On a Hybrid Approach for Recovering Multiple Obstacles (Communications in Computational Physics, 2022)
In this paper, a hybrid approach which combines linear sampling methodand the Bayesian method is proposed to simultaneously reconstruct multiple obstacles. The number of obstacles and the approximate geometric information are firstqualitatively obtained by the linear sampling method. Based on the reconstructions ofthe linear sampling method, the Bayesian method is employed to obtain more refineddetails of the obstacles. The well-posedness of the posterior distribution is proved byusing the Hellinger metric. The Markov Chain Monte Carlo algorithm is proposed toexplore the posterior density with the initial guesses provided by the linear samplingmethod. Numerical experiments are provided to testify the effectiveness and efficiencyof the proposed method.