汇报标题 (Title)：Diffeomorphic Optimal Transportation and Its Applications in Imaging Science(微分同构最优运输及其在成像科学中的利用)
汇报人 (Speaker)： 陈冲 副钻研员（中国科学院数学与系统科学钻研院）
汇报功夫 (Time)：2023年11月24日(周五) 9:00
汇报地址 (Place)：腾讯会议 533326207
约请人(Inviter)：彭亚新
主办部门：理学院数学系
汇报提要：Motivated by the image reconstruction in spatiotemporal dynamic medical imaging, we introduce a concept called diffeomorphic optimal transportation (DOT), which combines the Wasserstein distance with Benamou--Brenier formula in optimal transportation and the flow of diffeomorphisms in large deformation diffeomorphic metric mapping. Using DOT, we propose a new variational model for joint image reconstruction and motion estimation, which is suitable for spatiotemporal dynamic imaging with mass-preserving large diffeomorphic deformations. The proposed model is easy-to-implement and solved by an alternating gradient descent algorithm, which is compared against existing alternatives theoretically and numerically. Moreover, we present more extensions with applications to image registration based on DOT. Under appropriate conditions, the proposed algorithm can be adapted as a new algorithm to solve the models using quadratic Wasserstein distance. The performance is validated by several numerical experiments in spatiotemporal tomography, where the projection data is time-dependent sparse and/or high-noise.
