Bayesian inference based reconstruction for poisson statistics

Joyoni Dey, Louisiana State University
Jingzhu Xu, Louisiana State University
Narayan Bhusal, Louisiana State University
Dmytro Shumilov, Louisiana State University


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.