Image prior combination in super-resolution image reconstruction

In this paper a new combination of image priors is introduced and applied to Super Resolution (SR) image reconstruction. A sparse image prior based on the 1 norms of the horizontal and vertical first order differences is combined with a non-sparse SAR prior. Since, for a given observation model, each prior 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 minimize a linear convex combination of the Kullback-Leibler (KL) divergences associated with each posterior distribution. We find this distribution in closed form. The estimated HR images are compared with images provided by other SR reconstruction methods.