A variational method for Bayesian blind image deconvolution

In this paper the blind image deconvolution (BID) problem is solved using the Bayesian framework. In order to find the parameters of the proposed Bayesian model we present a new generalization of the expectation maximization (EM) algorithm based on the variational approximation methodology. The proposed variational-based algorithm for BID can be derived in closed form and can be implemented in the discrete Fourier domain. Thus, it is very efficient even for very large images. We demonstrate with numerical experiments that the algorithm which was derived by the variational methodology yields promising improvements as compared to previous Bayesian algorithms for BID. Furthermore, the methodology presented here is very general with potential applications to other Bayesian models for this and other imaging problems.