A deterministic-statistical approach to reconstruct moving sources using sparse partial data
Document Type
Article
Publication Date
6-7-2021
Department
Department of Mathematical Sciences
Abstract
We consider the reconstruction of moving sources using partial measured data. A two-step deterministic-statistical approach is proposed. In the first step, an approximate direct sampling method is developed to obtain the locations of the sources at different times. Such information is coded in the priors, which is critical for the success of the Bayesian method in the second step. The well-posedness of the posterior measure is analyzed in the sense of the Hellinger distance. Both steps are based on the same physical model and use the same set of measured data. The combined approach inherits the merits of the deterministic method and Bayesian inversion as demonstrated by the numerical examples.
Publication Title
Inverse Problems
Recommended Citation
Liu, Y.,
Guo, Y.,
&
Sun, J.
(2021).
A deterministic-statistical approach to reconstruct moving sources using sparse partial data.
Inverse Problems,
37(6).
http://doi.org/10.1088/1361-6420/abf813
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/15125