title: A Conway-Maxwell-Poisson (CMP) model to address data dispersion on positron emission tomography.
abstract: Positron emission tomography (PET) in medicine exploits the properties of positron-emitting unstable nuclei. The pairs of γ- rays emitted after annihilation are revealed by coincidence detectors and stored as projections in a sinogram. It is well known that radioactive decay follows a Poisson distribution; however, deviation from Poisson statistics occurs on PET projection data prior to reconstruction due to physical effects, measurement errors, correction of deadtime, scatter, and random coincidences. A model that describes the statistical behavior of measured and corrected PET data can aid in understanding the statistical nature of the data: it is a prerequisite to develop efficient reconstruction and processing methods and to reduce noise. The deviation from Poisson statistics in PET data could be described by the Conway-Maxwell-Poisson (CMP) distribution model, which is characterized by the centring parameter λ and the dispersion parameter ν, the latter quantifying the deviation from a Poisson distribution model. In particular, the parameter ν allows quantifying over-dispersion (ν<1) or under-dispersion (ν>1) of data. A simple and efficient method for λ and ν parameters estimation is introduced and assessed using Monte Carlo simulation for a wide range of activity values. The application of the method to simulated and experimental PET phantom data demonstrated that the CMP distribution parameters could detect deviation from the Poisson distribution both in raw and corrected PET data. It may be usefully implemented in image reconstruction algorithms and quantitative PET data analysis, especially in low counting emission data, as in dynamic PET data, where the method demonstrated the best accuracy.
authors: Institute of Clinical Physiology, National Research Council, via Moruzzi 1, 56124 Pisa, Italy; Fondazione CNR-Regione Toscana "G. Monasterio", via Moruzzi, 1, 56124 Pisa, Italy. Electronic address: santarel@ifc.cnr.it.
authors: Maria Filomena
authors: MF
authors: Santarelli
authors: Fondazione CNR-Regione Toscana "G. Monasterio", via Moruzzi, 1, 56124 Pisa, Italy.
authors: Daniele
authors: D
authors: Della Latta
authors: Department of Information Engineering: EIT, University of Pisa, via Diotisalvi 2, 56126 Pisa, Italy.
authors: Michele
authors: M
authors: Scipioni
authors: Fondazione CNR-Regione Toscana "G. Monasterio", via Moruzzi, 1, 56124 Pisa, Italy.
authors: Vincenzo
authors: V
authors: Positano
authors: Department of Information Engineering: EIT, University of Pisa, via Diotisalvi 2, 56126 Pisa, Italy; Fondazione CNR-Regione Toscana "G. Monasterio", via Moruzzi, 1, 56124 Pisa, Italy; Institute of Clinical Physiology, National Research Council, via Moruzzi 1, 56124 Pisa, Italy.
authors: Luigi
authors: L
authors: Landini
mesh_terms: D003198:Computer Simulation; D019788:Fluorodeoxyglucose F18; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D019047:Phantoms, Imaging; D016012:Poisson Distribution; D049268:Positron-Emission Tomography / Q000379:methods*
chemical_list: D019788:Fluorodeoxyglucose F18
keywords: Conway-Maxwell-Poisson (CMP) distribution; Maximum likelihood (ML) estimation; Poisson statistic deviation; Positron emission tomography (PET); Sinograms