Bayesian Blind Image Deconvolution using an Hyperbolic-Secant prior

Abstract

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In this paper we propose the use of the Hyperbolic Secant (HS) distribution as a prior for the Blind Image Deconvolution (BID) problem. It is well-known that when high-pass filters are applied to natural images, the resulting coefficients are sparse. We leverage this property using the HS distribution, a seldom explored Super Gaussian distribution with suitable properties for this problem. Using the Pólya-Gamma distribution, we derive an explicit Gaussian Scale Mixture representation. This representation is then used to propose a novel variational Bayesian algorithm that outperforms state-of-the-art BID methods.