Parametric GMM reconstruction for PET imaging from a reduced set of measurements

Abstract

In this paper, we present a novel method for estimating the unknown parameters of the Gaussian Mixture Model (GMM) in Positron Emission Tomography (PET). Most PET imaging methods are based on reconstruction models defined by values on a pixel or voxel grid. Instead, we propose a continuous parametric GMM model. Typically, Expectation–Maximization (EM) iterations are used to obtain GMM parameters from a set of point-wise measurements. The challenge in PET reconstruction is that measurements are represented by lines instead of points. The goal is to estimate the unknown parameters of the Gaussian mixture directly from a relatively small set of lines. Estimation relies on two key facts: the marginal distribution theorem of the multivariate normal distribution and the properties of the marginal distribution of lines. We propose an iterative algorithm resembling the maximum-likelihood method to determine the unknown parameters. Results show that the estimated parameters closely match the true ones with great accuracy. This promising result indicates that a high-quality parametric reconstruction model can be obtained from lower dose measurements, making it directly suitable for further processing.