Using the Kullback-Leibler divergence to combine image priors in Super-Resolution image reconstruction

This paper is devoted to the combination of image priors in Super Resolution (SR) image reconstruction. Taking into account that each combination of a given observation model and a prior model produces a different posterior distribution of the underlying High Resolution (HR) image, the use of variational posterior distribution approximation on each posterior will produce as many posterior approximations as priors we want to combine. A unique approximation is obtained here by finding the distribution on the HR image given the observations that minimizes a linear convex combination of the Kullback-Leibler divergences associated with each posterior distribution. We find this distribution in closed form and also relate the proposed approach to other prior combination methods in the literature. The estimated HR images are compared with images provided by other SR reconstruction methods.