Variational Methods in Bayesian Deconvolution

This paper gives an introduction to the use of variational methods in Bayesian inference and shows how variational methods can be used to approximate the intractable posterior distributions which arise in this kind of inference. The flexibility of these approximations allows us to include positivity constraints when attempting to infer hidden pixel intensities in images. The approximating posterior distribution is then optimised by minimising the Kullback-Leibler divergence between it and the true distribution. Unlike traditional methods such as Maximum Likelihood or Maximum-A-Posteriori methods, the variational approximation is immune to overfitting, since the sensitivity of the approximation is towards probability mass rather than probability density. The results show that the present algorithm is successful in interpolation and deconvolution problems.