Total Variation Image Restoration and Parameter Estimation using Variational Posterior Distribution Approximation

In this paper we propose novel algorithms for total variation (TV) based image restoration and parameter estimation utilizing variational distribution approximations. By following the hierarchical Bayesian framework, we simultaneously estimate the reconstructed image and the unknown hyper parameters for both the image prior and the image degradation noise. Our algorithms provide an approximation to the posterior distributions of the unknowns so that both the uncertainty of the estimates can be measured and different values from these distributions can be used for the estimates. We also show that some of the current approaches to TV-based image restoration are special cases of our variational framework. Experimental results show that the proposed approaches provide competitive performance without any assumptions about unknown hyper parameters and clearly outperform existing methods when additional information is included.