Positron emission tomography and random coefficients regression

Annals of the Institute of Statistical Mathematics

Volumn 52, Issue 1, 2000, Pages 123-138

  Feuerverger, Andrey ^a   Vardi, Yehuda ^b  

^a UNIVERSITY OF TORONTO   (Canada)

^b RUTGERS UNIVERSITY   (United States)

Author keywords

Computerized tomography; Fast Fourier transform; Nonparametric likelihood; Positron emission tomography; Projection slice theorem; Radon transform; Random coefficients regression; Regularization; Smoothed EM algorithm

Indexed keywords

EID: 6744247097     PISSN: 00203157     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1004141117010     Document Type: Article

References (26)

1. Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988). The New S Language, Wadsworth & Brooks/Cole, Pacific Grove, California.
2. Beran, R. (1993). Semiparametric random coefficient regression models, Ann. Inst. Statist. Math., 45, 639-653.
3. Beran, R. and Hall, P. (1992). Estimating coefficient distributions in random coefficient regressions, Ann. Statist., 20, 1970-1984.
4. Beran, R. and Millar, P. W. (1994). Minimum distance estimation in random coefficient regression models, Ann. Statist., 22, 1976-1992.
5. Beran, R., Feuerverger, A. and Hall, P. (1996). On nonparametric estimation of intercept and slope distributions in random coefficient regression, Ann. Statist., 24, 2569-2592.
6. Bickel, P. J., Klaasen, C. A. J., Ritov, Y. and Wellner, J. A. (1993). Efficient and Adaptive Estimation in Semiparametric Models, Johns Hopkins University Press, Baltimore.
7. Chang, I.-S. and Hsiung, C. A. (1994). Asymptotic consistency of the maximum likelihood estimate in positron emission tomography and applications, Ann. Statist., 22, 1871-1883.
8. Deans, S. R. (1983). The Radon Transform and Some of Its Applications, Wiley, New York.
9. Dempster, A. P., Laird, N. M. and Rubin, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm (with discussion), J. Roy. Statist. Soc. Ser. B, 39, 1-38.
10. Eggermont, P. P. B. and LaRiccia, V. N. (1995). Maximum smoothed likelihood density estimation for inverse problems, Ann. Statist., 23, 199-220.
11. Fan, J. (1992). Design-adaptive nonparametric regression, J. Amer. Statist. Assoc., 87, 998-1004.
12. Gehman, S. and McClure, D. E. (1987). Statistical methods for tomographic image reconstruction, Bulletin of the International Statistical Institute, 52, 5-21.
13. Green, P. J. (1990a). Bayesian reconstructions from emission tomography data using a modified EM algorithm, IEEE Transactions Medical Imaging, 9, 84-93.
14. Green, P. J. (1990b). On use of the EM algorithm for penalized likelihood estimation, J. Roy. Statist. Soc. Ser. B, 52, 443-452.
15. Higdon, D. M., Bowsher, J. E., Johnson, V. E., Turkington, T. G., Gilland, D. R. and Jaszczak, R. J. (1997). Fully Bayesian estimation of Gibbs Hyperparameters for emission computed tomography data, IEEE Transactions on Medical Imaging, 16(5), 516-526.
16. Iusem, A. N. and Svaiter, B. F. (1994). A new smoothing-regularization approach for a maximum-likelihood estimation problem, Appl. Math. Optim., 29, 225-241.
17. Kaufman, L. (1993). Maximum likelihood, least squares, and penalized least squares for PET, IEEE Transactions on Medical Imaging, 12, 200-214.
18. Lange, K. and Carson, R. (1984). EM reconstruction algorithms for emission and transmission tomography, Journal of Computer Assisted Tomography, 8, 306-316.
19. Longford, N. T. (1993). Random Coefficient Models, Oxford University Press.
20. Nicholls, D. F. and Pagan, A. R. (1985). Varying coefficient regression, Handbook of Statistics, Vol. 5 (eds. E. J. Hannan, P. R. Krishnaiah and M. M. Rao), 413-449, North-Holland, Amsterdam.
21. O'Sullivan, F. (1995). A study of least squares and maximum likelihood for image reconstruction in positron emission tomography, Ann. Statist., 23, 1267-1300.
22. Raj, B. and Ullah, A. (1981). Econometrics, A Varying Coeffients Approach, Croom-Helm, London.
23. Shepp, L. A. and Kruskal, J. B. (1978). Computerized tomography: The new medical X-ray technology, Amer. Math. Monthly, 85, 420-439.
24. Shepp, L. A. and Vardi, Y. (1982). Maximum likelihood reconstruction in positron emission tomography, IEEE Transactions on Medical Imaging, 1, 113-122.
25. Silverman, B. W., Jones, M. C., Wilson, J. D. and Nychka, D. W. (1990). A smoothed EM approach to indirect estimation problems, with particular reference to stereology and emission tomography (with discussion), J. Roy. Statist. Soc. Ser. B, 52, 271-324.
26. Vardi, Y., Shepp, L. A. and Kaufman, L. (1985). A statistical model for positron emission tomography (with discussion), J. Amer. Statist. Assoc., 80, 8-37.