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Titolo:
NOISE PROPERTIES OF THE EM ALGORITHM .1. THEORY
Autore:
BARRETT HH; WILSON DW; TSUI BMW;
Indirizzi:
UNIV ARIZONA,DEPT RADIOL TUCSON AZ 85721 UNIV ARIZONA,CTR OPT SCI TUCSON AZ 85724 UNIV N CAROLINA,DEPT BIOMED ENGN CHAPEL HILL NC 27514 UNIV N CAROLINA,DEPT RADIOL CHAPEL HILL NC 27514
Titolo Testata:
Physics in medicine and biology
fascicolo: 5, volume: 39, anno: 1994,
pagine: 833 - 846
SICI:
0031-9155(1994)39:5<833:NPOTEA>2.0.ZU;2-#
Fonte:
ISI
Lingua:
ENG
Soggetto:
MAXIMUM-LIKELIHOOD RECONSTRUCTION; EMISSION TOMOGRAPHY; IMAGES; DISTRIBUTIONS; SPECT;
Tipo documento:
Article
Natura:
Periodico
Settore Disciplinare:
Science Citation Index Expanded
Citazioni:
28
Recensione:
Indirizzi per estratti:
Citazione:
H.H. Barrett et al., "NOISE PROPERTIES OF THE EM ALGORITHM .1. THEORY", Physics in medicine and biology, 39(5), 1994, pp. 833-846

Abstract

The expectation-maximization (EM) algorithm is an important tool for maximum-likelihood (ML) estimation and image reconstruction, especially in medical imaging. It is a nonlinear iterative algorithm that attempts to find the ML estimate of the object that produced a data set. The convergence of the algorithm and other deterministic properties are well established, but relatively little is known about how noise in the data influences noise in the final reconstructed image. In this paper we present a detailed treatment of these statistical properties. Thespecific application we have in mind is image reconstruction in emission tomography, but the results are valid for any application of the EM algorithm in which the data set can be described by Poisson statistics. We show that the probability density function for the grey level at a pixel in the image is well approximated by a log-normal law. An expression is derived for the variance of the grey level and for pixel-to-pixel covariance. The variance increases rapidly with iteration number at first, but eventually saturates as the ML estimate is approached. Moreover, the variance at any iteration number has a factor proportional to the square of the mean image (though other factors may also depend on the mean image), so a map of the standard deviation resembles the object itself. Thus low-intensity regions of die image tend to have low noise. By contrast, linear reconstruction methods, such as filtered back-projection in tomography, show a much more global noise pattern, with high-intensity regions of the object contributing to noise atrather distant low-intensity regions. The theoretical results of thispaper depend on two approximations, but in the second paper in this series we demonstrate through Monte Carlo simulation that the approximations are justified over a wide range of conditions in emission tomography. The theory can, therefore, be used as a basis for calculation ofobjective figures of merit for image quality.

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Documento generato il 20/01/20 alle ore 23:10:42