An additive poisson data modeling of attenuation map reconstruction from post-injection positron emission tomography transmission scan

We present an additive Poisson data modeling of attenuation map reconstruction from post-injection positron emission tomography transmission scan. The transmission scan data are modeled as a collection of independent Poisson observations which consist of true transmission, cross-contamination emission and random coincidences. The mean values of cross-contamination emission and random data are estimated by using Luk's approximation and Zaers' method, respectively. The unknown attenuation map is also modeled using a Gibbs image prior. Under the paradigm of Bayesian statistics, a pre-conditioned conjugate gradient algorithm is then used to compute a maximum a posteriori estimate of the attenuation map by maximizing over the posterior density. Evaluations are conducted on clinical data collected from a CTI EXACT HR+ scanner. Experimental results have indicated that the reconstructed results of attenuation map by the proposed reconstruction algorithm match well with theoretical values of soft tissue, bone and lung under 511 keV photons.