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

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. The waves reflected from the impedance boundary cause the data collected by measurements to contain more information about the object to be determined.