Single image blind deblurring based on the fractional-order differential

Image deblurring is a fundamental problem in image processing. When the blur type is unknown, the problem becomes more challenging, which is called blind deblurring. In this paper, we propose a novel variational method for single image blind deblurring based on the fractional-order differential, which can overcome the staircase effect produced by the total variation regularization and alleviate the ringing artifact in deblurring. The fractional-order gradient fidelity term is added in the cost functional to improve the restoration. Moreover, we make use of the edge detect function with the fractional-order gradient to preserve sharp edges, and the Bregman iteration to reconstruct more structures. The primal–dual algorithm is developed to solve the proposed model. Numerical experiments show that our method is able to get the sharp image without the staircase effect and correctly estimate the unknown blur kernel.