Blind image deblurring by promoting group sparsity

Blind image deblurring aims to recover the sharp image from a blurred observation, which is an ill-posed inverse problem. Proper image priors for the unknown variables (i.e. latent sharp image and blur kernel) are crucial. Abundant previous methods have shown the effectiveness of the sparsity-based priors on both image gradients and the blur kernel. The correlation among the elements of the sparse variables is paid less attention, however. In this paper, we propose to handle the blind image deblurring problem by promoting group sparsity. The proposed group sparsity priors are based on the fact that the nonzero elements of natural image gradients and blur kernels tend to cluster in structured group pattern. Based on the proposed priors, we introduce proper algorithms to iteratively update latent image gradients and blur kernel, respectively. The proposed algorithms preserve the salient structures and smooth the minor components in image gradients and restrict the blur kernel in a domain of dynamic group sparse vector. To illustrate the reliability of the proposed algorithm, we conduct experiments to analyze the properties of the regularizers and the convergence property of the proposed algorithm. Experiments with both quantitative and visual comparison further prove the effectiveness of the proposed method.