Bayesian inference based reconstruction for poisson statistics

A new reconstruction method is explored using Bayesian inference for Poisson Statistics for emission tomography. The Gamma density function is chosen as the natural choice for the activity distribution at each voxel, being the conjugate-prior of Poisson distribution. The update equations of the shape and rate parameters for Gamma distribution are derived and tested on a simple 2D example using Metropolis-Hastings algorithm. The results show promise with quick convergence within ∼20 iterations and stable noise properties with iteration. A 3D algorithm and comparison with OSEM is underway.