This paper presents a new non-blind image restoration method based on the symmetric generalized Pareto (SGP) prior, which models the heavy-tailed distributions of gradients for natural images. Through experiments we show that the SGP model achieves log likelihood scores comparable to the hyper-Laplacian model when fitted to gradients and other band-pass filter responses. More importantly, when incorpo-rated into a Bayesian MAP framework for non-blind image restoration, the SGP model leads to a closed-form solution for a per-pixel subproblem, which affords computational advantages in comparison with the numerical solutions in-duced from the hyper-Laplacian model. Experimental results show that our method is comparable to existing methods in restoration quality and processing speed.

The maximum a posterior (MAP)-based blind deconvo-lution framework generally involves two stages: blur ker-nel estimation and non-blind restoration. For blur kernel estimation, sharp edge prediction and carefully designed image priors are vital to the success of MAP. In this pa-per, we propose a blind deconvolution framework together with iteration specific priors for better blur kernel estima-tion. The family of hyper-Laplacian (Pr(d) ∝ e−‖d‖pp/λ) is adopted for modeling iteration-wise priors of image gra-dients, where each iteration has its own model parameters {λ(t), p(t)}. To avoid heavy parameter tuning, all iteration-wise model parameters can be learned using our principled discriminative learning model from a training set, and can be directly applied to other dataset and real blurry images. Interestingly, with the generalized shrinkage / thresholding operator, negative p value (p < 0) is allowable and we find that it contributes more in estimating the coarse shape of blur kernel. Experimental results on synthetic and real world images demonstrate that our method achieves bet-ter deblurring results than the existing gradient prior-based methods. Compared with the state-of-the-art patch prior-based method, our method is competitive in restoration re-sults but is much more efficient. 1.

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