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On Parallelizing the EM Algorithm for PET Image Reconstruction
August 1994 (vol. 5 no. 8)
pp. 860-873

The expectation maximization (EM) algorithm is one of the most suitable iterative methods for positron emission tomography (PET) image reconstruction; however, it requires a long computation time and an enormous amount of memory space. To overcome these problems, we present two classes of highly efficient parallelization schemes: homogeneous and inhomogeneous partitionings. The essential difference between these two classes is that the inhomogeneous partitioning schemes may partially overlap the communication with computation by deliberate exploitation of the inherent data access pattern with a multiple-ring communication pattern. In theory, the inhomogeneous partitioning schemes may outperform the homogeneous partitioning schemes. However, the latter require a simpler communication pattern. In an attempt to estimate the achievable performance and to analyze the performance degradation factors without actual implementation, we have derived efficiency prediction formulas for closely estimating the performance for the proposed parallelization schemes. We propose new integration and broadcasting algorithms for hypercube, ring, and n-D mesh topologies, which are more efficient than the conventional algorithms when the link setup time is relatively negligible. The concept of the proposed task and data partitioning schemes, the integration and broadcasting algorithms, and the efficiency estimation methods can be applied to many other problems that are rich in data parallelism, but without balanced exclusive partitioning.

[1] L. A. Shepp and Y. Vardi, "Maximum likelihood reconstruction for emission tomography,"IEEE Trans. Med. Imaging, vol. 1, pp. 113-122, Oct. 1982.
[2] J. Llacer and J. D. Meng, "Matrix-based image reconstruction methods for tomography,"IEEE Trans. Nucl. Sci., vol. 32, pp. 855-864, Feb. 1985.
[3] W. F. Jones, L. G. Byars, and M. E. Casey, "Positron emission tomographic images and expection maximization: A VLSI architecture for multiple iterations per second,"IEEE Trans. Nucl. Sci., vol. 35, pp. 620-624, Feb. 1988.
[4] F. U. Rosenberger, D. G. Politte, G. C. Johns, and C. E. Molnar, "An efficient parallel implementation of the EM algorithm for PET image reconstruction utilizing transputers," in1990 Nuclear Sci. Symp. Conf. Rec., Oct. 1990.
[5] G. T. Herman, D. Odhner, K. D. Toennies, and S. A. Zenios, "A parallelized algorithm for image reconstruction from noisy projections," inLarge-Scale Numerical Optimization, Oct. 1989.
[6] K. A. Girodias, H. H. Barrett, and R. L. Shoemaker, "Parallel simulated annealing for emission tomography,"J. Phys. Med. Biol., vol. 36, pp. 921-938, 1991.
[7] L. Kaufman, "Implementing and accelerating the EM algorithm for positron emission tomography,"IEEE Trans. Med. Imaging, vol. 6, no. 1, pp. 37-50, Mar. 1987.
[8] C.-M. Chen, S.-Y. Lee, and Z. H. Cho, "Parallelization of the EM Algorithm for 3-D PET image reconstruction,"IEEE Trans. Med. Imaging, vol. 10, pp. 513-522, Dec. 1991.
[9] C.-M. Chen and S.-Y. Lee, "Parallelization of the EM algorithm for 3-D PET image reconstruction: Performance estimation and analysis," inProc. 1991 Int. Conf. Parallel Processing, vol. III, Aug. 1991, pp. 175-182.
[10] C. Aykanatet al., "Iterative algorithms for solution of large sparse system of linear equations on hypercubes,"IEEE Trans. Comput., vol. 37, pp. 1554-1568, Dec. 1988.
