A Bayesian level set method for the shape reconstruction of inverse scattering problems in elasticity

Abstract 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-Matern 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.