Blind deconvolution using a variational approach to parameter, image, and blur estimation.
Following the hierarchical Bayesian framework for blind deconvolution problems, in this paper, we propose the use of simultaneous autoregressions as prior distributions for both the image and blur, and gamma distributions for the unknown parameters (hyperparameters) of the priors and the image formation noise. We show how the gamma distributions on the unknown hyperparameters can be used to prevent the proposed blind deconvolution method from converging to undesirable image and blur estimates and also how these distributions can be inferred in realistic situations. We apply variational methods to approximate the posterior probability of the unknown image, blur, and hyperparameters and propose two different approximations of the posterior distribution. One of these approximations coincides with a classical blind deconvolution method. The proposed algorithms are tested experimentally and compared with existing blind deconvolution methods.
Molina
Rafael
R
Departamento de Ciencias de la Computación e I.A. Universidad de Granada, 18071 Granada, Spain. rms@decsai.ugr.es
Mateos
Javier
J
Katsaggelos
Aggelos K
AK
D000465:Algorithms; D016477:Artifacts; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D016247:Information Storage and Retrieval / Q000379:methods; D012044:Regression Analysis; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity