Journal
IEEE TRANSACTIONS ON MEDICAL IMAGING
Volume 19, Issue 5, Pages 493-506Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/42.870259
Keywords
covariance; fully 3-D PET; image reconstruction; MAP estimation; positron emission tomography; resolution analysis; uniform resolution
Categories
Funding
- NCI NIH HHS [R01 CA59794] Funding Source: Medline
- NHLBI NIH HHS [P01 HL25840] Funding Source: Medline
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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.
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