»ã±¨±êÌâ (Title)£ºDiffeomorphic Optimal Transportation and Its Applications in Imaging Science(΢·Öͬ¹¹×îÓÅÔËÊä¼°ÆäÔÚ³ÉÏñ¿ÆѧÖеÄÀûÓÃ)

»ã±¨ÈË (Speaker)£º ³Â³å ¸±×êÑÐÔ±£¨Öйú¿ÆѧԺÊýѧÓëϵͳ¿Æѧ×êÑÐÔº£©

»ã±¨¹¦·ò (Time)£º2023Äê11ÔÂ24ÈÕ(ÖÜÎå) 9:00

»ã±¨µØÖ· (Place)£ºÌÚѶ»áÒé 533326207

Ô¼ÇëÈË(Inviter)£ºÅíÑÇÐÂ

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»ã±¨ÌáÒª£ºMotivated 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.