.org/10.1109/TNS.2006.880974
  13. T. Hebert, R. Leahy, and M. Singh, 'Three-dimensional maximum-likelihood reconstructin for a electronically collimated single-photon-emission imaging system,' J. Opt. Soc. Am., A7, pp. 1305-1313, 1990
  14. A. C. Sauve, A. O. Hero III, W. L. Rogers, S. J. Wilderman, and N. H. Clinthome, '3D image reconstruction for Compton SPECT camera model,' IEEE Trans. Nucl. Sci., vol. 46, pp. 2075-2084, 1999 https://doi.org/10.1109/23.819285
  15. A. H. Compton, 'A quantum theory of the scattering of x-rays by light elements,' Phys. Rev., vol. 21, pp. 483-502, 1923 https://doi.org/10.1103/PhysRev.21.483
  16. S. M. Kim, J. S. Lee, M. N. Lee, J. H. Lee, C. S. Lee, C. H. Kim, D. S. Lee, S. J. Lee, 'Two approaches to implementing projector-backprojector pairs for 3D reconstruction from Compton scattered data,' Nuclear Instruments & Methods in Physics Research A, vol. 571, pp. 255-258, 2007 https://doi.org/10.1016/j.nima.2006.10.076
  17. R. Siddon, 'Fast calculation of the exact radiological path for a 3D CT array,' Med. Phys., vol. 12, pp. 252-255, 1985 https://doi.org/10.1118/1.595715
  18. L. A. Shepp and Y. Vardi, 'Maximum likelihood reconstruction for emission tomography,' IEEE Trans. Med. Imaging, vol. 1 , pp. 113-122, 1982 https://doi.org/10.1109/TMI.1982.4307558
  19. K. Lange and R. Carson, 'EM reconstruction algoritluns for emission and transmission tomography,' J. Comput. Assist. Tomog., vol. 8, pp. 306-316, 1984
  20. J. M. Ollinger and J. A. Fessler, 'Positron emission tomography,' IEEE Signal Processing Magazine, pp. 43-55, Jan. 1997
  21. R. M. Lewitt and S. Matej, 'Overview of methods for image reconstruction from projections in emission computed tomography,' in Proc. the IEEE, 2003, 91(10), pp. 1588-1611