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“Bayesian Reconstruction of PET Images: Quantitative Methodology and Performance Analysis”
by Erkan Mumcuoglu, Richard Leahy and Simon Cherry
October 1995
We describe a practical statistical methodology for the reconstruction of quantitative PET images. Our approach is based on a Bayesian formulation of the imaging problem. The data are modeled as independent Poisson random variables and the image is modeled using a Markov random field smoothing prior. We describe a sequence of calibration procedures which are performed before reconstruction: (i) calculation of accurate attenuation correction factors from reprojected Bayesian reconstructions of the transmission image; (ii) estimation of the mean of the randoms component in the data; and (iii) computation of the scatter component in the data using a Klein-Nishina based scatter estimation method. The Bayesian estimate of the PET image is then reconstructed using a preconditioned conjugate gradient method. We performed a quantitation study with a realistic chest phantom in a Siemens/CTI ECAT931 system. Using 40 one minute frames, we computed the ensemble mean and variance over several regions of interest for absolute and relative activity. Mean and variance for the Bayesian estimates were compared with the results of filtered backprojection. These results indicate the potential of the method described to produce improved quantitative accuracy in ROI analysis when compared with the standard filtered backprojection method.