Spatiotemporal imaging with diffeomorphic optimal transportation

doi:10.1088/1361-6420/ac2a91

	Spatiotemporal imaging with diffeomorphic optimal transportation
	Chen,Chong
刊名	Inverse Problems
	2021-10-13
卷号	37 期号:11
关键词	spatiotemporal imaging di?eomorphic optimal transportation mass-preserving deformation
ISSN号	0266-5611
DOI	10.1088/1361-6420/ac2a91
英文摘要	AbstractMotivated by the image reconstruction in spatiotemporal imaging, we introduce a concept named 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 imaging involving mass-preserving large diffeomorphic deformations. We further get its equivalent PDE-constrained optimal control formulation. The proposed model is easy-to-implement and solved by an alternating gradient descent algorithm, which is compared against existing alternatives theoretically and numerically. The performance is validated by several numerical experiments in spatiotemporal tomography, where the projection data is time-dependent sparse and/or high-noise. Moreover, we present several extensions based on DOT. Under appropriate conditions, the proposed algorithm can be adapted as a new algorithm to solve the models using quadratic Wasserstein distance.
语种	英语
出版者	IOP Publishing
WOS记录号	IOP:0266-5611-37-11-AC2A91
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/59129]
专题	中国科学院数学与系统科学研究院
通讯作者	Chen,Chong
作者单位	LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, People’s Republic of China
推荐引用方式 GB/T 7714	Chen,Chong. Spatiotemporal imaging with diffeomorphic optimal transportation[J]. Inverse Problems,2021,37(11).
APA	Chen,Chong.(2021).Spatiotemporal imaging with diffeomorphic optimal transportation.Inverse Problems,37(11).
MLA	Chen,Chong."Spatiotemporal imaging with diffeomorphic optimal transportation".Inverse Problems 37.11(2021).