Tomographic image reconstruction withaspatially varying Gaussian mixture prior

A spatially varying Gaussian mixture model (SVGMM) prior is employed to ensure the preservation of region boundaries in penalized likelihood tomographic image reconstruction. Spatially varying Gaussian mixture models are characterized by the dependence of their mixing proportions on location (contextual mixing proportions) and they have been successfully used in image segmentation. The proposed model imposes a Student´s t-distribution on the local differences of the contextual mixing proportions and its parameters are automatically estimated by a variational Expectation-Maximization (EM) algorithm. The tomographic reconstruction algorithm is an iterative process consisting of alternating between an optimization of the SVGMM parameters and an optimization for updating the unknown image using also the EM algorithm. Numerical experiments on various photon limited image scenarios show that the proposed model is more accurate than the widely used Gibbs prior.