Application of the factorization method to retrieve a crack from near field data

Abstract

Abstract We consider the inverse scattering problem of determining the shape of a crack with impedance boundary condition on one side from the complex conjugate of point sources placed on a closed curve which contains the crack. The near field factorization method is established to reconstruct the crack from the measurements on the same curve. Then, we deduce an inversion algorithm and present some numerical examples to show the viability of our method. So far as we know, when the incident waves are the point sources, the near field operator cannot be directly decomposed into the form that the factorization method required. However, we overcome this difficulty with the complex conjugate of point sources which are recently used in [Inverse Problems 30 (2014), Article ID 095005], [Inverse Problems 30 (2014), Article ID 045008] for the justification of the factorization method from near field data.