Journal of Biomedical Engineering Research (대한의용생체공학회:의공학회지)

The Korean Society of Medical and Biological Engineering (대한의용생체공학회)
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Three-Dimensional Image Reconstruction from Compton Scattered Data Using the Row-Action Maximum Likelihood Algorithm

행작용 최대우도 알고리즘을 사용한 컴프턴 산란 데이터로부터의 3차원 영상재구성

  • Lee, Mi-No (Department of Electronic Engineering, Paichai University) ;
  • Lee, Soo-Jin (Department of Electronic Engineering, Paichai University) ;
  • Nguyen, Van-Giang (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)
  • 이미노 (배재대학교 전자공학과) ;
  • 이수진 (배재대학교 전자공학과) ;
  • ;
  • 김수미 (서울대학교 의과대학 핵의학교실 및 방사선응용생명과학 협동과정) ;
  • 이재성 (서울대학교 의과대학 핵의학교실 및 방사선응용생명과학 협동과정)
  • Published : 2009.02.28
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Abstract

Compton imaging is often recognized as a potentially more valuable 3-D technique in nuclear medicine than conventional emission tomography. Due to inherent computational limitations, however, it has been of a difficult problem to reconstruct images with good accuracy. In this work we show that the row-action maximum likelihood algorithm (RAMLA), which have proven useful for conventional tomographic reconstruction, can also be applied to the problem of 3-D reconstruction of cone-beam projections from Compton scattered data. The major advantage of RAMLA is that it converges to a true maximum likelihood solution at an order of magnitude faster than the standard expectation maximiation (EM) algorithm. For our simulations, we first model a Compton camera system consisting of the three pairs of scatterer and absorber detectors placed at x-, y- and z-axes, and generate conical projection data using a software phantom. We then compare the quantitative performance of RAMLA and EM reconstructions in terms of the percentage error. The net conclusion based on our experimental results is that the RAMLA applied to Compton camera reconstruction significantly outperforms the EM algorithm in convergence rate; while computational costs of one iteration of RAMLA and EM are about the same, one iteration of RAMLA performs as well as 128 iterations of EM.

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References

  1. M. Singh, 'An electronically collimated gamma camera for single photon emission computed tomography: Part1 and 2', Med. Phys., vol. 10, no. 4, pp. 421-427, 1983 https://doi.org/10.1118/1.595313
  2. 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
  3. 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, vol. 4, pp. 2152-2154, 2004
  4. R. W. Todd, J. M. Nightingale, and D. B. Everett, 'A proposed Gamma camera', Nature, vol. 251, pp. 132-134, 1974 https://doi.org/10.1038/251132a0
  5. 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
  6. 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
  7. T. Tomitani and M. Hirasawa, 'Image reconstruction from limited angle Compton camera data', Phys, Med. Biol., vol. 47, pp. 1009-1026, 2002
  8. M. Hirasawa and T. Tomitani, 'An analytical image reconstruction algorithm to compensate for scattering angle broadening in Compton cameras', Phys. Med. biol., vol. 48, 1009-1026, 2003 https://doi.org/10.1088/0031-9155/48/8/304
  9. 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
  10. 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
  11. 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 https://doi.org/10.1364/JOSAA.7.001305
  12. A. C. Sauve, A. O. Hero , W. L. Rogers, S. J. Wilderman, and N. H. Clinthorne, '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
  13. L. A. Shepp and Y. Vardi, 'Maximum likelihod reconstruction for emission tomography', IEEE Trans. Med. Imaging, vol. 1, pp. 113-122, 1982 https://doi.org/10.1109/TMI.1982.4307558
  14. K. Lange and R. Carson, 'EM reconstruction algorithms for emission and transmission tomography', J. Comput. Assist. Tomog., vol. 8, pp. 306-316, 1984
  15. J. Browne and A. D. Pierro. 'A Row-Action Alternative to The EM Algorithm for Maximizing Likelihoods in Emission Tomography,' IEEE Trans. Med. Imaging, vol. 15, pp. 687-699, 1996 https://doi.org/10.1109/42.538946
  16. O. Klein and Y. Nishina, 'Experimental Study of the Compton Effect at 1.2 Mev', Phys. Rev., vol. 76, pp. 1269-1270, 1949 https://doi.org/10.1103/PhysRev.76.1269
  17. 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 projectorbackprojector 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
  18. M. N. Lee, S. -J. Lee, S. M. Kim, J. S. Lee, 'Ellipse-Stacking Methods for Image Reconstruction in Compton Cameras', J. Biomed. Eng. Res. vol. 28, no. 4, pp. 520-529, 2007
  19. Siddon R. L., 'Fast calculation of the exact radiological path for a three-dimensional CT array,' Med. Phys., vol. 12, pp. 252-255, 1985 https://doi.org/10.1118/1.595715
  20. A. Rosenfeld and A. C. Kak, Digital Picture Processing, volume 1, Academic Press, New York, NY, 1982
  21. G. T. Herman and L. B. Meyer, 'Algebraic reconstruction techniques can be made computationally efficient ' IEEE Trans. Med. Imaging, vol. 12, pp. 600-609, 1993 https://doi.org/10.1109/42.241889
  22. H. M. Hudson and R. S. Larkin, 'Accelerated image reconstruction using ordered subsets of projection data', IEEE Trans. Med. Imaging, vol. 13, pp. 601-609, 1994 https://doi.org/10.1109/42.363108
  23. E. Tanaka and H. Kudo 'Subset-dependent relaxation on blockiterative algorithms for image reconstruction in emission tomography', Phys. Med. biol., vol. 48, pp. 1405-1422, 2003 https://doi.org/10.1088/0031-9155/48/10/312
  24. A. Fukano, T. Nakayama and H. Kudo 'Performance evaluation of relaxed block-iterative algorithms for 3-D PET reconstruction', IEEE Nuclear Science Symposium Conference and Medical Imaging Conference Record, vol. 5, pp. 2830-2834, 2004
  25. A. D. Pierro and M. E. B. Yamagishi, 'Fast EM-like methods for maximum 'A Posteriori' estimates in Emission tomography', IEEE Trans. Med. Imaging, vol. 20, no. 4, pp. 280-288, 2001 https://doi.org/10.1109/42.921477