Non-convex fractional-order derivative for single image blind restoration.

l A non-convex fractional-order variational model is proposed to restore the image blurred by an unknown blur kernel. l Quaternion FTV with l p quasinorm constrained image and L 1 -norm constrained kernel are unified to a regularization framework. l The fractional-order total variation is extended to four-directional FTV including diagonal and back diagonal gradients. l An efficient algorithm based on the alternating direction method is proposed to address the non-convex optimization problem. This paper considers a variational model for single image blind restoration. By exploiting the fractional-order total variation (FTV) and L p quasinorm relaxation, a non-convex fractional-order variational model is proposed to restore the image blurred by an unknown blur kernel. A quaternion FTV model is first put forward to exploring more directional information of an image. The new model utilizes non-convex and non-smooth quaternion FTV with L p quasinorm to constrain the image and L 1 -norm to constrain the blur kernel, which are unified to a unified regularization framework. Further, an efficient algorithm is proposed to solve the non-convex problem via using the alternating direction minimization. The extensive experiments demonstrate the efficiency and viability of the proposed method and reveal superior performances in comparison with several existing methods. [ABSTRACT FROM AUTHOR]