Extended-Sampling-Bayesian Method for Limited Aperture Inverse Scattering Problems

Limited aperture inverse scattering problems arise in many important applications. In this paper, we propose a new method combining the extended sampling method (ESM) and the Bayesian approach for the inverse acoustic scattering problem to reconstruct the shape of a sound-soft obstacle using the limited aperture data. The problem is formulated as a statistical model using the Bayes formula. The well-posedness is proved in the sense of the Hellinger metric. A modified ESM is proposed to obtain the obstacle location, which is critical to the convergence of the MCMC algorithm. An extensive numerical study is presented to illustrate the performance of the method.