Interior-point methodology for 3-D PET reconstruction

IEEE Transactions on Medical Imaging

Volumn 19, Issue 4, 2000, Pages 271-285

  Johnson, Calvin A ^a,b,c,d   Seidel, Jürgen ^a,b,c,d   Sofer, Ariela ^a,b,c,d  

^a IEEE   (United States)

^b NATIONAL INSTITUTES OF HEALTH   (United States)

^c NATIONAL INSTITUTES OF HEALTH   (United States)

^d George Mason University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTER SIMULATION; CONVERGENCE OF NUMERICAL METHODS; IMAGE RECONSTRUCTION; ITERATIVE METHODS; LAGRANGE MULTIPLIERS; MAXIMUM LIKELIHOOD ESTIMATION; MONTE CARLO METHODS; OPTIMIZATION; POSITRON EMISSION TOMOGRAPHY;

INTERIOR-POINT METHODOLOGY;

MEDICAL IMAGING;

ALGORITHM; ANIMAL; ARTICLE; COMPUTER ASSISTED EMISSION TOMOGRAPHY; IMAGE PROCESSING; METHODOLOGY; MONTE CARLO METHOD; STATISTICAL MODEL;

ALGORITHMS; ANIMALS; IMAGE PROCESSING, COMPUTER-ASSISTED; LIKELIHOOD FUNCTIONS; MONTE CARLO METHOD; TOMOGRAPHY, EMISSION-COMPUTED;

EID: 0034164342     PISSN: 02780062     EISSN: None     Source Type: Journal    
DOI: 10.1109/42.848179     Document Type: Article

References (57)

