Martina Bevacqua

Inverse Scattering Via Virtual Experiments and Contrast Source Regularization

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.

Microwave Imaging of Nonweak Targets via Compressive Sensing and Virtual Experiments

Compressive sensing (CS)-based techniques can represent a very attractive approach to inverse scattering problems. In fact, if the unknown has a sparse representation and the measurements are properly organized, CS allows to considerably reduce the number of measurements and offers the possibility to achieve optimal (or nearly optimal) reconstruction performance. Unfortunately, the inverse scattering problem is nonlinear, while CS theory is well established only for linear recovery problems. As a contribution to overcome this issue, in this letter, we introduce two different CS-inspired approaches that exploit the “virtual experiments” framework, wherein it is possible to cast the inverse scattering problems in a linear form even in the case of nonweak targets.

A Compressive Sensing Approach for 3D Breast Cancer Microwave Imaging With Magnetic Nanoparticles as Contrast Agent

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.

An Algebraic Solution Method for Nonlinear Inverse Scattering

By using properly designed synthetic (or “virtual”) experiments and an original approximation of the contrast sources, we are able to recast the inverse scattering problem in an algebraic form (in a subset of points of the imaged domain) and, hence, to solve it by means of closed form formulas. The new approximation relies on the assumption that the contrast sources induced by the different virtual experiments are focused in given points belonging to the scatterer. As such, the method involves a preprocessing step in which the outcome of the original scattering experiments is recombined into the new, virtual, ones capable of enforcing the expected contrast sources behavior. Examples with numerical and experimental data are provided to assess the actual possibility of setting such a virtual experiments framework, and show the effectiveness of the proposed method.

Quasi — Invisibility via inverse scattering techniques

The paper investigates the feasibility of an approach to design effective cloaking devices by means of a joint exploitation of available degree of freedom in synthesis strategies and the physical mechanism underlying cloaking. A different point of view in the design of dielectric covers that minimize the scattering cross section of dielectric objects is introduced and new opportunities are outlined to perform an effective synthesis of cloaking profiles via inverse scattering techniques.

Microwave Imaging via Distorted Iterated Virtual Experiments

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.

SHAPE RECONSTRUCTION VIA EQUIVALENCE PRINCIPLES,CONSTRAINED INVERSE SOURCE PROBLEMS AND SPARSITY PROMOTION

A new approach for position and shape reconstruction of both penetrable and impenetrable objects from the measurements of the scattered fields is introduced and described. The approach takes advantage of the fact that for perfect electric conductors the induced currents are localized on the boundary, and equivalent sources also placed on the surface of the scatterers can be considered in the case of dielectric targets by virtue of the equivalence theorem. Starting from these considerations, a new inversion approach is formulated in order to retrieve the location and the boundary of unknown objects. Examples with both numerical and experimental data are given to demonstrate and assess the effectiveness of the method.

Improved TV-CS Approaches for Inverse Scattering Problem.

Total Variation and Compressive Sensing (TV-CS) techniques represent a very attractive approach to inverse scattering problems. In fact, if the unknown is piecewise constant and so has a sparse gradient, TV-CS approaches allow us to achieve optimal reconstructions, reducing considerably the number of measurements and enforcing the sparsity on the gradient of the sought unknowns. In this paper, we introduce two different techniques based on TV-CS that exploit in a different manner the concept of gradient in order to improve the solution of the inverse scattering problems obtained by TV-CS approach. Numerical examples are addressed to show the effectiveness of the method.

A (CS) 2 approach to inverse scattering

An innovative approach exploiting the Compressive Sensing theory in the solution of the non linear inverse scattering problem is presented. In fact, the proposed approach tackles the inverse problem in its full non linearity by adopting a Contrast-Source Inversion method. In particular, the problem is formulated as a minimization of a proper functional into a convex set defined by the i1-norm of the unknown.

A ‘virtual experiments’ framework for inverse scattering

In this communication we review the rationale and the outcomes of a new way of thinking we have recently introduced for solving inverse scattering problems, i.e., the ‘virtual experiments’ framework.