Imaging of cylindrical bodies buried in a layered half-space bounded by an impedance plane

In this paper we address an inverse scattering problem whose aim is to determine the geometrical as well as the physical properties of a cylindrical body buried in a layered half-space. The half-space is supposed to be bounded by a homogeneous impedance plane. The impenetrable impedance boundary leads to a mathematical problem which is not solvable by the classical techniques based on the Fourier transform. To overcome this difficulty, the resulting system of operator equations is solved by using a generalization of the algebraic reconstruction technique (ART). Due to the reflections from both sides of the layers, the body interacts with four plane waves in the spectral domain, which makes the problem very interesting from both mathematical and practical points of view. The waves reflected from the impedance boundary cause the data collected by measurements to contain more information about the object to be determined.