@article{Salvador2013a,
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 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. {\textcopyright} 2012 Elsevier Inc.},
author = {Villena, S. and Vega, M. and Babacan, S.D. and Molina, R. and Katsaggelos, A.K.},
doi = {10.1016/j.dsp.2012.10.002},
issn = {10512004},
journal = {Digital Signal Processing},
keywords = {Bayesian methods,Parameter estimation,Super resolution,Total variation,Variational methods},
month = {mar},
number = {2},
pages = {530--541},
title = {{Bayesian combination of sparse and non-sparse priors in image super resolution}},
url = {https://linkinghub.elsevier.com/retrieve/pii/S1051200412002400},
volume = {23},
year = {2013}
}

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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. © 2012 Elsevier Inc.","author":[{"propositions":[],"lastnames":["Villena"],"firstnames":["S."],"suffixes":[]},{"propositions":[],"lastnames":["Vega"],"firstnames":["M."],"suffixes":[]},{"propositions":[],"lastnames":["Babacan"],"firstnames":["S.D."],"suffixes":[]},{"propositions":[],"lastnames":["Molina"],"firstnames":["R."],"suffixes":[]},{"propositions":[],"lastnames":["Katsaggelos"],"firstnames":["A.K."],"suffixes":[]}],"doi":"10.1016/j.dsp.2012.10.002","issn":"10512004","journal":"Digital Signal Processing","keywords":"Bayesian methods,Parameter estimation,Super resolution,Total variation,Variational methods","month":"mar","number":"2","pages":"530–541","title":"Bayesian combination of sparse and non-sparse priors in image super resolution","url":"https://linkinghub.elsevier.com/retrieve/pii/S1051200412002400","volume":"23","year":"2013","bibtex":"@article{Salvador2013a,\nabstract = {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. {\\textcopyright} 2012 Elsevier Inc.},\nauthor = {Villena, S. and Vega, M. and Babacan, S.D. and Molina, R. and Katsaggelos, A.K.},\ndoi = {10.1016/j.dsp.2012.10.002},\nissn = {10512004},\njournal = {Digital Signal Processing},\nkeywords = {Bayesian methods,Parameter estimation,Super resolution,Total variation,Variational methods},\nmonth = {mar},\nnumber = {2},\npages = {530--541},\ntitle = {{Bayesian combination of sparse and non-sparse priors in image super resolution}},\nurl = {https://linkinghub.elsevier.com/retrieve/pii/S1051200412002400},\nvolume = {23},\nyear = {2013}\n}\n","author_short":["Villena, S.","Vega, M.","Babacan, S.","Molina, R.","Katsaggelos, A."],"key":"Salvador2013a","id":"Salvador2013a","bibbaseid":"villena-vega-babacan-molina-katsaggelos-bayesiancombinationofsparseandnonsparsepriorsinimagesuperresolution-2013","role":"author","urls":{"Paper":"https://linkinghub.elsevier.com/retrieve/pii/S1051200412002400"},"keyword":["Bayesian methods","Parameter estimation","Super resolution","Total variation","Variational methods"],"metadata":{"authorlinks":{}}},"bibtype":"article","biburl":"https://sites.northwestern.edu/ivpl/files/2023/06/IVPL_Updated_publications-1.bib","dataSources":["KTWAakbPXLGfYseXn","ePKPjG8C6yvpk4mEK","ya2CyA73rpZseyrZ8","D8k2SxfC5dKNRFgro","7Dwzbxq93HWrJEhT6","qhF8zxmGcJfvtdeAg","fvDEHD49E2ZRwE3fb","H7crv8NWhZup4d4by","DHqokWsryttGh7pJE","vRJd4wNg9HpoZSMHD","sYxQ6pxFgA59JRhxi","w2WahSbYrbcCKBDsC","XasdXLL99y5rygCmq","3gkSihZQRfAD2KBo3","t5XMbyZbtPBo4wBGS","bEpHM2CtrwW2qE8FP","teJzFLHexaz5AQW5z"],"keywords":["bayesian methods","parameter estimation","super resolution","total variation","variational methods"],"search_terms":["bayesian","combination","sparse","non","sparse","priors","image","super","resolution","villena","vega","babacan","molina","katsaggelos"],"title":"Bayesian combination of sparse and non-sparse priors in image super resolution","year":2013}