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In this paper, we provide a novel method for the estimation of unknownparameters of the Gaussian Mixture Model (GMM) in Positron Emission Tomography(PET). A vast majority of PET imaging methods are based on reconstruction modelthat is defined by values on some pixel/voxel grid. Instead, we propose acontinuous parametric GMM model. Usually, Expectation-Maximization (EM)iterations are used to obtain the GMM model parameters from some set ofpoint-wise measurements. The challenge of PET reconstruction is that themeasurement is represented by the so called lines of response (LoR), instead ofpoints. The goal is to estimate the unknown parameters of the Gaussian mixturedirectly from a relatively small set of LoR-s. Estimation of unknown parametersrelies on two facts: the marginal distribution theorem of the multivariatenormal distribution; and the properties of the marginal distribution of LoR-s.We propose an iterative algorithm that resembles the maximum-likelihood methodto determine the unknown parameters. Results show that the estimated parametersfollow the correct ones with a great accuracy. The result is promising, sincethe high-quality parametric reconstruction model can be obtained from lowerdose measurements, and is directly suitable for further processing.

Accurate PET Reconstruction from Reduced Set of Measurements based on GMM