The noninvasive imaging of unknown objects is of particular interest in several industrial applications. In this paper an iterative multiresolution strategy (IMRS) is applied to the reconstruction of metallic targets from experimental measurements. A representative test case is presented for evaluating the effectiveness of the IMRS for dealing with real data collected in a controlled environment in both TE
INTRODUCTIONMethodologies for the reconstruction of unknown objects in a noninvasive fashion are appealing for many industrial applications [1,2]. The methods that exploit microwaves can be used to obtain a quantitative description of dielectric and conductivity profiles by means of processing of the field data collected away from the scatterers.Because of the intrinsic ill-posedness, the arising inverse scattering problems are usually reformulated as optimization ones (see [3,4] and the references therein) by defining a suitable cost function that estimates the fitting with measured scattered field data.In this context, the iterative multiresolution strategy (IMRS) has been recently proposed in order to exploit in an efficient way the limited information [5] collected through the scattering experiments [6,7]. Such a methodology has demonstrated its effectiveness in terms of spatial resolution in correspondence with transverse magnetic (TM) illumination. However, no experiments have been performed using the transverse electric (TE) case.For completeness, this paper presents the results of the reconstruction of a metallic target from experimental data aimed at validating the robustness of the approach in a real controlled environment comparing two type of polarization (that is, TM versus TE). Such a test plays a relevant role in order to further investigate on the range of applicability of the IMRS in practical applications.
PROBLEM FORMULATION AND SOLUTION STRATEGYAn unknown object located in a bounded investigation domain D I is successively illuminated from V different directions with a monochromatic electric field (E inc v (r), v ϭ 1, . . . , V) at a fixed angular frequency . The total electric field, E tot v (r), inside and outside the scatterer satisfies the following integral equation:where k 0 2 is the free-space wave number, G(r/rЈ) is the dyadic Green's function, and rЈ denotes a point inside the investigation area D I . Moreover, (r) is the object function to be reconstructed, defined aswhere r (r) and (r) are the relative dielectric permittivity and the conductivity, respectively. Under tomographic conditions, the solution of Eq.(1) simplifies. Moreover, it reduces to a scalar relationship [4] in dealing with a TM illumination or to a two-component vectorial equation for the TE case [3]. In general, such relationships are exploited to define a suitable functional to be minimized in order to retrieve the problem unknowns (E tot v (r) and (r)). In a compact form, the cost function for the TE problem can be expressed in the following way (for the TM case, the reader may refer to [6]):where the...
