Journal ArticleDOI
Performance evaluation of an iterative image reconstruction algorithm for positron emission tomography
Gabor T. Herman,Dewey Odhner +1 more
TLDR
In this article, an image reconstruction method motivated by positron emission tomography (PET) is discussed and an iterative approach which requires the solution of simple quadratic equations is proposed.Abstract:
An image reconstruction method motivated by positron emission tomography (PET) is discussed. The measurements tend to be noisy and so the reconstruction method should incorporate the statistical nature of the noise. The authors set up a discrete model to represent the physical situation and arrive at a nonlinear maximum a posteriori probability (MAP) formulation of the problem. An iterative approach which requires the solution of simple quadratic equations is proposed. The authors also present a methodology which allows them to experimentally optimize an image reconstruction method for a specific medical task and to evaluate the relative efficacy of two reconstruction methods for a particular task in a manner which meets the high standards set by the methodology of statistical hypothesis testing. The new MAP algorithm is compared to a method which maximizes likelihood and with two variants of the filtered backprojection method. >read more
Citations
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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
Algebraic reconstruction techniques can be made computationally efficient (positron emission tomography application)
Gabor T. Herman,L.B. Meyer +1 more
TL;DR: Algebraic reconstruction techniques (ART) are iterative procedures for recovering objects from their projections as discussed by the authors, which is claimed to produce high-quality reconstructions with excellent computational efficiency This is demonstrated by an example based on a particular (but realistic) medical imaging task, showing that ART can match the performance of the standard expectation-maximization approach for maximizing likelihood, but at an order of magnitude less computational cost.
Journal ArticleDOI
A modified expectation maximization algorithm for penalized likelihood estimation in emission tomography
TL;DR: The new method is a natural extension of the EM for maximizing likelihood with concave priors for emission tomography and convergence proofs are given.
Journal ArticleDOI
A unified approach to statistical tomography using coordinate descent optimization
TL;DR: This work proposes a new approach to statistically optimal image reconstruction based on direct optimization of the MAP criterion, which requires approximately the same amount of computation per iteration as EM-based approaches, but the new method converges much more rapidly.
Journal ArticleDOI
A row-action alternative to the EM algorithm for maximizing likelihood in emission tomography
J. Browne,A.B. de Pierro +1 more
TL;DR: The authors present a row-action maximum likelihood algorithm (RAMLA) as an alternative to the EM algorithm for maximizing the Poisson likelihood in ECT and show that their modification converges to a ML solution whereas the standard OS-EM does not.
References
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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?.
Journal ArticleDOI
Algebraic Reconstruction Techniques (ART) for three-dimensional electron microscopy and X-ray photography
TL;DR: The method works for totally asymmetric objects, and requires little computer time or storage, and is also applicable to X-ray photography, and may greatly reduce the exposure compared to current methods of body-section radiography.
Book
Image reconstruction from projections
TL;DR: The article addresses the design, implementation, evaluation, and application of computer algorithms for solving the reconstruction problem in various biomedical areas and emphasizes the essential role of computers.
Journal ArticleDOI
A Statistical Model for Positron Emission Tomography
TL;DR: In this article, a mathematical model tailored to the physics of positron emissions is presented, and the model is used to describe the image reconstruction problem of PET as a standard problem in statistical estimation from incomplete data.