Bayesian combination of sparse and non-sparse priors in image super resolution

In this paper the application of image prior combinations to the Bayesian Super Resolution (SR) image registration and reconstruction problem is studied. Two sparse image priors, a Total Variation (TV) prior and a prior based on the ℓ1 norm of horizontal and vertical first-order differences (f.o.d.), are combined with a non-sparse Simultaneous Auto Regressive (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 approximation 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 Kullback–Leibler (KL) divergences. We find this distribution in closed form. The estimated HR images are compared with the ones obtained by other SR reconstruction methods.