Reconstruction by level sets of n -ary scattering obstacles

Some extensions of the level set representation are analysed for the reconstruction of the unknown cross-section of multiple phase material obstacles embedded in a homogeneous medium and illuminated by time-harmonic electromagnetic line sources. The a priori information assumed therein is that the scatterers are homogeneous by parts and of known characteristics. Two types of approaches are discussed with their pros and cons. In the first approach, a single level set is used to represent the different material phases. In the second approach, the material properties are coded on a binary basis and several level sets are combined, one for each bit of binary coding. Theoretical and numerical details are provided for both approaches, using synthetic and experimental measurements obtained in the anechoic chamber of Institut Fresnel.