Inverse scattering problem from an impedance crack via a composite method

In this paper we consider an inverse scattering problem from an open arc with impedance boundary conditions on both sides of the crack. Our aim is to recover both the impedance function and the unknown crack simultaneously from the far-field pattern with only one incident wave. Making the most out of the direct problem, a straightforward method of iterative nature is developed for the inverse problem. The ill-posedness of this problem is considered by incorporating the Tikhonov regularization. Numerical examples are provided at the end of the paper to show the feasibility of our method.