Fully 3D Bayesian image reconstruction for the ECAT EXACT HR+

A fully 3D Bayesian method is described for high resolution reconstruction of images from the Siemens/CTI ECAT EXACT HR+ whole body positron emission tomography (PET) scanner. To maximize resolution recovery from the system we model depth dependent geometric efficiency, intrinsic detector efficiency, photon pair non-colinearity, crystal penetration and inter-crystal scatter. We also explicitly model the effects of axial rebinning and angular mashing on the detection probability or system matrix. By fully exploiting sinogram symmetries and using a factored system matrix and automated indexing schemes, we are able to achieve substantial savings in both the storage size and time required to compute forward and backward projections. Reconstruction times are further reduced using multi-threaded programming on a four processor Unix server. Bayesian reconstructions are computed using a Huber prior and a shifted-Poisson likelihood model that accounts for the effects of randoms subtraction and scatter. Reconstructions of phantom data show that the 3D Bayesian method can achieve improved FWHM resolution and contrast recovery ratios at matched background noise levels compared to both the 3D reprojection method and an OSEM method based on the shifted-Poisson model.