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The possibility of ultimately control the power deposition represents the way towards a wide spread adoption of hyperthermia in the clinic. The end goal is represented by the possibility of uniformly shaping the temperature over the target area while keeping it arbitrarily bounded elsewhere. In this respect, an innovative SAR-based optimization strategy, the so called Focusing via Constrained power Optimization (FOCO), has been proposed and recently tested in the clinic. Thanks to its huge versatility (as well as several advantages), different derivations of FOCO were developed addressing different clinical needs. In this communication we aim at review some of these derivations under a common framework.

An efficient inverse scattering strategy is proposed to achieve dielectric characterization of buried objects in lossy soils. The approach takes advantage of Virtual Experiments and Compressive Sensing to obtain quantitative reconstructions of nonweak targets which are nonsparse in the pixel representation basis, commonly adopted in microwave imaging. In addition, an original strategy is adopted to overcome the relevant information lack arising when data are gathered under aspect-limited configurations, such as in ground penetrating radar (GPR) surveys. The proposed strategy significantly outperforms the results achievable with the "state of the art" standard approaches since it allows to achieve nearly optimal reconstructions within a linear framework and without increasing the overall computational burden. Numerical examples with simulated data are given to show the feasibility of the proposed strategy.

For future satellite antennas Active Direct Radiating Arrays exhibit good characteristics in terms of coverage re-configurability and power flexibility. Unfortunately canonical array antenna configurations present drawbacks due to the high number of active radiating elements with a consequent high complexity and costs. On the basis of the results obtained in the frame of previous ESA activities, sparse array configurations represent a promising solution because they permit minimizing the number of radiating elements and keeping all the power amplifiers at the same operative level still satisfying stringent pattern requirements in term of sidelobe level and isolation. The paper presents the first results obtained in the framework of a new ESA activity dedicated to the implementation of sparse active arrays. The problem areas are presented together with possible solutions. In particular, it appears important to exploit some geometrical modularity in the element positions in order to keep quite simple the beam forming network while implementing the required cooling devices (e.g. heatpipe).

In this communication, we discuss the potential and the perspectives of a new and effective framework to tackle the solution of inverse scattering problems. Starting from the statement that scattering phenomena can be recombined in many different ways (due to the linearity of Maxwell equations), it is possible to design suitable experiments where peculiar properties of the field or of the contrast source can be pursued. These virtual experiments, synthetically built by properly processing the available data, provide a convenient framework to recast the inverse problem, wherein the enforced properties can be exploited throughout the solution procedure. Accordingly, this concept is a powerful tool to derive new inversion approaches capable to handle as well as to overcome some of the typical difficulties and limitations in the solution of inverse scattering problems.

We introduce a novel strategy to synthesize an antenna array capable to focus a field in an unknown scenario. The underlying power synthesis problem is efficiently solved via convex programming and using an approximation of the fields radiated by the array elements. This approximation stems from an original exploitation of the equation underlying the Linear Sampling Method. As such, the proposed strategy takes advantage of the broad applicability of this well-known imaging approach. Some numerical examples are given to illustrate the performance of the strategy.

The problem of the optimal power pattern synthesis of shaped beams by means of circularly symmetric continuous aperture sources is addressed and solved. In particular, a necessary and sufficient existence criterion is provided to test a priori (i.e., without solving the overall synthesis problem) if a non-superdirective continuous aperture source of given size can radiate or not a circularly symmetric power pattern lying in a given arbitrary mask. In the affirmative case, the proposed approach guarantees the achievement of the global optimum by using local optimization techniques, and a number of equivalent aperture distributions are determined in a straightforward fashion. Numerical examples concerning applications of actual interest support the given theory and confirm the effectiveness of the developed approach.

Two-dimensional target characterization using inverse profiling approaches with total-field phaseless data is discussed. Two different inversion schemes are compared. In the first one, the intensity-only data are exploited in a minimization scheme, thanks to a proper definition of the cost functional. Specific normalization and starting guess are introduced to avoid the need for global optimization methods. In the second scheme [J. Opt. Soc. Am. A21, 622 (2004)], one exploits the field properties and the theoretical results on the inversion of quadratic operators to derive a two-step solution strategy, wherein the (complex) scattered fields embedded in the available data are retrieved first and then a traditional inverse scattering problem is solved. In both cases, the analytical properties of the fields allow one to properly fix the measurement setup and identify the more convenient strategy to adopt. Also, indications on the number and types of sources and receivers to be used are given. Results from experimental data show the efficiency of these approaches and the tools introduced.

Breast cancer is nowadays one of the main causes of death in women and its early detection is commonly understood as the most e®ective way to cure this disease. The state-of- the-art screening technique is X-ray mammography which, while sensitive to tumors, has indeed limitations in discriminating amongst malignant tumors and benign ones. Recently, it has been demonstrated that the electromagnetic properties of the malignant tissues at microwave frequencies are very di®erent from those of the normal ones. Accordingly, microwave tomography has emerged as a complementary diagnostic tool, which can be potentially exploited to perform morphological and functional screening. On the other hand, the ambitious aim of achieving quantitative information on the imaged tumors involves the solution of a non-linear and ill-posed inverse scattering problem that, besides not-trivial computational issues, claims for reliable approaches capable of avoiding false alarms or lack of detection. In this communication, in order to address the above problems and proceed towards an e®ective microwave screening of breast cancer, we will show how, by properly acting on the degrees of freedom of the problem (i.e., type of immersion liquid, working frequency and so on), it is possible to achieve accurate tomographic reconstructions and to actually discriminate between di®erent types of tumors when they are contemporary present. In particular, by reasoning on the electromagnetic characteristics of the coupling medium, the desired spatial resolution and the factors a®ecting non-linearity of the underlying inverse scat- tering problem, we ¯rst derive some guidelines for an \optimal" choice of the working frequency and the electromagnetic characteristics of immersion liquid. Then, considering the so determined work- ing conditions, we test the reconstruction capabilities of a Contrast Source inversion ap- proach wherein a regularization by projection is properly exploited in order to increase robustness against false solutions. Numerical examples related to 2D and 3D imaging experiments will be shown at the conference.

Starting from the concept of “degree of non-linearity” of the relationship amongst unknown parameters and scattered fields, we discuss how knowledge of the geometrical features of the targets favorably affects the solution of inverse scattering problems. The same concept is also exploited to optimize the contrast source-extended Born (CS-EB) model, resulting in the optimized CS-EB (O-CS-EB) inversion approach, which remarkably reduces false solutions occurrence. Then, a two-steps approach is proposed as a reliable and effective inversion strategy. The first step consists in retrieving the shape of the targets using the linear sampling method, while in the second step, the estimated shapes and the O-CS-EB are exploited to reconstruct the permittivity profile. The approach has been tested against experimental data, showing that very accurate reconstructions are achieved from monochromatic data.

Efficient and reliable reconstruction of location and shape of dielectric targets via microwave imaging is relevant in many applications. In this respect, the linear sampling method is an effective candidate to pursue this task. However, despite its simplicity and computational effectiveness, still its use is restricted to the mathematical community wherein it has been originally developed. Starting from this observation, in this paper we propose and test a simple and original "physical" interpretation of the linear sampling methods, which shows its relationship with electromagnetic focusing problems. Taking advantage of this result we discuss merits and limitations of the method and suggest new guidelines for a successful application. The analysis is supported with results against experimental data.