Browse > Article
http://dx.doi.org/10.9718/JBER.2009.30.1.056

Three-Dimensional Image Reconstruction from Compton Scattered Data Using the Row-Action Maximum Likelihood Algorithm  

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)
Publication Information
Journal of Biomedical Engineering Research / v.30, no.1, 2009 , pp. 56-65 More about this Journal
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.
Keywords
Compton camera; emission tomography; statistical image reconstruction; maximum likelihood estimation; maximum a posteriori estimation;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
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   DOI   ScienceOn
2 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
3 L. C. Parra, 'Reconstruction of cone-beam projections from Compton scattered data', IEEE Trans. Nucl. Sci., vol. 47, pp. 1543-1550, 2000   DOI   ScienceOn
4 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   DOI
5 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   DOI   ScienceOn
6 T. Tomitani and M. Hirasawa, 'Image reconstruction from limited angle Compton camera data', Phys, Med. Biol., vol. 47, pp. 1009-1026, 2002
7 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   DOI   ScienceOn
8 K. Lange and R. Carson, 'EM reconstruction algorithms for emission and transmission tomography', J. Comput. Assist. Tomog., vol. 8, pp. 306-316, 1984   ScienceOn
9 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   DOI   ScienceOn
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   DOI   ScienceOn
11 O. Klein and Y. Nishina, 'Experimental Study of the Compton Effect at 1.2 Mev', Phys. Rev., vol. 76, pp. 1269-1270, 1949   DOI
12 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   DOI   ScienceOn
13 R. W. Todd, J. M. Nightingale, and D. B. Everett, 'A proposed Gamma camera', Nature, vol. 251, pp. 132-134, 1974   DOI
14 L. A. Shepp and Y. Vardi, 'Maximum likelihod reconstruction for emission tomography', IEEE Trans. Med. Imaging, vol. 1, pp. 113-122, 1982   DOI   ScienceOn
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   DOI   ScienceOn
16 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   DOI   ScienceOn
17 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
18 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   DOI   ScienceOn
19 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   DOI   ScienceOn
20 A. Rosenfeld and A. C. Kak, Digital Picture Processing, volume 1, Academic Press, New York, NY, 1982
21 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   DOI   ScienceOn
22 Siddon R. L., 'Fast calculation of the exact radiological path for a three-dimensional CT array,' Med. Phys., vol. 12, pp. 252-255, 1985   DOI   ScienceOn
23 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   과학기술학회마을   ScienceOn
24 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   DOI   ScienceOn
25 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   DOI   ScienceOn