Abstract
Correction for tissue attenuation is the most important factor affecting the Poisson characteristics of positron emission tomography (PET) data. Although a weighting scheme incorporating the attenuation correction factors in the update rule of expectation-maximization (EM) image reconstruction algorithm has previously been presented, no exact distribution of pre-corrected measurements has been proposed to date. This paper introduces a fixed multiplicative Poisson distribution to model the PET data compensated for the effect of photon attenuation. We show that the attenuation-weighted EM update rule can be derived in a formal way via maximizing the log-likelihood of pre-corrected measurements. We use the proposed distribution to develop a joint penalized-likelihood approach for reconstruction of regional time activity curves (TACs) and regions-of-interest from dynamic brain PET projection data. The new method yields lower error in reconstructed TACs compared to the joint reconstruction approach based on ordinary Poisson approximation.
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