## 1. Introduction

[2] Within the framework of the medicine [*Louis*, 1992] and biomedical engineering [see, e.g., *Liu et al.*, 2003, and references therein], without forgetting the industrial quality control in industrial processes [*Hoole*, 1991] and the subsurface sensing [*Dubey*, 1995; *Daniels*, 1996], many different applications require a noninvasive sensing of inaccessible areas. Towards this end, microwave imaging methodologies [*Steinberg*, 1991] have recently gained a growing attention since they allow to retrieve information on the environment probed with electromagnetic fields by fully exploiting the scattering phenomena [*Colton and Krees*, 1992].

[3] Unfortunately, the inverse problem to be faced is intrinsically nonlinear, ill-posed, and nonunique [*Denisov*, 1999]. In particular, the ill-posedness and the nonuniqueness arise from the limited amount of information collectable during the acquisition of the scattered field. The number of independent scattering data is limited [*Bertero et al.*, 1995; *Bucci and Franceschetti*, 1989] and they can only be used to retrieve a finite number of parameters of the unknown contrast function. To fully exploit such an information and to achieve a suitable resolution accuracy, several multiresolution strategies have been proposed [*Miller and Willsky*, 1996a, 1996b; *Bucci et al.*, 2000a, 2000b; *Baussard et al.*, 2004a, 2004b].

[4] The Iterative Multiscaling Approach belongs to this class of algorithms [*Caorsi et al.*, 2003]. The unknown scatterers are iteratively reconstructed by considering initially a rough estimate of the dielectric distribution and by enhancing successively the spatial resolution in a set of regions-of-interest (RoIs) where the objects have been localized. (The IMSA is initialized by considering the free space distribution, then no a priori information on the scenario under test is exploited. Moreover, the initialization of the intermediate steps is obtained from the reconstruction of the previous step with a simple mapping of the retrieved profile in the new discretization of the RoI.) Such a strategy is mathematically formulated by defining a suitable multiresolution cost function whose global minimum is assumed as the estimated solution. The functional is iteratively minimized by using a conjugate-gradient-based procedure [*Kleinman and Van den Berg*, 1992], but stochastic [*Massa*, 2002] or hybrid algorithms can be suitably applied.

[5] In order to validate such an approach, the multiresolution algorithm has been tested against experimental data [*Caorsi et al.*, 2004a] collected in a controlled environment [*Belkebir and Saillard*, 2001], since synthetically generated data can give only limited indications and they model an ideal scenario.

[6] In dealing with real data, one of the key issue is the modeling of the electromagnetic source or of the related radiated field. In general, the electromagnetic field emitted by the probing system is measured only in the observation domain. However, iterative methods based on “*Data*” and “*State*” equations require the knowledge of the incident field (i.e., the field without the scatterers) generated from the source in the investigation domain. Towards this end, an accurate but simply model (i.e., requiring a reasonable computational burden) of the source should be developed. Complicated numerical models accurately reproduce real data, but they are difficult to be implemented starting from a limited number of samples of the radiated electromagnetic field collected in a portion of the observation domain. On the other hand, a rough model could introduce erroneous constraints to the reconstruction process. Nevertheless, whatever the source model, an effective inversion procedure should be able to reconstruct the scatterer under test with an acceptable accuracy according to its robustness to the noise.

[7] In this framework, to assess the effectiveness and the robustness of the IMSA, the results of a set of experiments, where different models for approximating the illuminating source are considered, will be shown.

[8] The paper is organized as follows. In section 2, the statement of the inverse problem and the mathematical formulation of the IMSA will be briefly resumed, while in section 3 the numerical models used to synthesize the probing electromagnetic source will be described. A numerical validation and an exhaustive analysis of the dependence of the reconstruction accuracy on the modeling of the radiated field will be carried out in section 4 by considering some experimental test cases. Finally, some conclusions will be drawn (section 5).