基于贝叶斯方法的非均匀介质内混合障碍反散射问题研究
Research on Mixed Obstacles Scattering in Inhomogeneous Medium Based on Bayesian Method
摘要: 考虑二维情况下非均匀介质内的声波混合障碍反散射问题。在非均匀介质折射率是二元函数时，提出了一种同时重构裂缝和不可穿透障碍的贝叶斯方法。将混合障碍物的位置信息作为贝叶斯方法的先验信息，使用马尔科夫链蒙特卡罗(MCMC)算法重构裂缝和不可穿透障碍的形状参数。数值实验的结果表明，该方法能有效重构非均匀介质内混合障碍的形状。
Abstract: In this paper, the problem of acoustic wave inverse scattering by mixed obstacles in inhomogeneous media in two dimensions is considered. In the case that the refractive index of inhomogeneous me-dia is a binary function, a Bayesian method for simultaneously reconstructing cracks and impene-trable obstacles is proposed. The position information of mixed obstacles is taken as the prior in-formation of Bayesian method. Markov chain Monte Carlo (MCMC) algorithm is used to reconstruct the shape parameters of cracks and impenetrable obstacles. The results of numerical experiments show that this method can effectively reconstruct the shape of mixed obstacles in inhomogeneous media.
文章引用：史星雨, 尹伟石. 基于贝叶斯方法的非均匀介质内混合障碍反散射问题研究[J]. 应用数学进展, 2023, 12(3): 962-968. https://doi.org/10.12677/AAM.2023.123098

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