Image deblurring is an important pre-processing step in image analysis. The research for efficient image deblurring methods is still a great challenge. Most of the currently used methods are based on integer-order derivatives, but they typically lead to texture elimination and staircase effects. To overcome these drawbacks, some researchers have proposed fractional-order derivative-based models. However, the existing fractional-order derivative-based models only exploit nonlocal smoothness of spatial dimensions and fail to consider the other dimensional information for three-dimensional (3D) images. To address this issue, we propose a three-dimensional fractional total variation (3DFTV) based-model for 3D image deblurring problem. In this paper, we mathematically formulate the proposed model under the tensor algebra. Furthermore, we develop an efficient algorithm based on the alternating direction method of multipliers (ADMM) to solve our model. Experimental results demonstrate the superiority of our model against comparing models in terms of quality metrics and visual effects.

图像去模糊是图像分析中重要的预处理步骤。对于有效的图像去模糊方法的研究仍然是一个巨大的挑战。当前使用的大多数方法都是基于整数阶导数，但是它们通常会导致纹理消除和阶梯效应。为了克服这些缺点，一些研究人员提出了基于分数阶导数的模型。但是，现有的基于分数阶导数的模型仅利用空间维度的非局部平滑度，而没有考虑三维（3D）图像的其他维度信息。为解决此问题，我们针对3D图像去模糊问题提出了基于三维分数总变化（3DFTV）的模型。在本文中，我们在张量代数下用数学公式表示了所提出的模型。此外，我们基于乘数交替方向法（ADMM）开发了一种有效的算法来求解模型。实验结果证明了我们的模型在质量指标和视觉效果方面优于比较模型。