Abstract: Bayesian method was used to simultaneously reconstruct inhomogeneous medium and embedded sound-soft obstacle. Firstly, we parameterized inhomogeneous medium and embedded obstacles, and gave a prior information of parameters. Secondly, we used Markov chain Monte Carlo (MCMC) method and a prior information of parameters to solve a posteriori information of parameters. Finally, the feasibility and effectiveness of Bayesian method were verified by some numerical examples.

Key words: inverse scattering problem, inhomogeneous medium, embedded obstacle, Bayesian method