1. H. H. Barrett, D. W. Wilson, and B. W. Tsui, Noise properties of the EM algorithm-I. Theory, Phys. Med. Biol., vol. 39, pp. 833-846, 1994.
2. C. Bouman and K. Sauer, A unified approach to statistical tomography using coordinate descent optimization, IEEE Trans. Image Processing, vol. 5, pp. 480-492, Mar., 1996.
3. C. M. Chen and S. Y. Lee, On parallelizing the EM algorithm for PET image reconstruction, IEEE Trans. Parallel Distrib. Syst., vol. 5, pp. 860-873, Aug., 1994.
4. G. Chinn and S.-C. Huang, A general class of preconditioners for statistical iterative reconstruction of emission computed tomography, IEEE Trans. Med. Imag., vol. 16, no. 1, pp. 1-10, Feb., 1997.
5. N. H. Clinthorne, T.-S. Pan, P.-C. Chiao, W. L. Rogers, and J. A. Stamos, Preconditioning methods for improved convergence rates in iterative reconstructions, IEEE Trans. Med. Imag., vol. 12, pp. 78-83, 1993.
6. A. R. Conn, N. Gould, and Ph. L. Toint, A primal-dual algorithm for minimizing a nonconvex function subject to bound and linear equality constraints, IBM T. J. Watson Research Center, Tech. Rep. 96/9, 1996.
7. R. S. Dembo and T. Steihaug, Truncated-Newton algorithms for large-scale unconstrainted optimization, Math Programming, vol. 26, pp. 190-212, 1983.
8. A. R. DePierro, A modified expectation maximization algorithm for penalized likelihood estimation in emission tomography, IEEE Trans Med. Imag, vol. 14, pp. 132-137, Mar., 1995.
9. On the convergence of an EM-type algorithm for penalized likelihood estimation in emission tomography, IEEE Trans. Med. Imag., vol. 14, pp. 762-765, Dec., 1995.
10. J. A. Fessier, Penalized maximum-likelihood image reconstruction using space-alternating generalized EM algorithms, IEEE Trans. Image Processing, vol. 4, pp. 1417-1429, Oct., 1995.
11. J. A. Fessier, E. P. Ficaro, N. H. Clinthorne, and K. Lange, Grouped-coordinate ascent algorithms for penalized-likelihood transmission image reconstruction, IEEE Trans. Med. Imag., vol. 16, pp. 166-175, Apr., 1997.
12. J. A. Fessier and S. D. Booth, Conjugate-gradient preconditioning methods for shift-invariant PET image reconstruction, IEEE Trans. Image Processing, to be published.
13. A. V. Fiacco and G. P. McCormick, Nonlinear Programming: Sequential Unconstrained Minimization Techniques. New York: Wiley, 1968.
14. A. Forsgen and P. E. Gill, Primal-dual interior methods for nonconvex nonlinear programming, Department of Mathematics, Univ. California San Diego, Rep. NA 96-3, 1996.
15. G. Golub and C. Van Loan, Matrix Computations, 3rd ed. Baltimore,
16. MD: Johns Hopkins Univ. Press, 1996.
17. P. J. Green, On use of the EM algorithm for penalized likelihood estimation, J. R. Stat. Soc. B, vol. 52, pp. 443-452, 1990.
18. Bayesian reconstructions from emission tomography data using a modified EM algorithm, IEEE. Trans. Med. Imag., pp. 84-93, Mar., 1990.
19. T. Hebert and R. Leahy, A generalized EM algorithm for 3-D Bayesian reconstruction from Poisson data using Gibbs priors, IEEE Trans. Med. Mag., vol. 8, pp. 194-202, June, 1989.
20. G. T. Herman, Image Reconstruction from Projections: The Fundamentals of Computerized Tomography. New York: Academic, 1980.
21. G. T. Herman, D. Odhner, K. D. Toennies, and S. A. Zenios, A parallelized algorithm for image reconstruction from noisy projections, in Large Scale Numerical Optimization, Proc. in Applied Mathematics, vol. 46, T. Coleman and Y. Li, Eds. Philadelphia, PA, 1990, pp. 3-21.
22. G. T. Herman and D. Odhner, Performance evaluation of an iterative image reconstruction algorithm for Poisson emission tomography, IEEE Trans. Med. Imag, vol. 10, pp. 336-346, Sept., 1991.
23. C. A. Johnson, Y Yan, R. E. Carson, R. L. Martino, and M. E. DaubeWitherspoon, A system for the 3D reconstruction of retracted-septa PET data using the EM algorithm, IEEE Trans. Nucl. Sci., vol. 42, pp. 1223-1227, June, 1995.
24. C. A. Johnson, J. Seidel, R. E. Carson, W. R. Gandler, A. Sofer, M. V. Green, andM. E. Daube-Witherspoon, Evaluation of 3D reconstruction algorithms for a small animal PET camera, IEEE Trans Nucl. Sci., vol. 44, pp. 1303-1308, June, 1997.
25. C. A. Johnson, Nonlinear optimization for volume PET reconstructions, Ph.D. dissertation, Dep. Operations Research Engineering, George Mason Univ. , Fairfax, VA, 1997.
26. L. Kaufman, Implementing and accelerating the EM algorithm for positron emission tomography, IEEE Trans. Med. Imag, vol. 6, pp. 37-51, Mar., 1987.
27. Solving emission tomography problems on vector machines, Ann. Oper. Res., vol. 22, pp. 325-353, 1990.
28. Maximum likelihood, least squares, and penalized least squares for PET, IEEE Trans. Med. Imag., vol. 12, pp. 200-214, June, 1993.
29. P. E. Kinahan and J. G. Rogers, Analytic 3D reconstruction using all detected events, IEEE Trans Nucl. Sci., vol. 36, pp. 964-968, Feb., 1989.
