Imaging a coated dielectric with various unknown buried objects inside

Abstract

In this paper, we consider the inverse scattering problem of determining a penetrable coated inhomogeneous dielectric with different kinds of unknown buried objects inside. The variational approach is adapted to show the well‐posedness of the direct scattering problem. For the inverse problem, we intend to reconstruct the shape and location of the coated dielectric from measured far‐field data by developing a modified factorization method. In fact, we shall first prove that the classical factorization method is effective for the case when a Neumann boundary condition is imposed on the buried object. However, for the case when a Dirichlet boundary condition is imposed on the buried object, the classical factorization method is no longer valid due to the loss of the coercivity of the middle operator of the associated factorization of the far‐field operator. In this case, we are expected to develop a modified factorization method to overcome this difficulty. Finally, some numerical examples are carried out to confirm the validity of the developed algorithms.