Spatiotemporal imaging with diffeomorphic optimal transportation

doi:10.1088/1361-6420/ac2a91

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	Spatiotemporal imaging with diffeomorphic optimal transportation
	Chen,Chong
	2021-10-13
发表期刊	Inverse Problems
ISSN	0266-5611
卷号	37 期号:11
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.
关键词	spatiotemporal imaging di?eomorphic optimal transportation mass-preserving deformation
DOI	10.1088/1361-6420/ac2a91
语种	英语
WOS记录号	IOP:0266-5611-37-11-ac2a91
出版者	IOP Publishing
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/59130
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).