Accurate PET Reconstruction from Reduced Set of Measurements based on GMM

TL;DR

This paper introduces a novel continuous parametric GMM approach for PET image reconstruction from limited line-of-response measurements, enabling accurate parameter estimation with fewer measurements and lower radiation doses.

Contribution

It proposes a new GMM-based PET reconstruction method that directly estimates parameters from LoRs, reducing measurement requirements compared to traditional pixel-based models.

Findings

Parameters estimated with high accuracy.

Reconstruction quality from fewer measurements.

Potential for lower dose PET imaging.

Abstract

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