An extended sampling-Bayesian approach for inverse elastic scattering problems with limited aperture data

This paper proposes an extended sampling-Bayesian approach to reconstruct the shape and location of the obstacle for inverse elastic scattering problems with limited aperture data. The approach consists of two main steps. Firstly, an extended sampling technique is used to identify the location of the obstacle. Secondly, the shape of the obstacle is reconstructed using the Bayesian approach, where the samples of the posterior distribution are drawn via the preconditioned Crank-Nicholson Parallel Tempering (pCN-PT) algorithm. The pCN-PT algorithm extends the standard preconditioned Crank-Nicholson Markov chain Monte Carlo (pCN-MCMC) approach by incorporating parallel tempering. It leads to a more efficient exploration of the posterior distribution through multiple parallel Markov chains at different temperatures and hence converges to a stationary distribution faster. Numerical experiments demonstrate that the proposed method is effective to determine the location and shape of the obstacle with limited aperture data.