Dynamic GMRF priors for MAP reconstructions

The maximum a posteriori method has been intensively studied in the literature of tomographic reconstructions, especially in the noisy emission computer tomography. It is well acknowledged that the quality of reconstructed images from MAP could be improved by a carefully chosen prior. The prior not only improve the condition number of the optimization problem, but also couple in information about the object being imaged. Here, we propose a new dynamic Gaussian Markov Random Field (GMRF) prior extended from a Membrane prior. The dynamic GMRF prior provides adaptive penalty scheme according to signal magnitude. It could be realized with little extra computational load compared to a Membrane prior, but could supply more flexible and better performance than the membrane prior. The idea is generalizable to other priors. We compare the performance of MAP reconstructions by simulations with an Membrane prior favoring uniform smoothness and with this new dynamic GMRF prior favoring nonuniform smoothness that correlates with signal magnitudes by simulations. Our results show that the dynamic GMRF prior exhibits improved resolution and contrast for high value region and visually improves the lesion-detectability.