An Integrated Multi-Scaling Strategy based on a Particle Swarm Algorithm for Inverse Scattering Problems

The application of a multiscale strategy integrated with a stochastic technique to the solution of nonlinear inverse scattering problems is presented. The approach allows for the explicit and easy handling of many difficulties associated with such a problem ranging from ill-conditioning to nonlinearity and false solutions drawback. The choice of a finite dimensional representation for the unknowns, due to the upper bound to the essential dimension of the data, is iteratively accomplished by means of an adaptive multi-resolution model, which offers considerable flexibility for the inclusion of the a-priori knowledge and of the knowledge acquired during the iterative steps of the multiscaling process. Even though a suitable representation of the unknowns could limit the local minima problem, the multi-resolution strategy is integrated with a customized stochastic optimizer based on the behavior of a particle swarm (PSO), which allows to prevent that nonlinearity could induce the solution algorithm into false solutions without a large increasing of the overall computational burden. Selected examples are presented by considering a two-dimensional microwave imaging problem so as to illustrate the key features of the integrated stochastic multi-scaling strategy.