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Ordered subset expectation maximization

About: Ordered subset expectation maximization is a research topic. Over the lifetime, 448 publications have been published within this topic receiving 11918 citations.


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TL;DR: Ordered subsets EM (OS-EM) provides a restoration imposing a natural positivity condition and with close links to the EM algorithm, applicable in both single photon (SPECT) and positron emission tomography (PET).
Abstract: The authors define ordered subset processing for standard algorithms (such as expectation maximization, EM) for image restoration from projections. Ordered subsets methods group projection data into an ordered sequence of subsets (or blocks). An iteration of ordered subsets EM is defined as a single pass through all the subsets, in each subset using the current estimate to initialize application of EM with that data subset. This approach is similar in concept to block-Kaczmarz methods introduced by Eggermont et al. (1981) for iterative reconstruction. Simultaneous iterative reconstruction (SIRT) and multiplicative algebraic reconstruction (MART) techniques are well known special cases. Ordered subsets EM (OS-EM) provides a restoration imposing a natural positivity condition and with close links to the EM algorithm. OS-EM is applicable in both single photon (SPECT) and positron emission tomography (PET). In simulation studies in SPECT, the OS-EM algorithm provides an order-of-magnitude acceleration over EM, with restoration quality maintained. >

3,740 citations

Journal Article
TL;DR: The general principles behind all EM algorithms are discussed and in detail the specific algorithms for emission and transmission tomography are derived and the specification of necessary physical features such as source and detector geometries are discussed.
Abstract: Two proposed likelihood models for emission and transmission image reconstruction accurately incorporate the Poisson nature of photon counting noise and a number of other relevant physical features As in most algebraic schemes, the region to be reconstructed is divided into small pixels For each pixel a concentration or attenuation coefficient must be estimated In the maximum likelihood approach these parameters are estimated by maximizing the likelihood (probability of the observations) EM algorithms are iterative techniques for finding maximum likelihood estimates In this paper we discuss the general principles behind all EM algorithms and derive in detail the specific algorithms for emission and transmission tomography The virtues of the EM algorithms include (a) accurate incorporation of a good physical model, (b) automatic inclusion of non-negativity constraints on all parameters, (c) an excellent measure of the quality of a reconstruction, and (d) global convergence to a single vector of parameter estimates We discuss the specification of necessary physical features such as source and detector geometries Actual reconstructions are deferred to a later time

1,921 citations

Journal ArticleDOI
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.
Abstract: The maximum likelihood (ML) expectation maximization (EM) approach in emission tomography has been very popular in medical imaging for several years. In spite of this, no satisfactory convergent modifications have been proposed for the regularized approach. Here, a modification of the EM algorithm is presented. The new method is a natural extension of the EM for maximizing likelihood with concave priors. Convergence proofs are given. >

506 citations

Journal ArticleDOI
TL;DR: The expectation maximization method is applied to find the a posteriori probability maximizer and is demonstrated to be superior to pure likelihood maximization, in that the penalty function prevents the occurrence of irregular high amplitude patterns in the image with a large number of iterations.
Abstract: The expectation maximization method for maximum likelihood image reconstruction in emission tomography, based on the Poisson distribution of the statistically independent components of the image and measurement vectors, is extended to a maximum aposteriori image reconstruction using a multivariate Gaussian a priori probability distribution of the image vector. The approach is equivalent to a penalized maximum likelihood estimation with a special choice of the penalty function. The expectation maximization method is applied to find the a posteriori probability maximizer. A simple iterative formula is derived for a penalty function that is a weighted sum of the squared deviations of image vector components from their a priori mean values. The method is demonstrated to be superior to pure likelihood maximization, in that the penalty function prevents the occurrence of irregular high amplitude patterns in the image with a large number of iterations (the so-called "checkerboard effect" or "noise artifact").

442 citations

Journal ArticleDOI
TL;DR: Current commercially available SPECT/CT technology using OSEM-3D reconstruction, scatter correction, and CT-based attenuation correction allows quantification of 99mTc radioactivity concentration in absolute terms within 3.6% in phantoms and 1.1% in patients with a focus on the bladder.
Abstract: We present a calibration method of a clinical SPECT/CT device for quantitative 99mTc SPECT. We use a commercially available reconstruction package including ordered-subset expectation maximization (OSEM) with depth-dependent 3-dimensional resolution recovery (OSEM-3D), CT-based attenuation correction, and scatter correction. We validated the method in phantom studies and applied it to images from patients injected with 99mTc-diphosponate. Methods: The following 3 steps were performed to derive absolute quantitative values from SPECT reconstructed images. In step 1, we used simulations to characterize the SPECT/CT system and derive emission recovery values for various imaging parameter settings. We simulated spheres of varying diameters and focused on the dependencies of activity estimation errors on structure size and position, pixel size, count density, and reconstruction parameters. In step 2, we cross-calibrated our clinical SPECT/CT system with the well counter using a large cylinder phantom. This step provided the mapping from image counts to kBq/mL. And in step 3, correction factors from steps 1 and 2 were applied to reconstructed images. We used a cylinder phantom with variable-sized spheres for verification of the method. For in vivo validation, SPECT/CT datasets from 16 patients undergoing 99mTc-diphosponate SPECT/CT examinations of the pelvis including the bladder were acquired. The radioactivity concentration in the patients9 urine served as the gold standard. Mean quantitative accuracy and SEs were calculated. Results: In the phantom experiments, the mean accuracy in quantifying radioactivity concentration in absolute terms was within 3.6% (SE, 8.0%), with a 95% confidence interval between −19.4% and +12.2%. In the patient studies, the mean accuracy was within 1.1% (SE, 8.4%), with a 95% confidence interval between −15.4% and +17.5%. Conclusion: Current commercially available SPECT/CT technology using OSEM-3D reconstruction, scatter correction, and CT-based attenuation correction allows quantification of 99mTc radioactivity concentration in absolute terms within 3.6% in phantoms and 1.1% in patients with a focus on the bladder. This opens up the opportunity of SPECT quantitation entering the routine clinical arena. Still, the imprecision caused by unavoidable measurement errors is a dominant factor for absolute quantitation in a clinical setup.

224 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202119
202016
201914
201817
201719
201625