30. M. Kojima, S. Mizuno, and A. Yoshise, A primal-dual interior point algorithm for linear programming, in Progress in Mathematical Programming: Interior-Point and Related Methods, N. Megiddo, Ed. New York: Springer-Verlag, 1989, pp. 29-47.
31. D. S. Lalush and B. M. W. Tsui, A fast and stable maximum a posteriori conjugate gradient reconstruction algorithm, Med. Phys., vol. 22, no. 2, pp. 1273-1284, 1995.
32. The importance of preconditioners in fast Poisson-based iterative reconstruction algorithms for SPECT, in 1995 IEEE Nuclear Science Symp. Conf. Rec., 1996, pp. 1326-1330.
33. A. A. Lammertsma, S. P. Hume, R. Myers, S. Ashworth, P. M. Bloomfield, S. Rajeswaran, T. Spinks, and T. Jones, PET scanners for small animals, J. Nucl. Med., vol. 36, pp. 2391-2392, 1995.
34. K. Lange, M. Bahn, and R. Little, A theoretical study of some maximum likelihood algorithms for emission and transmission tomography, IEEE Trans. Med. Imag., vol. 6, pp. 106-114, June, 1987.
35. K. Lange, Convergence of EM image reconstruction algorithms with Gibbs smoothing, IEEE Trans. Med. Imag., vol. 9, pp. 439-446, Dec., 1990.
36. E. Levitan and G. T. Herman, A maximum a posteriori probability expectation maximization algorithm for image reconstruction in emission tomography, IEEE Trans. Med. Imag, vol. 6, pp. 185-192, 1987.
37. J. Liow and S. Strother, Practical tradeoffs between noise, quantitation and number of iterations for maximum likelihood-based reconstructions, IEEE Trans. Med. Imag, vol. 13, pp. 601-609, Dec., 1994.
38. I. Lustig, R. E. Marsten, and D. F. Shanno, Interior point methods for linear programming: Computational state of the art, ORSA J. Comp., vol. 6, pp. 1-14, 1994.
39. S. Matej, G. T. Herman, T. K. Nayaran, S. S. Furuie, R. M. Lewitt, and P. E. Kinahan, Evaluation of task-oriented performance of several fully 3D PET reconstruction algorithms, Phys. Med. Biol., vol. 39, pp. 355-367, 1994.
40. E.Ü Mumcuoglu, Statistical modeling and fast Bayesian reconstruction in positron tomography, Ph.D. dissertation, Univ. Southern California, 1994.
41. E.Ü Mumcuoglu, R. M. Leahy, S. R. Cherry, and Z. Zhou, Fast gradient-based methods for Bayesian reconstruction of transmission and emission PET Images, IEEE Trans. Med. Imag., vol. 13, pp. 687-701, Dec., 1994.
42. E.Ü Mumcuoglu, R. M. Leahy, andS. R. Cherry, Bayesian reconstruction of PET images: Methodology and performance analysis, Phys. Med. Biol., vol. 41, pp. 1777-1807, 1996.
43. W. Murray, Analytic expressions for the eigenvalues and eigenvectors of the Hessian matrices of barrier and penalty functions,/ Optimization Theory A. vol. 7, pp. 189-196, 1971.
44. S. G. Nash, Preconditioning of truncated-Newton methods, SIAM J. Sci. Stat. Comput., vol. 6, pp. 599-616, 1985.
45. S. G. Nash and A. Sofer, Block truncated-Newton methods for parallel optimization, Math. Programming, vol. 45, pp. 529-546, 1989.
46. Assessing a search direction within a truncated-Newton method, Oper. Res. Let., vol. 9, pp. 219-221, 1990.
47. A general-purpose parallel algorithm for unconstrained optimization, SIAM J. Opt., vol. 1, pp. 530-547, 1991.
48. A barrier method for large-scale constrained optimizaton, ORSA J. Comp., vol. 5, pp. 40-53, 1993.
49. Linear and Nonlinear Programming. New York: McGraw-Hill, 1996.
50. J. M. Ollinger and J. A. Fessier, Positron-emission tomography, IEEE Signal Processing Mag., vol. 14, pp. 43-55, Jan. 1997.
51. J. Seidel, M. V. Green, and W. R. Gandler, Estimated spatial resolution of a single slice, small animal PET scanner using position-sensitive photomultiplier tubes for event pair localization, in Proc. 29th Anna. Meeting Assoc. Advancement Medical Instrumentation, 1994, p. 85.
52. J. Seidel, W. R. Gandler, and M. V. Green, A very high resolution single-slice animal PET scannerbased on direct detection of coincidence endpoints, / Nucl. Med., vol. 35, p. 40P, 1994.
53. Characteristics of a pair of small field-of-view LSO scintillation cameras, IEEE Trans Nucl. Sci., vol. 43, pp. 1968-1973, June, 1996.
54. J. Seidel, C. Johnson, E. Jagoda, L. Sha, W. C. Eckelman, and M. V. Green, A high resolution scanner for investigating technical requirements and selected biological applications of continuous 3D detectors in small animal PET, J. Nucl. Med., to be published.
55. D. L. Snyder, M. I. Miller, L. J. Thomas Jr., and D. G. Politte, Noise and edge artifacts in maximum-likelihood constructions for emission tomography, IEEE Trans. Med. Imag., vol. 6, pp. 228-238, 1987.
56. Y. Vardi, L. A. Shepp, and L. Kaufman, A statistical model for positron emission tomography,/ Amer. Stat. Assoc., vol. 80, no. 389, pp. 8-37, 1985.
57. D. W. Wilson and B. M. W. Tsui, Noise properties of filtered-backprojection and ML-EM reconstructed emission tomography images, IEEE Trans. Nucl. Sci., vol. 40, pp. 1198-1203, 1993.