The DOI matches its Crossref record; 28 of the 28 references it cites were found in a registry or an index.
A Statistical Model for Positron Emission Tomography
Abstract
Positron emission tomography (PET)—still in its research stages—is a technique that promises to open new medical frontiers by enabling physicians to study the metabolic activity of the body in a pictorial manner. Much as in X-ray transmission tomography and other modes of computerized tomography, the quality of the reconstructed image in PET is very sensitive to the mathematical algorithm to be used for reconstruction. In this article, we tailor a mathematical model to the physics of positron emissions, and we use the model to describe the basic image reconstruction problem of PET as a standard problem in statistical estimation from incomplete data. We describe various estimation procedures, such as the maximum likelihood (ML) method (using the EM algorithm), the method of moments, and the least squares method. A computer simulation of a PET experiment is then used to demonstrate the ML and the least squares reconstructions. The main purposes of this article are to report on what we believe is an important contribution of statistics to PET and to familiarize statisticians with this exciting field that can benefit from further statistical methodologies to be developed with PET problems in mind. Thus no background in physics or previous knowledge of computerized tomography is assumed. The emphasis is on the basic PET model and the statistical methodology needed for it.
Overview
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
In the citing paper
“Estimates of I maximizing Eq. 1 can be obtained with an expectation maximization algorithm (6, 33–35), but the outcome is typically unstable (36).”
From Socioeconomic status determines COVID-19 incidence and related mortality in Santiago, Chile (2021) · cites this paper as [34]
Citations
Cites
Maximum Likelihood from Incomplete Data Via the EM Algorithm
Dempster, A. P., Laird, N. M., & Rubin, D. B. (1977) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1977.tb01600.x · Cited by 50,444
Linear Statistical Inference and its Applications
Rao, C. R. (1973) · Wiley series in probability and statistics · doi:10.1002/9780470316436 · Cited by 10,474
Iterative Solution of Nonlinear Equations in Several Variables
Ortega, J. M., & Rheinboldt, W. C. (2000) · Society for Industrial and Applied Mathematics eBooks · doi:10.1137/1.9780898719468 · Cited by 6,919
Journal of The American Statistical Association
Fienberg, S. E. (2004) · Encyclopedia of Statistical Sciences · doi:10.1002/0471667196.ess1317 · Cited by 6,289
Maximum likelihood estimation from incomplete data via the EM algorithm
Dempster, A. P. (1977) · Journal of the Royal Statistical Society Series A (Statistics in Society) · Cited by 4,543
Maximum Likelihood Reconstruction for Emission Tomography
Shepp, L. A., & Vardi, Y. (1982) · IEEE Transactions on Medical Imaging · doi:10.1109/tmi.1982.4307558 · Cited by 4,429
Self-citationThe Fourier reconstruction of a head section
Shepp, L. A., & Logan, B. F. (1974) · IEEE Transactions on Nuclear Science · doi:10.1109/tns.1974.6499235 · Cited by 2,202
Self-citationEM reconstruction algorithms for emission and transmission tomography.
Lange, K. L., & Carson, R. E. (1984) · PubMed · Cited by 1,775
Nonlinear Programming: A Unified Approach.
Beale, E. M. L., & Zangwill, W. I. (1970) · Journal of the Royal Statistical Society Series A (General) · doi:10.2307/2343701 · Cited by 1,059
Nonlinear Programming: A Unified Approach
Peterson, D. W., & Zangwill, W. I. (1972) · Econometrica · doi:10.2307/1909424 · Cited by 1,011
Ramachandran, G. N., & Lakshminarayanan, A. V. (1971) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.68.9.2236 · Cited by 986
Introduction to Probability and Statistics from a Bayesian Viewpoint
Lindley, D. V. (1965) · Cambridge University Press eBooks · doi:10.1017/cbo9780511662973 · Cited by 766
Information geometry and alternating minimization procedures
Csiszár, I. (1984) · Medical Entomology and Zoology · Cited by 596
On the Asymptotic Behaviour of Posterior Distributions
Walker, A. M. (1969) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/j.2517-6161.1969.tb00767.x · Cited by 337
Good, I. J., & Gaskins, R. A. (1980) · Journal of the American Statistical Association · doi:10.1080/01621459.1980.10477419 · Cited by 245
A Natural Identity for Exponential Families with Applications in Multiparameter Estimation
Hudson, H. M. (1978) · The Annals of Statistics · doi:10.1214/aos/1176344194 · Cited by 231
