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 distributionnormalized emission intensity of the spatial poisson processis 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 kdimensions) 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 NormalInverse Wishart (NIW) model as base distribution of the Dirichlet Process. As in EMfamily 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 »
 Authors:

 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), 813 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 0094243X
 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 distributionnormalized emission intensity of the spatial poisson processis 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 kdimensions) 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 NormalInverse Wishart (NIW) model as base distribution of the Dirichlet Process. As in EMfamily 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 MAPEM.},
doi = {10.1063/1.2821285},
url = {https://www.osti.gov/biblio/21039277},
journal = {AIP Conference Proceedings},
issn = {0094243X},
number = 1,
volume = 954,
place = {United States},
year = {2007},
month = {11}
}