On a Hybrid Approach for Recovering Multiple Obstacles

In this paper, a hybrid approach which combines linear sampling method and the Bayesian method is proposed to simultaneously reconstruct multiple obstacles. The number of obstacles and the approximate geometric information are first qualitatively obtained by the linear sampling method. Based on the reconstructions of the linear sampling method, the Bayesian method is employed to obtain more refined details of the obstacles. The well-posedness of the posterior distribution is proved by using the Hellinger metric. The Markov Chain Monte Carlo algorithm is proposed to explore the posterior density with the initial guesses provided by the linear sampling method. Numerical experiments are provided to testify the effectiveness and efficiency of the proposed method.