{"title":"被动反向散射问题的贝叶斯模型误差法","authors":"Yunwen Yin, Liang Yan","doi":"10.1088/1361-6420/ad3f40","DOIUrl":null,"url":null,"abstract":"\n This paper focuses on the passive inverse scattering problem, which uses passive measurements corresponding to randomly distributed incident sources to recover the shape of the sound-soft obstacle from a Bayesian perspective. Due to the unpredictability and randomness of incident sources, the classical Bayesian inversion framework may be unable to capture the likelihood involving the passive forward model for this inverse problem. We present the Bayesian model error method (BMEM), a novel passive imaging technique, to overcome this difficulty. The cross-correlations and the Helmholtz-Kirchhoff identity are specifically used to build an approximate active scattering model. This approximate model and the model error that it produces can be combined effectively by the suggested BMEM. The well-posedness of the posterior measure in the BMEM is proved. To further estimate the model error, an online scheme is utilized in conjunction with a pCN-MCMC method to numerically approximate the posterior. Numerical experiments illustrate the effectiveness of the proposed method and also show that the online evaluation of model error can significantly improve reconstruction accuracy.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":null,"pages":null},"PeriodicalIF":2.0000,"publicationDate":"2024-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Bayesian model error method for the passive inverse scattering problem\",\"authors\":\"Yunwen Yin, Liang Yan\",\"doi\":\"10.1088/1361-6420/ad3f40\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"\\n This paper focuses on the passive inverse scattering problem, which uses passive measurements corresponding to randomly distributed incident sources to recover the shape of the sound-soft obstacle from a Bayesian perspective. Due to the unpredictability and randomness of incident sources, the classical Bayesian inversion framework may be unable to capture the likelihood involving the passive forward model for this inverse problem. We present the Bayesian model error method (BMEM), a novel passive imaging technique, to overcome this difficulty. The cross-correlations and the Helmholtz-Kirchhoff identity are specifically used to build an approximate active scattering model. This approximate model and the model error that it produces can be combined effectively by the suggested BMEM. The well-posedness of the posterior measure in the BMEM is proved. To further estimate the model error, an online scheme is utilized in conjunction with a pCN-MCMC method to numerically approximate the posterior. Numerical experiments illustrate the effectiveness of the proposed method and also show that the online evaluation of model error can significantly improve reconstruction accuracy.\",\"PeriodicalId\":50275,\"journal\":{\"name\":\"Inverse Problems\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.0000,\"publicationDate\":\"2024-04-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Inverse Problems\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1088/1361-6420/ad3f40\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Inverse Problems","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1088/1361-6420/ad3f40","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Bayesian model error method for the passive inverse scattering problem
This paper focuses on the passive inverse scattering problem, which uses passive measurements corresponding to randomly distributed incident sources to recover the shape of the sound-soft obstacle from a Bayesian perspective. Due to the unpredictability and randomness of incident sources, the classical Bayesian inversion framework may be unable to capture the likelihood involving the passive forward model for this inverse problem. We present the Bayesian model error method (BMEM), a novel passive imaging technique, to overcome this difficulty. The cross-correlations and the Helmholtz-Kirchhoff identity are specifically used to build an approximate active scattering model. This approximate model and the model error that it produces can be combined effectively by the suggested BMEM. The well-posedness of the posterior measure in the BMEM is proved. To further estimate the model error, an online scheme is utilized in conjunction with a pCN-MCMC method to numerically approximate the posterior. Numerical experiments illustrate the effectiveness of the proposed method and also show that the online evaluation of model error can significantly improve reconstruction accuracy.
期刊介绍:
An interdisciplinary journal combining mathematical and experimental papers on inverse problems with theoretical, numerical and practical approaches to their solution.
As well as applied mathematicians, physical scientists and engineers, the readership includes those working in geophysics, radar, optics, biology, acoustics, communication theory, signal processing and imaging, among others.
The emphasis is on publishing original contributions to methods of solving mathematical, physical and applied problems. To be publishable in this journal, papers must meet the highest standards of scientific quality, contain significant and original new science and should present substantial advancement in the field. Due to the broad scope of the journal, we require that authors provide sufficient introductory material to appeal to the wide readership and that articles which are not explicitly applied include a discussion of possible applications.