Author:
Huang Jiangfeng,Deng Zhiliang,Xu Liwei
Abstract
<p style='text-indent:20px;'>In this work, we are interested in the determination of the shape of the scatterer for the two dimensional time harmonic inverse medium scattering problems in acoustics. The scatterer is assumed to be a piecewise constant function with a known value inside inhomogeneities and its shape is represented by the level set functions for which we investigate the information using the Bayesian method. In the Bayesian framework, the solution of the geometric inverse problem is defined as a posterior probability distribution. The well-posedness of the posterior distribution is discussed and the Markov chain Monte Carlo (MCMC) method is applied to generate samples from the posterior distribution. Numerical experiments are presented to demonstrate the effectiveness of the proposed method.</p>
Publisher
American Institute of Mathematical Sciences (AIMS)
Subject
Control and Optimization,Discrete Mathematics and Combinatorics,Modelling and Simulation,Analysis,Control and Optimization,Discrete Mathematics and Combinatorics,Modeling and Simulation,Analysis
Reference52 articles.
1. G. Bao, S. Hou, P. Li.Recent studies on inverse medium scattering problems, Modeling and Computations in Electromagnetics, Lect. Notes Comput. Sci. Eng., Springer, Berlin, 59 (2008), 165-186.
2. G. Bao, P. Li.Inverse medium scattering problems for electromagnetic waves, SIAM Journal on Applied Mathematics, 65 (2005), 2049-2066.
3. G. Bao, P. J. Li.Shape reconstruction of inverse medium scattering for the Helmholtz equation, Computational Methods for Applied Inverse Problems, Inverse Ill-posed Probl. Ser., Walter de Gruyter, Berlin, 56 (2012), 283-305.
4. G. Bao, P. Li, J. Lin and F. Triki, Inverse scattering problems with multi-frequencies, Inverse Problems, 31 (2015), 093001, 21 pp.
5. T. Bui-Thanh, O. Ghattas.An analysis of infinite dimensional Bayesian inverse shape acoustic scattering and its numerical approximation, SIAM/ASA Journal on Uncertainty Quantification, 2 (2014), 203-222.
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