A Bayesian level set method for the shape reconstruction of inverse scattering problems in elasticity. (1st September 2021)

• Record Type: Journal Article
• Authors: Huang, Jiangfeng; Li, Zhaoxing; Wang, Bo
• Is Part Of: Computers & mathematics with applications. Volume 97(2021)
• Page Start: 18
• Page End: 27
• Publication Date: 2021-09-01
• Subjects: Inverse elastic scattering problems -- Bayesian level set method -- Markov chain Monte Carlo (MCMC) method -- Whittle-Matérn Gaussian random fields; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2021.05.024
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: This paper is concerned with recovering the shape of the scatterer for the two-dimensional time-harmonic inverse scattering problem in elasticity. The level set method is used for representing the geometry shape of the scatterer. The Bayesian inference approach provides a natural framework in which we are able to formulate the inverse problem as a statistical inference problem. The priors for the level set functions are achieved via the Whittle-Matérn Gaussian random fields, and the Markov chain Monte Carlo (MCMC) method is applied to extract the information of the posterior distribution whose well-posedness would be discussed as well. Numerical experiments demonstrate the effectiveness of the proposed approach.