Tomographic Image Reconstruction with a Spatially Varying Gamma Mixture Prior

A spatially varying Gamma mixture model prior is employed for tomographic image reconstruction, ensuring effective noise elimination and the preservation of region boundaries. We define a line process, modeling edges between image segments, through appropriate Markov random field smoothness terms which are based on the Student’s t-distribution. The proposed algorithm consists of two alternating steps. In the first step, the mixture model parameters are automatically estimated from the image. In the second step, the reconstructed image is estimated by optimizing the maximum-a-posteriori criterion using the one-step-late expectation–maximization and preconditioned conjugate gradient algorithms. Numerical experiments on various photon-limited image scenarios show that the proposed model outperforms the compared state-of-the-art reconstruction models.