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

Authors:
S. Villena;M. Vega;S. D. Babacan;R. Molina;A. K. Katsaggelos
Affiliations:
Dept. de Lenguajes y Sistemas Informáticos, Universidad de Granada, 18071 Granada, Spain;Dept. de Lenguajes y Sistemas Informáticos, Universidad de Granada, 18071 Granada, Spain;Beckman Institute University of Illinois at Urbana-Cahmpaign, USA;Dept. de Ciencias de la Computación e I.A., Universidad de Granada, 18071 Granada, Spain;Dept. of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL 60208-3118, USA
Venue:
Digital Signal Processing
Year:
2013

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Abstract

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 @?1 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.