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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.
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Estimates of I maximizing Eq. 1 obtained with an expectation maximization algorithm are typically unstable.
“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]
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An EM algorithm for estimating SPECT emission and transmission parameters from emission data only
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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
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