Blind Deconvolution with Scale Ambiguity

Recent years have witnessed significant advances in single image deblurring due to the increasing popularity of electronic imaging equipment. Most existing blind image deblurring algorithms focus on designing distinctive image priors for blur kernel estimation, which usually play regularization roles in deconvolution formulation. However, little research effort has been devoted to the relative scale ambiguity between the latent image and the blur kernel. The well-known L 1 normalization constraint, i.e., fixing the sum of all the kernel weights to be one, is commonly selected to remove this ambiguity. In contrast to this arbitrary choice, we in this paper introduce the L p -norm normalization constraint on the blur kernel associated with a hyper-Laplacian prior. We show that the employed hyper-Laplacian regularizer can be transformed into a joint regularized prior based on a scale factor. We quantitatively show that the proper choice of p makes the joint prior sufficient to favor the sharp solutions over the trivial solutions (the blurred input and the delta kernel). This facilitates the kernel estimation within the conventional maximum a posterior (MAP) framework. We carry out numerical experiments on several synthesized datasets and find that the proposed method with p = 2 generates the highest average kernel similarity, the highest average PSNR and the lowest average error ratio. Based on these numerical results, we set p = 2 in our experiments. The evaluation on some real blurred images demonstrate that the results by the proposed methods are visually better than the state-of-the-art deblurring methods.