Journal ArticleDOI
The Use of Sieves to Stabilize Images Produced with the EM Algorithm for Emission Tomography
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TLDR
It is shown how Grenader's method of sieves can be used with the EM algorithm to remove the instability and thereby decrease the 'noise' artifact introduced into the images with little or no increase in computational complexity.Abstract:
Images produced in emission tomography with the expectation-maximization (EM) algorithm have been observed to become more 'noisy' as the algorithm converges towards the maximum-likelihood estimate. We argue in this paper that there is an instability which is fundamental to maximum-likelihood estimation as it is usually applied and, therefore, is not a result of using the EM algorithm, which is but one numerical implementation for producing maximum-likelihood estimates. We show how Grenader's method of sieves can be used with the EM algorithm to remove the instability and thereby decrease the 'noise' artifact introduced into the images with little or no increase in computational complexity.read more
Citations
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Bayesian reconstructions from emission tomography data using a modified EM algorithm
TL;DR: This method builds on the expectation-maximization approach to maximum likelihood reconstruction from emission tomography data, but aims instead at maximum posterior probability estimation, which takes account of prior belief about smoothness in the isotope concentration.
Journal ArticleDOI
Computational anatomy: an emerging discipline
Ulf Grenander,Michael I. Miller +1 more
TL;DR: In this article, the authors formalize the Brown/Washington University model of anatomy following the global pattern theory introduced in [1, 2], in which anatomies are represented as deformable templates, collections of 0,1,2,3-dimensional manifolds.
Journal ArticleDOI
A generalized EM algorithm for 3-D Bayesian reconstruction from Poisson data using Gibbs priors
T. Hebert,Richard M. Leahy +1 more
TL;DR: A generalized expectation-maximization (GEM) algorithm is developed for Bayesian reconstruction, based on locally correlated Markov random-field priors in the form of Gibbs functions and on the Poisson data model, which reduces to the EM maximum-likelihood algorithm.
Journal ArticleDOI
Penalized weighted least-squares image reconstruction for positron emission tomography
TL;DR: Qualitative results suggest that the streak artifacts common to the FBP method are nearly eliminated by the PWLS+SOR method, and indicate that the proposed method for weighting the measurements is a significant factor in the improvement over FBP.
Journal ArticleDOI
A local update strategy for iterative reconstruction from projections
TL;DR: It is shown that Bayesian segmentation using Gauss-Seidel iteration produces useful estimates at much lower signal-to-noise ratios than required for continuously valued reconstruction.
References
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Journal ArticleDOI
Maximum likelihood from incomplete data via the EM algorithm
Journal ArticleDOI
On Estimation of a Probability Density Function and Mode
TL;DR: In this paper, the problem of the estimation of a probability density function and of determining the mode of the probability function is discussed. Only estimates which are consistent and asymptotically normal are constructed.
Journal ArticleDOI
Maximum Likelihood Reconstruction for Emission Tomography
L. A. Shepp,Y. Vardi +1 more
TL;DR: In this paper, the authors proposed a more accurate general mathematical model for ET where an unknown emission density generates, and is to be reconstructed from, the number of counts n*(d) in each of D detector units d. Within the model, they gave an algorithm for determining an estimate? of? which maximizes the probability p(n*|?) of observing the actual detector count data n* over all possible densities?.
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Remarks on Some Nonparametric Estimates of a Density Function
TL;DR: In this article, some aspects of the estimation of the density function of a univariate probability distribution are discussed, and the asymptotic mean square error of a particular class of estimates is evaluated.
Journal ArticleDOI
Nonparametric roughness penalties for probability densities
TL;DR: A method is presented here that should help to overcome the difficulty of deciding whether “bumps” are genuinely in the population.
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