{"title":"Parametric GMM reconstruction for PET imaging from a reduced set of measurements","authors":"Tomislav Matulić, Damir Seršić","doi":"10.1016/j.sigpro.2025.110181","DOIUrl":null,"url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":49523,"journal":{"name":"Signal Processing","volume":"238 ","pages":"Article 110181"},"PeriodicalIF":3.4000,"publicationDate":"2025-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Signal Processing","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0165168425002956","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ENGINEERING, ELECTRICAL & ELECTRONIC","Score":null,"Total":0}
引用次数: 0
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.
期刊介绍:
Signal Processing incorporates all aspects of the theory and practice of signal processing. It features original research work, tutorial and review articles, and accounts of practical developments. It is intended for a rapid dissemination of knowledge and experience to engineers and scientists working in the research, development or practical application of signal processing.
Subject areas covered by the journal include: Signal Theory; Stochastic Processes; Detection and Estimation; Spectral Analysis; Filtering; Signal Processing Systems; Software Developments; Image Processing; Pattern Recognition; Optical Signal Processing; Digital Signal Processing; Multi-dimensional Signal Processing; Communication Signal Processing; Biomedical Signal Processing; Geophysical and Astrophysical Signal Processing; Earth Resources Signal Processing; Acoustic and Vibration Signal Processing; Data Processing; Remote Sensing; Signal Processing Technology; Radar Signal Processing; Sonar Signal Processing; Industrial Applications; New Applications.