A Fractional-order Differential Based Variational Model for Image Blind Deblurring

Image deblurring is a fundamental problem in image processing. The blind deblurring is a more challenge problem because we need to recover the true image but the blur type is unknown. The total variation method has been proposed by Tony Chan et al. [1] for image blind deblurring, but it often produces the staircase effect. To avoid this effect, in this paper, based on the fractional-order differential, we propose a novel variational method for blind deblurring. Moreover, in image regularization, we add a fractional-order edge detect function to preserve sharp edges. The primal-dual algorithm are developed to solve the proposed model. Numerical experiments show that our method is able to get the sharp images without the staircase effect and correctly estimate the unknown blur kernel.