Sparse Bayesian image restoration

In this paper we propose a novel Bayesian algorithm for image restoration and parameter estimation. We utilize an image prior where Gaussian distributions are placed per pixel in the high-pass filter outputs of the image. By following the hierarchical Bayesian framework, we simultaneously estimate the unknown image and hyperparameters for both the image prior and the image degradation noise. We show that the proposed formulation is a special case of the popular l_p-norm based formulations with p = 0, and therefore enforces sparsity to an high extent in the filtered image coefficients. Moreover, the proposed formulation results in a convex optimization problem, and therefore does not suffer from the robustness issues common with non-convex image priors. Experimental results demonstrate that the proposed algorithm provides superior performance compared to state-of-the-art restoration algorithms although no user-supervision is required.