SIAM Journal on Imaging Sciences, Volume 13, Issue 3, Page 1240-1271, January 2020.
In order to echo with fractional-order smoothness of image texture and eliminate mesh folding in image registration, we propose a diffeomorphic image registration model with fractional-order regularization and Cauchy--Riemann constraint. For the convenience of numerical implementation, a relaxed model is discussed. The existence of solution for the relaxed model is proved. A convex optimization numerical algorithm is presented, and the convergence of minimizing sequence is proved. Moreover, numerical tests are performed to show the efficiency of the proposed algorithm.

中文翻译：

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具有分数阶正则和柯西-黎曼约束的微分图像配准模型

SIAM影像科学杂志，第13卷，第3期，第1240-1271页，2020
年1月。为了回荡图像纹理的分数阶平滑度并消除图像配准中的网格折叠，我们提出了一种分数阶微分形图像配准模型。阶正则化和Cauchy-Riemann约束。为了方便数值实现，讨论了一个松弛模型。证明了松弛模型解的存在性。提出了凸优化数值算法，并证明了最小化序列的收敛性。此外，进行了数值测试以表明所提出算法的效率。