Blind deconvolution of images corrupted by Gaussian noise using Expectation Propagation

Blind image deconvolution consists of inferring an image from its blurry and noisy version when the blur is unknown. To solve this highly ill-posed inverse problem, Expectation Maximization (EM)-based algorithms can be adopted. In several previous studies, Variational Bayes (VB) approaches were deployed to approximate the intractable conditional probability distribution of the image that appears in the E-step of the traditional EM algorithm. In this paper, we propose to use an Expectation Propagation (EP) algorithm to derive an alternative approximation of the conditional probability distribution. The simulations conducted show that the resulting EP-EM approach can provide more reliable approximations, reflected by better image estimates and more reliable uncertainty maps than VB-EM for a comparable computational time.