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Volume 31, Issue 3
On a Hybrid Approach for Recovering Multiple Obstacles

Yunwen Yin, Weishi Yin, Pinchao Meng & Hongyu Liu

DOI: 10.4208/cicp.OA-2021-0124

Commun. Comput. Phys., 31 (2022), pp. 869-892.

Published online: 2022-03

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  • Abstract

In this paper, a hybrid approach which combines linear sampling method and the Bayesian method is proposed to simultaneously reconstruct multiple obstacles. The number of obstacles and the approximate geometric information are first qualitatively obtained by the linear sampling method. Based on the reconstructions of the linear sampling method, the Bayesian method is employed to obtain more refined details of the obstacles. The well-posedness of the posterior distribution is proved by using the Hellinger metric. The Markov Chain Monte Carlo algorithm is proposed to explore the posterior density with the initial guesses provided by the linear sampling method. Numerical experiments are provided to testify the effectiveness and efficiency of the proposed method.

  • Keywords

Inverse scattering, multiple obstacles, linear sampling method, Bayesian method, hybridization.

  • AMS Subject Headings

62F15, 78A46, 65N21, 35R30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-31-869, author = {Yin , YunwenYin , WeishiMeng , Pinchao and Liu , Hongyu}, title = {On a Hybrid Approach for Recovering Multiple Obstacles}, journal = {Communications in Computational Physics}, year = {2022}, volume = {31}, number = {3}, pages = {869--892}, abstract = {

In this paper, a hybrid approach which combines linear sampling method and the Bayesian method is proposed to simultaneously reconstruct multiple obstacles. The number of obstacles and the approximate geometric information are first qualitatively obtained by the linear sampling method. Based on the reconstructions of the linear sampling method, the Bayesian method is employed to obtain more refined details of the obstacles. The well-posedness of the posterior distribution is proved by using the Hellinger metric. The Markov Chain Monte Carlo algorithm is proposed to explore the posterior density with the initial guesses provided by the linear sampling method. Numerical experiments are provided to testify the effectiveness and efficiency of the proposed method.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2021-0124}, url = {http://global-sci.org/intro/article_detail/cicp/20301.html} }
TY - JOUR T1 - On a Hybrid Approach for Recovering Multiple Obstacles AU - Yin , Yunwen AU - Yin , Weishi AU - Meng , Pinchao AU - Liu , Hongyu JO - Communications in Computational Physics VL - 3 SP - 869 EP - 892 PY - 2022 DA - 2022/03 SN - 31 DO - http://doi.org/10.4208/cicp.OA-2021-0124 UR - https://global-sci.org/intro/article_detail/cicp/20301.html KW - Inverse scattering, multiple obstacles, linear sampling method, Bayesian method, hybridization. AB -

In this paper, a hybrid approach which combines linear sampling method and the Bayesian method is proposed to simultaneously reconstruct multiple obstacles. The number of obstacles and the approximate geometric information are first qualitatively obtained by the linear sampling method. Based on the reconstructions of the linear sampling method, the Bayesian method is employed to obtain more refined details of the obstacles. The well-posedness of the posterior distribution is proved by using the Hellinger metric. The Markov Chain Monte Carlo algorithm is proposed to explore the posterior density with the initial guesses provided by the linear sampling method. Numerical experiments are provided to testify the effectiveness and efficiency of the proposed method.

Yin , YunwenYin , WeishiMeng , Pinchao and Liu , Hongyu. (2022). On a Hybrid Approach for Recovering Multiple Obstacles. Communications in Computational Physics. 31 (3). 869-892. doi:10.4208/cicp.OA-2021-0124
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