STATISTICAL MODELING OF ATTENUATION-CORRECTED PET DATA WITH APPLICATION TO RECONSTRUCTION OF REGIONAL TIME ACTIVITY CURVES

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.