Deblurring Natural Image Using Super-Gaussian Fields

Blind image deblurring is a challenging problem due to its ill-posed nature, of which the success is closely related to a proper image prior. Although a large number of sparsity-based priors, such as the sparse gradient prior, have been successfully applied for blind image deblurring, they inherently suffer from several drawbacks, limiting their applications. Existing sparsity-based priors are usually rooted in modeling the response of images to some specific filters (e.g., image gradients), which are insufficient to capture the complicated image structures. Moreover, the traditional sparse priors or regularizations model the filter response (e.g., image gradients) independently and thus fail to depict the long range correlation among them. To address the above issues, we present a novel image prior for image deblurring based on a Super-Gaussian field model with adaptive structures. Instead of modeling the response of the fixed short-term filters, the proposed Super-Gaussian fields capture the complicated structures in natural images by integrating potentials on all cliques (e.g., centring at each pixel) into a joint probabilistic distribution. Considering that the fixed filters in different scales are impractical for the coarse-to-fine framework of image deblurring, we define each potential function as a super-Gaussian distribution. Through this definition, the partition function, the curse for traditional MRFs, can be theoretically ignored, and all model parameters of the proposed Super-Gaussian fields can be data-adaptively learned and inferred from the blurred observation with a variational framework. Extensive experiments on both blind deblurring and non-blind deblurring demonstrate the effectiveness of the proposed method.