Reconstruction of an impenetrable obstacle in anisotropic inhomogeneous background

In this paper, we are interested in the problem of determining the shape of sound-soft or impedance obstacles in the acoustic wave scattering with an anisotropic inhomogeneous medium. The main theme is to extend the factorization method to this setting. Precisely, we can reconstruct the obstacle by the eigenvalues and eigenfunctions of the far-field operator. We also provide some numerical simulations in the paper. ? 2021 The Author(s) 2021. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.