Multi-Resolution Techniques Based on Shape-Optimization for the Solution of Inverse-Scattering Problems

In the framework of inverse electromagnetic scattering techniques, the thesis focuses on the development and the analysis of the integration between a multi-resolution imaging procedure and a shape-optimization-based technique. The arising methodology allows, on one hand, to fully exploit the limited amount of information collectable from scattering measurements by means of the iterative multi-scaling approach (IMSA) which enables a detailed reconstruction only where needed without increasing the number of unknowns. On the other hand, the use of shape-optimization, such as the level-set-based minimization, provide an effective description of the class of targets to be retrieved by using "a-priori" information about the homogeneity of the scatterers. In order to assess strong points and drawbacks of such an hybrid approach when dealing with one or multiple scatterers, a numerical validation of the proposed implementations is carried out by processing both synthetic and laboratory-controlled scattering data