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 would be discussed, and the Markov chain Monte Carlo (MCMC) methods will be applied to generate samples from the arising posterior distribution. Numerical experiments will be presented to demonstrate the effectiveness of the proposed method.

翻译：在这项工作中,我们有兴趣确定音响中两个维时调反向介质散射问题散射器的形状。 散射器被假定为一个片断常态函数,其内部的异质值为已知的异质,其形状由我们使用巴耶斯方法调查信息的定级函数所代表。 在巴耶斯框架中,几何反向问题的解决方案被定义为后方概率分布。 将讨论后方分布的妥善位置,并将采用马尔科夫链条蒙特卡洛(MMCC)方法从后方分布中提取样本。 将进行数量实验,以证明拟议方法的有效性。