In Han and Wang (2020), a 2D diffeomorphic image registration model is proposed to eliminate mesh folding. To solve the 2D diffeomorphic model, a diffeomorphic fractional-order image registration algorithm(DFIRA for short) is proposed in Han and Wang (2020). DFIRA achieves a satisfactory image registration result but it costs too much CPU time. To accelerate DFIRA, we propose a fast multi grid algorithm for 2D diffeomorphic image registration model in this paper. This algorithm achieves a satisfactory image registration result by using only one-tenth CPU time of DFIRA. At the same time, no mesh folding occurs in proposed algorithm. Furthermore, convergence analysis of the proposed algorithm is also presented. Moreover, numerical tests are also performed to show that the proposed algorithm is competitive compared with some other algorithms.

在Han和Wang（2020）中，提出了一种2D微分图像配准模型来消除网格折叠。为了解决二维微分模型，Han and Wang（2020）提出了一种微分分数阶图像配准算法（简称DFIRA）。DFIRA获得令人满意的图像配准结果，但是它花费了太多的CPU时间。为了加快DFIRA的速度，本文提出了一种快速的多网格2D变形图像配准模型算法。该算法仅使用DFIRA的十分之一的CPU时间即可获得令人满意的图像配准结果。同时，在所提出的算法中没有网格折叠发生。此外，还提出了该算法的收敛性分析。此外，还进行了数值测试，表明该算法与其他算法相比具有竞争优势。