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Title: A Nonparametric Bayesian Approach For Emission Tomography Reconstruction

Abstract

We introduce a PET reconstruction algorithm following a nonparametric Bayesian (NPB) approach. In contrast with Expectation Maximization (EM), the proposed technique does not rely on any space discretization. Namely, the activity distribution--normalized emission intensity of the spatial poisson process--is considered as a spatial probability density and observations are the projections of random emissions whose distribution has to be estimated. This approach is nonparametric in the sense that the quantity of interest belongs to the set of probability measures on R{sup k} (for reconstruction in k-dimensions) and it is Bayesian in the sense that we define a prior directly on this spatial measure. In this context, we propose to model the nonparametric probability density as an infinite mixture of multivariate normal distributions. As a prior for this mixture we consider a Dirichlet Process Mixture (DPM) with a Normal-Inverse Wishart (NIW) model as base distribution of the Dirichlet Process. As in EM-family reconstruction, we use a data augmentation scheme where the set of hidden variables are the emission locations for each observed line of response in the continuous object space. Thanks to the data augmentation, we propose a Markov Chain Monte Carlo (MCMC) algorithm (Gibbs sampler) which is able to generate drawsmore » from the posterior distribution of the spatial intensity. A difference with EM is that one step of the Gibbs sampler corresponds to the generation of emission locations while only the expected number of emissions per pixel/voxel is used in EM. Another key difference is that the estimated spatial intensity is a continuous function such that there is no need to compute a projection matrix. Finally, draws from the intensity posterior distribution allow the estimation of posterior functionnals like the variance or confidence intervals. Results are presented for simulated data based on a 2D brain phantom and compared to Bayesian MAP-EM.« less

Authors:
;  [1]
  1. CEA Saclay, Electronics and Signal Processing Laboratory, 91191 Gif sur Yvette (France)
Publication Date:
OSTI Identifier:
21039277
Resource Type:
Journal Article
Journal Name:
AIP Conference Proceedings
Additional Journal Information:
Journal Volume: 954; Journal Issue: 1; Conference: 27. International workshop on Bayesian inference and maximum entropy methods in science and engineering, Saratoga Springs, NY (United States), 8-13 Jul 2007; Other Information: DOI: 10.1063/1.2821285; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0094-243X
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGORITHMS; COMPUTERIZED SIMULATION; DENSITY; DISTRIBUTION; EMISSION; HIDDEN VARIABLES; IMAGE PROCESSING; MARKOV PROCESS; MIXTURES; MONTE CARLO METHOD; MULTIVARIATE ANALYSIS; PHANTOMS; POSITRON COMPUTED TOMOGRAPHY; PROBABILITY; RANDOMNESS

Citation Formats

Barat, Eric, and Dautremer, Thomas. A Nonparametric Bayesian Approach For Emission Tomography Reconstruction. United States: N. p., 2007. Web. doi:10.1063/1.2821285.
Barat, Eric, & Dautremer, Thomas. A Nonparametric Bayesian Approach For Emission Tomography Reconstruction. United States. https://doi.org/10.1063/1.2821285
Barat, Eric, and Dautremer, Thomas. 2007. "A Nonparametric Bayesian Approach For Emission Tomography Reconstruction". United States. https://doi.org/10.1063/1.2821285.
@article{osti_21039277,
title = {A Nonparametric Bayesian Approach For Emission Tomography Reconstruction},
author = {Barat, Eric and Dautremer, Thomas},
abstractNote = {We introduce a PET reconstruction algorithm following a nonparametric Bayesian (NPB) approach. In contrast with Expectation Maximization (EM), the proposed technique does not rely on any space discretization. Namely, the activity distribution--normalized emission intensity of the spatial poisson process--is considered as a spatial probability density and observations are the projections of random emissions whose distribution has to be estimated. This approach is nonparametric in the sense that the quantity of interest belongs to the set of probability measures on R{sup k} (for reconstruction in k-dimensions) and it is Bayesian in the sense that we define a prior directly on this spatial measure. In this context, we propose to model the nonparametric probability density as an infinite mixture of multivariate normal distributions. As a prior for this mixture we consider a Dirichlet Process Mixture (DPM) with a Normal-Inverse Wishart (NIW) model as base distribution of the Dirichlet Process. As in EM-family reconstruction, we use a data augmentation scheme where the set of hidden variables are the emission locations for each observed line of response in the continuous object space. Thanks to the data augmentation, we propose a Markov Chain Monte Carlo (MCMC) algorithm (Gibbs sampler) which is able to generate draws from the posterior distribution of the spatial intensity. A difference with EM is that one step of the Gibbs sampler corresponds to the generation of emission locations while only the expected number of emissions per pixel/voxel is used in EM. Another key difference is that the estimated spatial intensity is a continuous function such that there is no need to compute a projection matrix. Finally, draws from the intensity posterior distribution allow the estimation of posterior functionnals like the variance or confidence intervals. Results are presented for simulated data based on a 2D brain phantom and compared to Bayesian MAP-EM.},
doi = {10.1063/1.2821285},
url = {https://www.osti.gov/biblio/21039277}, journal = {AIP Conference Proceedings},
issn = {0094-243X},
number = 1,
volume = 954,
place = {United States},
year = {2007},
month = {11}
}