Single-frame image recovery using a Pearson type VII MRF

Compressive imaging and image super-resolution aim at recovering a high-resolution scene from its compressed or low resolution measurements. The main difficulty lies with the ill-posedness of the problem, and there is no consensus as to how best to formulate image models that can both impose smoothness and preserve the edges in the image. Here we develop a new image prior based on the Pearson type VII density integrated with a Markov random field model, which has desirable robustness properties. We develop a fully automated hyperparameter estimation procedure for this approach, which makes it advantageous in comparison with alternatives. Our recovery algorithm, although very simple to implement, it achieves statistically significant improvements over previous results in under-determined problem settings, and it is able to recover images that contain texture.