행작용 최대우도 알고리즘을 사용한 컴프턴 산란 데이터로부터의 3차원 영상재구성
Three-Dimensional Image Reconstruction from Compton Scattered Data Using the Row-Action Maximum Likelihood Algorithm
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초록
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.
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.
참고문헌 (25)
- M. Singh, "An electronically collimated gamma camera for single photon emission computed tomography: Part1 and 2", Med. Phys, 10(4), pp.421~427 (1983)
- Y. F. Yang, "A compton camera for multi-tracer imaging", IEEE Trans. Nucl. Sci, 48, pp.656~661 (2001)
- S. Motomura, "Gamma-ray Compton imaging of multitracer in bio-samples by strip germanium telescope", IEEE Nuclear Science Symposium and Medical Imaging Conference Record, 통권 : 4, pp.2152~2154 (2004)
- R.W. Todd, "A proposed Gamma camera", Nature, 251, pp.132~134 (1974)
- R. Basko, "Application of spherical harmonics to image reconstruction for the Compton camera", Phys. Med. Biol, 43, pp.887~894 (1998)
- L.C. Parra, "Reconstruction of cone-beam projections from Compton scattered data", IEEE Trans. Nucl. Sci, 47, pp.1543~1550 (2000)
- T. Tomitani, "Image reconstruction from limited angle Compton camera data", Phys, Med. Biol, 47, pp.1009~1026 (2002)
- M. Hirasawa, "An analytical image reconstru- ction algorithm to compensate for scattering angle broadening in Compton cameras", Phys. Med. biol, 48, pp.1009~1026 (2003)
- B. Smith, "Reconstruction methods and completeness conditions for two Compton data models", J. Opt. Soc. Am. A, 22(3), pp.445~459 (2005)
- D. Xu, "Filtered back-projection in 4π Compton imaging with a single 3D position sensitive CdZnTe detector", IEEE Trans. Nucl. Sci, 53(5), pp.2787~2793 (2006)
- T. Hebert, "Three-dimensional maxi- mum-likelihood reconstructin for a electronically collimated single-photon-emission imaging system", J. Opt. Soc. Am, A7, pp.1305~1313 (1990)
- A.C. Sauve, "3D image reconstruction for Compton SPECT camera model", IEEE Trans. Nucl. Sci, 46, pp.2075~2084 (1999)
- L.A. Shepp, "Maximum likelihod reconstruction for emission tomography", IEEE Trans. Med. Imaging, 1, pp.113~122 (1982)
- K. Lange, "EM reconstruction algorithms for emission and transmission tomography", J. Comput. Assist. Tomog, 8, pp.306~316 (1984)
- J.Browne, "A Row-Action Alternative to The EM Algorithm for Maximizing Likelihoods in Emission Tomography", IEEE Trans. Med. Imaging, 15, pp.687~699 (1996)
- O. Klein, "Experimental Study of the Compton Effect at 1.2 Mev", Phys. Rev, 76, pp.1270~ (1949)
- S.M. Kim, "Two approaches to implementing projector- backprojector pairs for 3D reconstruction from Compton scattered data", Nuclear Instruments & Methods in Physics Research A, 571, pp.255~258 (2007)
- 이미노, "컴프턴 카메라 영상재구성을 위한 타원 누적법", 의공학회지, 28(4), pp.520~529 (2007), 대한의용생체공학회
- Siddon RL, "Fast calculation of the exact radiological path for a three-dimensional CT array", Med. Phys, 12, pp.252~255 (1985)
- A. Rosenfeld, "Digital Picture Processing" (1982), Academic Press
- G.T. Herman, "Algebraic reconstruction techniques can be made computationally efficient", IEEE Trans. Med. Imaging, 12, pp.600~609 (1993)
- H.M. Hudson, "Accelerated image reconstr- uction using ordered subsets of projection data", IEEE Trans. Med. Imaging, 13, pp.601~609 (1994)
- E. Tanaka, "Subset-dependent relaxation on block- iterative algorithms for image reconstruction in emission tomog- raphy", Phys. Med. biol, 48, pp.1405~1422 (2003)
- A. Fukano, "Performance evaluation of relaxed block-iterative algorithms for 3-D PET reconstruction", IEEE Nuclear Science Symposium Conference and Medical Imaging Conference Record, 통권 : 5, pp.2830~2834 (2004)
- A.D. Pierro, "Fast EM-like methods for maximum ‘A Posteriori’ estimates in Emission tomography", IEEE Trans. Med. Imaging, 20(4), pp.280~288 (2001)