Shape inversion from TM and TE real data by controlled evolution of levelsets

Abstract

The retrieval of the cross-sectional contour of a homogeneous, multiply connectedcylindrical obstacle located in free space is performed via controlled evolutionof a level set from experimental data in either the transverse magnetic(TM) or transverse electric (TE) polarization case as is described in theintroductory paper of the special section. Theoretical and algorithmicdetails on the solution method are found in Ramananjaona et al (2001Inverse Problems 17 1087–111) for the buried object configuration—thefree-space configuration is a straightforward simplification—and only keyelements are recalled here. Focus is on the display and discussion of shapeidentification results for the two dielectric circular cylinders (TM data), therectangularly shaped metal cylinder (TM and TE data), and the U-shaped metalcylinder (TM data). In addition to the fact that TE data are often seen asmore of a challenge that TM data, those cases appear to be the mostdemanding ones in the microwave data base in terms of geometry (theU-shaped one) or in view of the inversion algorithm itself (developed forpenetrable objects, the metal case is in principle off limits) whilst the twocylinders illustrate how multiply connected, dielectric objects are retrieved.