A Statistical Model for Positron Emission Tomography

@article{Vardi1985ASM,
  title={A Statistical Model for Positron Emission Tomography},
  author={Y. Vardi and L. Shepp and L. Kaufman},
  journal={Journal of the American Statistical Association},
  year={1985},
  volume={80},
  pages={8-20}
}
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… Expand

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References

SHOWING 1-10 OF 38 REFERENCES
Positron-emission tomography.
TLDR
A promising improvement in PET consists in the incorporation of photon time-of-flight information in the image reconstruction process, which requires large computer memory capabilities and fast processing systems. Expand
EM reconstruction algorithms for emission and transmission tomography.
TLDR
The general principles behind all EM algorithms are discussed and in detail the specific algorithms for emission and transmission tomography are derived and the specification of necessary physical features such as source and detector geometries are discussed. Expand
COMPUTERIZED TOMOGRAPHY: THE NEW MEDICAL X-RAY TECHNOLOGY
Computerized X-ray tomography is a completely new way of using X-rays for medical diagnosis. It gives physicians a more accurate way of seeing inside the human body and permits safe, convenient, andExpand
Maximum Likelihood Reconstruction for Emission Tomography
Previous models for emission tomography (ET) do not distinguish the physics of ET from that of transmission tomography. We give a more accurate general mathematical model for ET where an unknownExpand
Design and construction of the donner 280-crystal positron ring for dynamic transverse section emission imaging
We describe the design and construction of a medical imaging system for the rapid, accurate, three-dimensional imaging of positron-labeled compounds in the human body. Our medical research goalsExpand
Three-dimensional reconstruction from radiographs and electron micrographs: application of convolutions instead of Fourier transforms.
TLDR
Tests of the convolution method with computer-simulated shadowgraphs show that it is also more accurate than the Fourier transform method, and has good potentialities for application in electron microscopy and x-radiography. Expand
Positron Tomography and Nuclear Magnetic Resonance Imaging
TLDR
New developments in emission tomography, nuclear magnetic resonance imaging, and in vivo spectroscopy offer new horizons for medical research and clinical activities. Expand
A Matheematical Model for Positron-Emission Tomography Systems Having Time-of-Flight Measurements
Improvements in high speed electronics and scintillation-crystal technology now permit usable differential time-of-flight measurements to be made in tomography systems that employ coincidenceExpand
The Fourier reconstruction of a head section
TLDR
The authors compare the Fourier algorithm and a search algorithm using a simulated phantom to speed the search algorithm by using fewer interactions leaves decreased resolution in the region just inside the skull which could mask a subdural hematoma. Expand
Maximum Likelihood PET with Real Data
We compare the maximum likelihood and convolution-backprojection reconstructions of a particular real phantom with count data obtained from the Columbia University Positron Emission TomographicExpand
...
1
2
3
4
...