A Diffeomorphic Image Registration Model with Fractional-Order Regularization and Cauchy--Riemann Constraint

Abstract

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.