Using Local Median as the Location of the Prior Distribution in Iterative Emission Tomography Image Reconstruction

Iterative reconstruction algorithms like MLEM (Maximum Likelihood Expectation Maximization) can be regularized using a weighted roughness penalty term according to certain a priori assumptions of the desired image. In the MRP (Median Root Prior) algorithm the penalty is set according to the deviance of a pixel from the local median. This allows both noise reduction and edge preservation. The prior distribution is Gaussian located around the median of a neighborhood of the pixel. Non-monotonic details smaller than a given limit are considered as noise and are penalized. Thus, MRP implicitly contains the general description of the characteristics of the desired emission image, and good localization of tissue boundaries is achieved without anatomical data. In contrast to the MLEM method, the number of iterations needs not be restricted and unlike many other Bayesian methods MRP has only one parameter. The penalty term can be applied to various iterative reconstruction algorithms. The assumption that the true pixel value is close to the local median applies to any emission images, including the 3D acquisition and images reconstructed from parametric sinograms.