Resolution and noise properties of MAP reconstruction for fully 3-D PET

Jinyi Qi, Richard M. Leahy

Research output: Contribution to journalArticle

264 Citations (Scopus)

Abstract

We derive approximate analytical expressions for the local impulse response and covariance of images reconstructed from fully three-dimensional (3-D) positron emission tomography (PET) data using maximum a posteriori (MAP) estimation. These expressions explicitly account for the spatially variant detector response and sensitivity of a 3-D tomograph. The resulting spatially variant impulse response and covariance are computed using 3-D Fourier transforms. A truncated Gaussian distribution is used to account for the effect on the variance of the nonnegativity constraint used in MAP reconstruction. Using Monte Carlo simulations and phantom data from the microPET small animal scanner, we show that the approximations provide reasonably accurate estimates of contrast recovery and covariance of MAP reconstruction for priors with quadratic energy functions. We also describe how these analytical results can be used to achieve near-uniform contrast recovery throughout the reconstructed volume.

Original languageEnglish (US)
Pages (from-to)493-506
Number of pages14
JournalIEEE Transactions on Medical Imaging
Volume19
Issue number5
DOIs
StatePublished - May 2000

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Positron emission tomography
Normal Distribution
Fourier Analysis
Impulse response
Positron-Emission Tomography
Noise
Recovery
Gaussian distribution
Fourier transforms
Animals
Detectors
Monte Carlo simulation

ASJC Scopus subject areas

  • Biomedical Engineering
  • Radiology Nuclear Medicine and imaging
  • Radiological and Ultrasound Technology
  • Electrical and Electronic Engineering
  • Computer Science Applications
  • Computational Theory and Mathematics

Cite this

Resolution and noise properties of MAP reconstruction for fully 3-D PET. / Qi, Jinyi; Leahy, Richard M.

In: IEEE Transactions on Medical Imaging, Vol. 19, No. 5, 05.2000, p. 493-506.

Research output: Contribution to journalArticle

Qi, Jinyi ; Leahy, Richard M. / Resolution and noise properties of MAP reconstruction for fully 3-D PET. In: IEEE Transactions on Medical Imaging. 2000 ; Vol. 19, No. 5. pp. 493-506.
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