A two step linear inversion strategy for imaging simple shapes

Abstract

In this paper an innovative procedure for the localization and reconstruction of objects composed of elementary shapes is described. Sparse backscattered multifrequency field data are assumed to be known. The strategy is based on two steps in order to decrease the computational costs and to allow the use of few measurement points (with respect of Number of Degrees of Freedom). At first an Interferometric-Migration (IM) strategy is introduced with the purpose of reducing the dimension of the solution space. The second step is founded on the assumption that the elementary shapes are known and their geometrical features can characterized by a small amount of parameters. Then an Interferometric-MUSIC (I-MUSIC) algorithm is applied by combining results at single frequency. The overall approach is numerically tested in a 2D geometry for electrically large objects and has been proved robust against uncertainties on data.