Bayesian approach for inverse interior scattering problems with limited aperture

Abstract

In this paper, we consider a cavity reconstruction problem for the interior acoustic scattering from limited-aperture measurements. To recover the shape of the cavity, the Bayesian inference technique is applied with the information of posterior distribution of the unknown object being explored in terms of the measured data. The posterior distribution provides us with sufficient knowledge about the unknowns, and therefore it can be used to give the corresponding estimation. We discuss the well-posedness of the posterior distribution in the sense of the Hellinger metric and use the preconditioned Crank–Nicolson (pCN) sampling technique to generate the posterior samples. Numerical examples show the effectiveness of the proposed algorithm.