[11] G. C. Fox, "Load balancing and sparse matrix vector multiplication on the hypercube," Tech. Rep.C3P-327, California Inst. of Technol., 1986.
[12] C. P. Kruskal, L. Rudolph, and M. Snir, "Techniques for parallel manipulation of sparse matrices,"Theoretical Comput. Sci., pp. 135-157, 1989.
[13] K. Lange and R. Carson, "EM reconstruction algorithms for emission and transmission tomography,"J. Comput. Assist. Tomog., vol. 8, pp. 306-316, 1984.
[14] R. M. Lewitt and G. Muehllehner, "Accelerated iterative reconstruction for positron emission tomography based on the EM algorithm for maximum likelihood estimation,"IEEE Trans. Med. Imaging, vol. 5, no. 1, pp. 16-22, Mar. 1986.
[15] E. Tanaka, N. Nohara, T. Tomitani, M. Yamamoto, and H. Murayama, "Stationary positron emission tomography and its image reconstruction,"IEEE Trans. Med. Imaging, vol. 5, no. 4, pp. 199-206, Dec. 1986.
[16] K. Lange, M. Bahn, and R. Little, "A theoretical study of some maximum likelihood algorithms for emission and transmission tomography,"IEEE Trans. Med. Imaging, vol. 6, no. 2, pp. 106-114, June 1987.
[17] H. Hart and Z. Liang, "Bayesian image processing in two dimensions,"IEEE Trans. Med. Imaging, vol. 6, no. 3, pp. 199-206, Sept. 1987.
[18] E. Levitan and G. T. Herman, "A maximuma posterioriprobability expectation maximization algorithm for image reconstruction in emission tomography,"IEEE Trans. Med. Imaging, vol. 6, no. 3, pp. 185-191, Sept. 1987.
[19] P. R. Phillips, "Bayesian statics, factor analysis, and PET images--Part I: Mathematical background,"IEEE Trans. Med. Imaging, vol. 8, pp. 125-132, June 1989.
[20] Z. Liang, R. Jaszczak, and K. Greer, "On Bayesian image reconstruction from projections: Uniform and nonuniforma priorisource information,"IEEE Trans. Med. Imaging, vol. 8, pp. 227-235, Sept. 1989.
[21] P. J. Green, "Bayesian reconstruction from emission tomography data using a modified EM algorithm,"IEEE Trans. Med. Imaging, vol. 9, pp. 84-93, 1990.
[22] D. P. Bertsekas and J. N. Tsitsiklis,Parallel and Distributed Computations. Englewood Cliffs, NJ: Prentice-Hall, 1989.
[23] S.-Y. Lee, H. D. Chang, K.-G. Lee, and B. Y. Ku, "Parallel power system transient stability analysis on hypercube multiprocessors,"IEEE Trans. Power Syst., vol. 6, pp. 1337-1343, Aug. 1991.
[24] P. Heidelberger and S. S. Lavenberg, "Computer performance evaluation,"IEEE Trans. Comput., vol. C-33, no. 12, pp. 1195-1220, Dec. 1984.
[25] C.-M. Chen, "On miniminzing data sharing overhead for large-scale data-parallel algorithms: Replication and allocation of shared data," Ph.D. dissertation, Cornell Univ., Ithaca, NY, 1993.

Index Terms:
Index Termsradioisotope scanning and imaging; iterative methods; optimisation; parallel algorithms; image reconstruction; performance evaluation; parallelization; expectation maximization algorithm; EM algorithm; PET image reconstruction; iterative methods; positron emission tomography; computation time; memory space; homogeneous partitioning; inhomogeneous partitioning; communication/computation overlap; inherent data access pattern; multiple-ring communication pattern; achievable performance estimation; performance degradation factors; efficiency prediction formulas; integration algorithms; broadcasting algorithms; hypercube topology; ring topology; n-dimensional mesh topology; link setup time
Citation:
C.M. Chen, S.Y. Lee, "On Parallelizing the EM Algorithm for PET Image Reconstruction," IEEE Transactions on Parallel and Distributed Systems, vol. 5, no. 8, pp. 860-873, Aug. 1994, doi:10.1109/71.298213
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