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A Statistical Model for Positron Emission Tomography
300
Citations
0
References
1985
Year
Computed TomographyImage ReconstructionEngineeringX-ray ImagingPositron Emission TomographyBiostatisticsComputational ImagingDance ImagesRadiation ImagingNuclear MedicineMaximum LikelihoodRadiologyHealth SciencesEm AlgorithmReconstruction TechniqueMedical ImagingNeuroimagingInverse ProblemsMedical Image ComputingLeast Squares ReconstructionsBiomedical Imaging
Positron emission tomography (PET) is a research‑stage imaging technique that visualizes metabolic activity, but its image quality is highly sensitive to the reconstruction algorithm, and the method requires no prior physics knowledge. The article develops a statistical model for PET reconstruction, demonstrating its importance and aiming to introduce statisticians to this emerging field. The authors formulate the PET reconstruction as a statistical estimation problem, outlining maximum‑likelihood (via EM), method‑of‑moments, and least‑squares procedures, and validate them with a computer simulation.
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.