Statistical Modeling and Reconstruction of Randoms Precorrected PET Data
Quanzheng LiLeahy, R.M.
Signal & Image Process. Inst., Univ. of Southern California, Los Angeles, CA
This paper appears in: Medical Imaging, IEEE Transactions on Publication Date: Dec. 2006
Volume: 25
,
Issue: 12
On page(s):
1565
- 1572
Location: Davis, CA, USA
ISSN: 0278-0062
Digital Object Identifier: 10.1109/TMI.2006.884193
Current Version Published: 2006-11-30
Abstract
Randoms precorrected positron emission tomography (PET) data is formed as the difference of two Poisson random variables. Its exact probability mass function (PMF) is inconvenient for use in likelihood-based iterative image reconstruction as it contains an infinite summation. The shifted Poisson model is a tractable approximation to this PMF but requires that negative values are truncated, resulting in positively biased reconstructions in low count studies. Here we analyze the properties of the exact PMF and propose a simple but accurate approximation that allows negative valued data. We investigate the properties of this approximation and demonstrate its application to penalized maximum likelihood image reconstruction
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