Regularized Quasi-Newton method for inverse scattering problems

We study the weak scattering case of a 3-D inverse scattering problem. The iterative sequence is defined in the framework of a Quasi-Newton method. Using the measurements of the scattering field from the carefully chosen set of directions, we are able to recover (finitely many) Fourier coefficients of the sought parameters of the model. In this method, the linearized (Born) approximation is just the first iteration, and further iterations improve the identification by an order of magnitude. A special regularization for the Frechet derivative's inverse provides a significant improvement in the algorithm's performance. Numerical experiments for the scattering from coaxial circular cylinders with exact data are presented.