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Convergence of the maximum likelihood reconstruction algorithm for emission computed tomography.

Publication ,  Journal Article
Floyd, CE; Jaszczak, RJ; Coleman, RE
Published in: Phys Med Biol
April 1987

Convergence properties of the maximum likelihood estimator (MLE) for emission computed tomographic (ECT) image reconstruction are evaluated as a function of Poisson noise, precision of the assumed system resolution model and iteration number up to 10,000 iterations. In the ECT reconstruction problem, the photon-emitting source distribution is to be estimated from measurements of projections of the emitted photon flux. The MLE algorithm seeks a source distribution which will maximise the maximum likelihood function relating the estimated and the measured projections. A Monte Carlo model of the system transfer function of a single photon emission computed tomographic (SPECT) system allowed realistic projection data to be simulated from a known source distribution. Poisson noise was added to the Monte Carlo simulations. By using projection data from a known source distribution generated through a known system transfer function, we were able to simultaneously evaluate the convergence of both the projection estimations as well as the source distribution estimations. As predicted by theory, the estimates of the projections did continue to improve (or remain the same) for all combinations of Poisson noise (up to 10% RMS) and system resolution (+/- 10% of true value) tested. Convergence of source distribution estimates to the true value was found for up to 10,000 iterations only for low noise (0.1% RMS) with the correct resolution function. For all other combinations, there was some optimum iteration (between 30 and 400) after which the source estimate was degraded even though the estimate of the projections was improved.

Duke Scholars

Published In

Phys Med Biol

DOI

ISSN

0031-9155

Publication Date

April 1987

Volume

32

Issue

4

Start / End Page

463 / 476

Location

England

Related Subject Headings

  • Tomography, Emission-Computed
  • Probability
  • Nuclear Medicine & Medical Imaging
  • Monte Carlo Method
  • Models, Theoretical
  • Humans
  • Algorithms
  • 5105 Medical and biological physics
  • 1103 Clinical Sciences
  • 0903 Biomedical Engineering
 

Citation

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Floyd, C. E., Jaszczak, R. J., & Coleman, R. E. (1987). Convergence of the maximum likelihood reconstruction algorithm for emission computed tomography. Phys Med Biol, 32(4), 463–476. https://doi.org/10.1088/0031-9155/32/4/005
Floyd, C. E., R. J. Jaszczak, and R. E. Coleman. “Convergence of the maximum likelihood reconstruction algorithm for emission computed tomography.Phys Med Biol 32, no. 4 (April 1987): 463–76. https://doi.org/10.1088/0031-9155/32/4/005.
Floyd CE, Jaszczak RJ, Coleman RE. Convergence of the maximum likelihood reconstruction algorithm for emission computed tomography. Phys Med Biol. 1987 Apr;32(4):463–76.
Floyd, C. E., et al. “Convergence of the maximum likelihood reconstruction algorithm for emission computed tomography.Phys Med Biol, vol. 32, no. 4, Apr. 1987, pp. 463–76. Pubmed, doi:10.1088/0031-9155/32/4/005.
Floyd CE, Jaszczak RJ, Coleman RE. Convergence of the maximum likelihood reconstruction algorithm for emission computed tomography. Phys Med Biol. 1987 Apr;32(4):463–476.
Journal cover image

Published In

Phys Med Biol

DOI

ISSN

0031-9155

Publication Date

April 1987

Volume

32

Issue

4

Start / End Page

463 / 476

Location

England

Related Subject Headings

  • Tomography, Emission-Computed
  • Probability
  • Nuclear Medicine & Medical Imaging
  • Monte Carlo Method
  • Models, Theoretical
  • Humans
  • Algorithms
  • 5105 Medical and biological physics
  • 1103 Clinical Sciences
  • 0903 Biomedical Engineering