Local motion deblurring using an effective image prior based on both the first- and second-order gradients

Local motion deblurring is a highly challenging problem as both the blurred region and the blur kernel are unknown. Most existing methods for local deblurring require a specialized hardware, an alpha matte, or user annotation of the blurred region. In this paper, an automatic method is proposed for local motion deblurring in which a segmentation step is performed to extract the blurred region. Then, for blind deblurring, i.e., simultaneously estimating both the blur kernel and the latent image, an optimization problem in the form of maximum-a-posteriori (MAP) is introduced. An effective image prior is used in the MAP based on both the first- and second-order gradients of the image. This prior assists to well reconstruct salient edges, providing reliable edge information for kernel estimation, in the intermediate latent image. We examined the proposed method for both global and local deblurring. The efficiency of the proposed method for global deblurring is demonstrated by performing several quantitative and qualitative comparisons with the state-of-the-art methods, on both a benchmark image dataset and real-world motion blurred images. In addition, in order to demonstrate the efficiency in local motion deblurring, the proposed method is examined to deblur some real-world locally linear motion blurred images. The qualitative results show the efficiency of the proposed method for local deblurring at various blur levels.