The basic concepts and models used in the study of nuclear magnetic resonance are introduced. A simple imaging experiment is described, as well as, the reduction of the problem of selective excitation to a classical problem in inverse scattering.
We consider the inverse scattering of time-harmonic plane waves to reconstruct the shape of a sound-soft crack from a knowledge of the given incident field and the phaseless data, and we check the invariance of far field data with respect to translation of the crack. We present a numerical method that is based on a system of nonlinear and ill-posed integral equations, and our scheme is easy and simple to implement. The numerical implementation is described and numerical examples are presented to...