Breast cancer represents one of the main reasons of death among women. As an alternative to the gold standard techniques for breast cancer diagnosis, microwave imaging has been proposed from research community and many microwave systems have been designed mainly to work at low microwave frequencies. Based both on the results of recent dielectric characterization campaigns on human breast ex-vivo tissues up to 50 GHz and on the promising feasibility studies of mm-wave imaging systems, in this article, we propose and test inverse scattering techniques as effective tool to process mm-wave data to image breast cancer. Differently from the radar techniques so far adopted in conjunction with mm-wave imaging system, inverse scattering techniques turn out to be more versatile and robust with respect to the reduction of the number of processed frequencies and eventually also able to characterize the anomaly in terms of electromagnetic properties. In particular, in the above, two image reconstruction techniques, the Linear Sampling Method and the Born Approximation, are proposed and compared against both simulated and experimental data.

In microwave imaging, the linearity of the relationship between the incident and the scattered field offers the possibility of a posteriori recombining the performed scattering experiments and then to cast the underlying inverse problem with respect to the resulting, virtual, ones. The interest of such a circumstance is that properly designed virtual experiments can enforce particular and convenient conditions. In this paper, we present an application of this paradigm to the popular contrast source inversion (CSI) method. In particular, we first design a set of virtual experiments capable to induce contrast sources exhibiting circular symmetries (with respect to some pivot points). Then, we devise an original and effective regularized CSI scheme, in which a penalty term is added to the usual cost functional, in order to account for the symmetry of the auxiliary unknowns. Notably, the approach does not require any apriori assumption on the unknown contrast, as it relies on the particular nature of the virtual contrast sources. Results with single frequency Fresnel experimental data are given to assess the capabilities of the proposed approach.

In microwave breast cancer imaging magnetic nanoparticles have been recently proposed as contrast agent. Due to the non-magnetic nature of human tissues, magnetic nanoparticles make possible the overcoming of some limitations of conventional microwave imaging techniques, thus providing reliable and specific diagnosis of breast cancer. In this paper, a Compressive Sensing inspired inversion technique is introduced for the reconstruction of the magnetic contrast induced within the tumor. The applicability of Compressive Sensing theory is guaranteed by the fact that the underlying inverse scattering problem is linear and the searched magnetic perturbation is sparse. From the numerical analysis, performed in realistic conditions in 3D geometry, it has been pointed out that the adoption of this new tool allows improving resolution and accuracy of the reconstructions, as well as reducing the number of required measurements.

The linearity of the scattering phenomenon with respect to primary sources allows to recombine a posteriori the available experiments and build, in a synthetic fashion, new “virtual” experiments. Starting from this circumstance, an iterative procedure is proposed as an effective approach to tackle nonlinear inverse scattering problems. In this procedure, the virtual experiments, the Green's function, and the corresponding physical inspired field approximations are updated at each iteration. The structure and the complexity of the approach are comparable with those of the widely adopted distorted Born iterative method, but its performances are remarkably better, thanks to extended validity of the exploited field approximation. The overall approach also takes advantage of a compressive sensing inspired regularization scheme to promote sparsity in the search of piecewise constant dielectric profiles and further improve the accuracy of the imaging results. Examples with numerical and experimental data are given to assess the method.

A new approach to the design of Graded Artificial Material (GAM)-based devices is proposed by exploiting the inverse scattering framework as a synthesis tool. The introduced general methodology can be applied to arbitrary far-field specifications, thus allowing the design of non-canonical devices. In particular, two different strategies are developed for GAMs based on either graded refractive index (GAMR) or graded filling factor (GAMF). In both strategies, the inverse scattering problem is solved by a proper reformulation of the Contrast Source Inversion method, wherein a proper rescaling of the amplitude of the primary sources is also used. In particular, in the first strategy, the GAMF is obtained by exploiting homogenization theories. In the second strategy, the GAMR is synthesized by exploiting a suitable representation basis for the unknown contrast function, and, then, simple analytical formulas are used to determine the corresponding GAMF. The proposed approach is assessed through the synthesis of an antenna generating a Σ/Δ reconfigurable pattern.

Ground penetrating radar (GPR) technology for underground exploration consists in the transmission of an electromagnetic signal in the ground for sensing the presence of buried objects. While monostatic or bistatic configurations are usually adopted, a limited number of multistatic GPR systems have been proposed in the scientific literature. In this manuscript, we investigate the recovery performance of a specific and unconventional contactless multistatic GPR system, designed at the Georgia Institute of Technology for the subsurface imaging of anti-tank and anti-personnel plastic mines. In particular, for the first time, tomographic approaches are tested against this experimental multistatic GPR system, while most GPR processing in the scientific literature processes multi-monostatic experimental data sets. Firstly, by mimicking the system at hand, an accurate theoretical as well as numerical analysis is performed in order to estimate the data information content and the performance achievable. Two different tomographic linear approaches are adopted, i.e. the linear sampling method (LSM) and the Born approximation (BA) method, this latter enhanced by means of the compressive sensing (CS) theoretical framework. Then, the experimental data provided by the Georgia Institute of Technology are processed by means of a multi-frequency CS and BA-based method, thus generating very accurate 3D maps of the investigated underground scenario.