Measured PET Data Characterization with the Negative Binomial Distribution Model

Luigi Landini,Vincenzo Positano,Maria Filomena Santarelli

doi:10.1007/s40846-017-0236-2

Abstract

Accurate statistical model of PET measurements is a prerequisite for a correct image reconstruction when using statistical image reconstruction algorithms, or when pre-filtering operations must be performed. Although radioactive decay follows a Poisson distribution, deviation from Poisson statistics occurs on projection data prior to reconstruction due to physical effects, measurement errors, correction of scatter and random coincidences. Modelling projection data can aid in understanding the statistical nature of the data in order to develop efficient processing methods and to reduce noise. This paper outlines the statistical behaviour of measured emission data evaluating the goodness of fit of the negative binomial (NB) distribution model to PET data for a wide range of emission activity values. An NB distribution model is characterized by the mean of the data and the dispersion parameter α that describes the deviation from Poisson statistics. Monte Carlo simulations were performed to evaluate: (a) the performances of the dispersion parameter α estimator, (b) the goodness of fit of the NB model for a wide range of activity values. We focused on the effect produced by correction for random and scatter events in the projection (sinogram) domain, due to their importance in quantitative analysis of PET data. The analysis developed herein allowed us to assess the accuracy of the NB distribution model to fit corrected sinogram data, and to evaluate the sensitivity of the dispersion parameter α to quantify deviation from Poisson statistics. By the sinogram ROI-based analysis, it was demonstrated that deviation on the measured data from Poisson statistics can be quantitatively characterized by the dispersion parameter α, in any noise conditions and corrections.

Highlights

In Positron emission tomography (PET) tomography, a radioactive isotope containing emitting positrons is fed into the body to produce a body’s metabolism map
6 Conclusion In PET data analysis, the importance of accurately modeling data is paramount for helping us to understand the statistical nature of the data in order to develop efficient reconstruction algorithms and processing methods that reduce noise
The negative binomial (NB) distribution seems suitable for assessing the statistical nature of the sinogram data, when they deviate from Poisson, due to its capacity to measure overdispersion in a wide range of k values

Summary

Introduction

In PET tomography, a radioactive isotope containing emitting positrons is fed into the body to produce a body’s metabolism map. In routine use PET scanners, deviation from Poisson statistics occurs and has different causes Such causes can compromise accuracy in determining the system matrix when not suitably accounted for. One cause of deviation from Poisson statistics is the correction of scatter and random coincidences on the projection data (sinograms) [4, 6]: once corrections are applied, the data are no longer Poisson distributed. It compromises the estimation of the emission density based on ML reconstruction [7, 8]. In such papers an improvement in the model accuracy and/or in the computation are demonstrated; no quantitative evaluation of deviation from Poisson statistics is defined

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