Blind Deconvolution Using a Variational Approach to Parameter, Image, and Blur Estimation

Abstract

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.

Image Blur Classification and Parameter Identification Using Two-stage Deep Belief Networks

“…The image blurring can be modeled as the following degradation process from the high exposed image to the observed image [24]:…”

Extensions of the Justen–Ramlau blind deconvolution method

“…Most of the available blind deconvolution methods are iterative; see, e.g., [2, 3,5,6,7,10,12,14,15,16,18,19,21] and references therein. Recently, Justen and Ramlau [13] introduced a novel non-iterative method.…”

Generalized Gaussian Markov random field image restoration using variational distribution approximation

“…Several methods tackle the deconvolution problem using the variational approach (see, for example, [5][6] [7][8]).…”

“…Using the variational framework we utilize a hierarchical Bayesian paradigm (see, for example, [7][9]) to jointly provide estimates of the posterior distributions of the restored image and the hyperparameters when a GGMRF prior is used. We develop two algorithms using our framework.…”