A two step method in inverse scattering problem for a crack

In this paper, we present a method for solving a time-harmonic acoustic inverse scattering problem for a sound-soft crack in R ². Based on the integral equation method, our method splits the nonlinear, severely ill-posed inverse problem into a linear well-posed direct problem and a nonlinear ill-posed problem. At this setting, not only the regularized Newton's method can still be used to solve the inverse problem numerically but also with the advantage of keeping the structure of the algorithm simple and efficient.