A Matheematical Model for Positron-Emission Tomography Systems Having Time-of-Flight Measurements
Snyder, D. L., Thomas, L. J., & Ter‐Pogossian, M. M. (1981) · IEEE Transactions on Nuclear Science · doi:10.1109/tns.1981.4332168 · Cited by 222
Computerized Tomography: The New Medical X-Ray Technology
Shepp, L. A., & Kruskal, J. B. (1978) · American Mathematical Monthly · doi:10.1080/00029890.1978.11994611 · Cited by 200
Self-citationTer‐Pogossian, M. M., Raichle, M. E., & Sobel, B. E. (1980) · Scientific American · doi:10.1038/scientificamerican1080-170 · Cited by 173
An algorithm for maximizing expected log investment return
Cover, T. M. (1984) · IEEE Transactions on Information Theory · doi:10.1109/tit.1984.1056869 · Cited by 148
Computerized Tomography: The New Medical X-Ray Technology
Shepp, L. A., & Kruskal, J. B. (1978) · American Mathematical Monthly · doi:10.2307/2320062 · Cited by 137
Self-citationPositron Tomography and Nuclear Magnetic Resonance Imaging
Brownell, G. L., Budinger, T. F., Lauterbur, P. C., & McGeer, P. L. (1982) · Science · doi:10.1126/science.215.4533.619 · Cited by 109
Simultaneous Estimation of the Means of Independent Poisson Laws
Clevenson, M. L., & Zidek, J. V. (1975) · Journal of the American Statistical Association · doi:10.1080/01621459.1975.10482497 · Cited by 108
(1942) · Nature · doi:10.1038/150222d0 · Cited by 108
Maximum Likelihood PET with Real Data
Shepp, L. A., Vardi, Y., Ra, J. B., Hilal, S. K., & Cho, Z. H. (1984) · IEEE Transactions on Nuclear Science · doi:10.1109/tns.1984.4333398 · Cited by 64
Self-citationSimultaneous Estimation of Several Poisson Parameters Under $K$-Normalized Squared Error Loss
Tsui, K., & Press, S. J. (1982) · The Annals of Statistics · doi:10.1214/aos/1176345692 · Cited by 57
Journal of Computer Assisted Tomography
&NA; (1983) · Journal of Computer Assisted Tomography · doi:10.1097/00004728-198312000-00082 · Cited by 54
Derenzo, S. E., Banchero, P., Cahoon, J. L., Huesman, R. H., Vuletich, T., & Budinger, T. F. (1977) · IEEE Conference on Decision and Control (CDC) · doi:10.1109/cdc.1977.271594 · Cited by 3
Research works printed but not linked: 2
- Lakshminarayanan , A. V. 1975 . “Reconstruction From Divergent Ray Data,” , State University of New York at Buffalo, Computer Science Dept. . Technical Report No. 92
- Peng , J. C. M. 1975 . “Simultaneous Estimation of the Parameters of Independent Poisson Distributions,” , Stanford University, Dept. of Statistics . Technical Report No. 78
Cited by
Sorted by citations
On the Statistical Analysis of Dirty Pictures
Besag, J. E. (1986) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/j.2517-6161.1986.tb01412.x · Cited by 4,204
Accelerated image reconstruction using ordered subsets of projection data
Hudson, H. M., & Larkin, R. S. (1994) · IEEE Transactions on Medical Imaging · doi:10.1109/42.363108 · Cited by 3,713
Neural Networks and the Bias/Variance Dilemma
Geman, S., Bienenstock, E., & Doursat, R. (1992) · Neural Computation · doi:10.1162/neco.1992.4.1.1 · Cited by 3,578
Support Vector Method for Function Approximation, Regression Estimation, and Signal Processing
Vapnik, V. N., Golowich, S. E., & Smola, A. J. (1996) · Cited by 2,776
A unified treatment of some iterative algorithms in signal processing and image reconstruction
Byrne, C. L. (2003) · Inverse Problems · doi:10.1088/0266-5611/20/1/006 · Cited by 1,343
Metadata
- Authors
- Vardi, Y., Shepp, L. A., & Kaufman, L.
- Affiliations
- AT&T (United States) (US)
- Venue
- Journal of the American Statistical Association
- Publisher
- Informa UK Limited
- Published
- 1985-03
- Volume
- 80
- Issue
- 389
- Pages
- 8-20
- ISSN
- 0162-1459 (ISSN-L)
- 1537-274X
- OpenAlex
- W1967374611
- Cited by
- 863
- References
- 27
- Citations by year
- 2026: 10 · 2025: 12 · 2024: 10 · 2023: 14 · 2022: 14 · 2021: 29 · 2020: 25 · 2019: 44 · 2018: 19 · 2017: 22 · 2016: 32 · 2015: 31 · 2014: 31 · 2013: 25 · 2012: 27
- FWCI
- 13.32
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of the American Statistical Association (publishedVersion)
- Topics
- Health Sciences › Medicine › Radiology, Nuclear Medicine and Imaging › Medical Imaging Techniques and Applications
- Physical Sciences › Mathematics › Mathematical Physics › Numerical methods in inverse problems
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Image and Signal Denoising Methods
- Keywords
- positron emission tomography, image reconstruction, statistical models, missing data, maximum likelihood estimation, expectation-maximization algorithm, method of moments, least squares, statistical estimation
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
