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.

本文关注的是如何恢复弹性中二维时谐逆散射问题的散射体形状。水平集方法用于表示散射体的几何形状。贝叶斯推理方法提供了一个自然框架，我们可以在其中将逆问题表述为统计推理问题。水平集函数的先验是通过 Whittle-Matérn 高斯随机场实现的，并应用马尔可夫链蒙特卡罗 (MCMC) 方法提取后验分布的信息，其适定性也将被讨论。数值实验证明了所提出方法的有效性。