Bayesian Method for Inverse Scattering Problem of Interior Cavity with Phaseless Data

Abstract This paper is concerned with the inverse acoustic scattering problem of a sound soft cavity based on phaseless near-field data. By combining the reference circle technique with the Bayesian method, this paper presents a numerical algorithm to retrieve the shape of the interior cavity from phaseless data. In this paper, the well-posedness of the Bayesian method is discussed. The posterior distribution of the shape parameters is obtained by DRAM algorithm and the reconstruction of the cavity boundary is acquired by taking the average value of the posterior distribution.