A Bayesian level set method for an inverse medium scattering problem in acoustics

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.