Deterministic-statistical approach for an inverse acoustic source problem using multiple frequency limited aperture data
Document Type
Article
Publication Date
4-2023
Department
Department of Mathematical Sciences
Abstract
We propose a deterministic-statistical method for an inverse source problem using multiple frequency limited aperture far field data. The direct sampling method is used to obtain a disc such that it contains the compact support of the source. The Dirichlet eigenfunctions of the disc are used to expand the source function. Then the inverse problem is recast as a statistical inference problem and the Bayesian inversion is employed to reconstruct the coefficients of the eigen-expansion for the source function. The stability of the statistical inverse problem with respect to the measured data is justified in the sense of Hellinger distance. A preconditioned Crank-Nicolson (pCN) Metropolis-Hastings (MH) algorithm is implemented to explore the posterior density function. Numerical examples show that the proposed method is effective for both smooth and non-smooth sources.
Publication Title
Inverse Problems and Imaging
Recommended Citation
Liu, Y.,
Wu, Z.,
Sun, J.,
&
Zhang, Z.
(2023).
Deterministic-statistical approach for an inverse acoustic source problem using multiple frequency limited aperture data.
Inverse Problems and Imaging.
http://doi.org/10.3934/ipi.2023018
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/17291