Detection, Location and Imaging of Multiple Scatterers by means of the Iterative Multiscaling Method

In this paper, a new version of the iterative multiscaling method (IMM) is proposed for reconstructing multiple scatterers in two-dimensional microwave imaging problems. The manuscript describes the new procedure evaluating the effectiveness of the IMM previously assessed for single object detection. Starting from inverse scattering integral equations, the problem is recast in a minimization one by defining iteratively (at each level of the scaling procedure) a suitable cost function allowing firstly a detection of the unknown objects, successively a location of the scatterers and finally a quantitative reconstruction of the scenario under test. Thanks to its properties, the approach allows an effective use of the information achievable from inverse scattering data. Morover, the adopted kind of expansion is able to deal with all possible multiresolution combinations in an easy and computationally inexpensive way. Selected numerical examples concerning dielectric as well as dissipative objects in noisy enviroments or starting from experimantally-acquired data are reported in order to confirm the usefulness of the introduced tool and of the effectiveness of the proposed procedure.