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 L₁-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.

本文考虑了一种用于单图像盲恢复的变分模型。通过利用分数阶总变分（FTV）和L _p quasinorm松弛，提出了一种非凸分数阶变分模型来恢复被未知模糊核模糊的图像。首先提出四元数 FTV 模型来探索图像的更多方向信息。新模型利用具有L _p quasinorm 的非凸非光滑四元数 FTV来约束图像和L ₁-norm 来约束模糊核，这些核被统一到一个统一的正则化框架。此外，提出了一种有效的算法来通过使用交替方向最小化来解决非凸问题。广泛的实验证明了所提出方法的效率和可行性，并与几种现有方法相比显示出优越的性能。