Noise properties of the EM algorithm. II. Monte Carlo simulations

D. W. Wilson, Benjamin Tsui, H. H. Barrett

Research output: Contribution to journalArticle

Abstract

In pt.I the authors derived a theoretical formulation for estimating the statistical properties of images reconstructed using the iterative maximum-likelihood expectation-maximization (ML-EM) algorithm. To gain insight into this complex problem, two levels of approximation were considered in the theory. These techniques revealed the dependence of the variance and covariance of the reconstructed image noise on the source distribution, imaging system transfer function, and iteration number. Here, a Monte Carlo approach was taken to study the noise properties of the ML-EM algorithm and to test the predictions of the theory. The study also served to evaluate the approximations used in the theory. Simulated data from phantoms were used in the Monte Carlo experiments. The ML-EM statistical properties were calculated from sample averages of a large number of images with different noise realizations. The agreement between the more exact form of the theoretical formulation and the Monte Carlo formulation was better than 10% in most cases examined, and for many situations the agreement was within the expected error of the Monte Carlo experiments. Results from the studies provide valuable information about the noise characteristics of ML-EM reconstructed images. Furthermore, the studies demonstrate the power of the theoretical and Monte Carlo approaches for investigating noise properties of statistical reconstruction algorithms.

Original languageEnglish (US)
Article number005
Pages (from-to)847-871
Number of pages25
JournalPhysics in Medicine and Biology
Volume39
Issue number5
DOIs
StatePublished - 1994
Externally publishedYes

Fingerprint

Maximum likelihood
Noise
formulations
simulation
Imaging systems
Transfer functions
approximation
transfer functions
Experiments
iteration
estimating
Monte Carlo simulation
predictions

ASJC Scopus subject areas

  • Radiological and Ultrasound Technology
  • Radiology Nuclear Medicine and imaging
  • Physics and Astronomy (miscellaneous)
  • Biomedical Engineering

Cite this

Noise properties of the EM algorithm. II. Monte Carlo simulations. / Wilson, D. W.; Tsui, Benjamin; Barrett, H. H.

In: Physics in Medicine and Biology, Vol. 39, No. 5, 005, 1994, p. 847-871.

Research output: Contribution to journalArticle

Wilson, D. W. ; Tsui, Benjamin ; Barrett, H. H. / Noise properties of the EM algorithm. II. Monte Carlo simulations. In: Physics in Medicine and Biology. 1994 ; Vol. 39, No. 5. pp. 847-871.
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