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The Phase Retrieval problem is dealt with for the challenging case where just a single set of (phaseless) radiated field data is available. In particular, even still emulating the solution of crosswords puzzles, we provide decisive improvements over our recent approaches. In fact, by exploiting bandlimitedness and a suitable set of intersecting curves, we definitively lower the computational complexity (thus eliminating drawbacks) of our previous techniques. Numerical examples, concerning applications of actual interest, support the given theory and confirm the effectiveness of the developed procedure.

Nonlinearity arising from mutual interactions is one of the two main difficulties to be addressed in inverse scattering. In this paper, we review and describe under a common rationale some approaches which have been introduced in literature in order to counteract nonlinearity. In particular, we focus on possible rewritings of the Lippman Schwinger basic equation such to reduce the degree of nonlinearity of inverse scattering problem. In detail, three different rewritings are discussed and compared by emphasizing similarities and the differences, and in the same rewriting spirit, we also summarize and discuss the Virtual Experiments framework. Then, some possible joint exploitations of the above concepts are introduced, discussed and tested against numerical examples., in IEEE Open Journal of Antennas and Propagation, 2021

In this paper, a new inversion model for 2D microwave imaging is introduced by means of a convenient rewriting of the usual Lippmann Schwinger integral scattering equation. Such model is derived by decomposing the Greens function and the corresponding internal radiation operator in two different contributions. In fact, one of them can be easily computed from the collected scattered data. In case of lossless backgrounds, the resulting model turns out to be more convenient than the traditional one, as it exhibits a lower degree of nonlinearity with respect to parameters embedding the unknown dielectric characteristics. This interesting property suggests its exploitation in the solution of the inverse scattering problem. The achievable performances are tested by comparing the proposed model with the usual one based on the Lippman-Schwinger equation in both cases of linearly approximated and full non-linear frameworks. Both numerical and experimental data are considered., Comment: in IEEE Transactions on Antennas and Propagation (2021)

Quantitative estimation of both conductivity and permittivity of biological tissues is essential in many biomedical applications, ranging from therapeutic treatments to safety assessment of medical devices and dosimetry. Typically, the electromagnetic field distribution inside the body is predicted based on available ex-vivo measured electrical properties. Unfortunately, these values may be quite different from the ones measured in-vivo and cannot account for the differences among individuals. As a result, their use can introduce significant errors affecting therapeutic treatments and dose estimation. To cope with this problem, in this paper a new approach for estimation of effective electrical properties of human tissues is introduced. The proposed strategy is based on the solution of an inverse scattering problem (by means of a contrast source inversion scheme) and the use of an effective representation of the unknowns based on spatial priors derived by magnetic resonance imaging or computed tomography. The approach is tested in controlled conditions against simulated single frequency data and realistic and anthropomorphic head and neck phantoms. Moreover, the inherent advantages have been assessed in the framework of hyperthermia treatment planning.

The estimation of the effective electrical properties of biological tissues is relevant to different medical applications, ranging from hyperthermia treatment planning to dosimetry. In this contribution, we introduce a novel inverse scattering approach to cope with this problem. This latter is relevant to microwave tomography and is herein formulated in 3D geometry. More in details, the procedure performs the inversion of measured fields scattered by the investigated biological scenario by taking advantage from the spatial priors derived from segmented medical images and conveniently representing the unknown electrical properties.

Tomographic approaches represent an emerging way to process GPR data and to investigate stratified media, since they allow to obtain images that are more readable than those achieved with standard data processing, which require human expertise and may show high probability of false alarms. In this contest, an efficient inverse scattering strategy is proposed to achieve dielectric characterization of buried objects in lossy and stratified soils. The approach exploits the framework of the 'virtual scattering experiments' in a stratified media, thus allowing to deal with not only the non linearity of the underlying physical phenomena, but also to counteract the difficulty arising from the aspect limited measurement configuration adopted in GPR surveys. The proposed method is tested through a numerical example, by considering Compressive Sensing regularization scheme in order to enhance imaging resolution capabilities.

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.

3D field shaping is a canonical problem in wave physics that could impact next generation of therapeutic systems. In this framework, we present an innovative and effective strategy that relies on the convex relaxation of the original NP hard problem by taking inspiration from the optimal constrained power focusing method. The formulation presented in this paper in terms of convex programming allows an efficient solution of the problem at hand by means of local search algorithms.

The capability of controlling the spatial distribution of a field into a given scenario is relevant to many applications as different as hyperthermia treatment planning and wireless network optimization. In this respect, many strategies to focus the field into a target point have been presented, whereas the possibility of arbitrarily shaping a field still remains an open challenge. In this communication, we present an innovative approach to field intensity shaping that unravels the original NP hard problem into several convex programming ones, by means of the proper equality constrained method. The approach is discussed and assessed with a numerical example.

A method for constrained focusing or shaping of the Specific Absorption Rate deposition is proposed and discussed. The approach contemporarily takes advantage from multifre-quency applicators, which allow a better control of possible hot-spots, as well as from the proposed formulation, which allows to reduce the problem to a single or a series of Convex programming problems. The approach is presented for the case of scalar fields but it can be extended to vector fields as well.

Electron Cyclotron Resonance Ion Sources (ECRIS) are among the candidates to support the growing request of intense beams of multicharged ions. Their further development is related to the availability of new diagnostic tools, nowadays consisting of few types only of devices designed on purpose for such compact machines. Microwave Interferometry is a non-invasive method for plasma diagnostics and represents the best candidate for the whole plasma density measurements. Interferometry in ECR Ion Sources is a challenging task due to their compact size. The typical density range of ECR plasmas (10¹¹-10¹² cm⁻³) causes the probing beam wavelength to be in the order of few centimetres, which is comparable to the chamber radius. The paper describes the design of a new microwave interferometer based on the so-called "frequency sweep" method: the density is here derived by the frequency shift of a beating signal obtained during the fast sweep of both probing and reference microwave signals; inner cavity multipaths contributions can thereby be suppressed by cleaning the spurious frequencies from the beating signal spectrum., Proceedings of the 6th Int. Particle Accelerator Conf., IPAC2015, Richmond, VA, USA

Time Reversal (TR) is a well known spatial/temporal re-focusing process based on the time invariance of the wave equation in lossless media. This communication deals with an aspect of Time Reversal as applied to vector fields that has never been discussed before, that is, the polarization of the point source physically or synthetically located into the target point during the 'sensing' phase of TR process. It will be shown its huge impact on TR focusing performances.

International audience

International audience

International audience

A new approach providing new theoretical results to the optimal far-field focusing of uniformly spaced arrays, subject to a completely arbitrary mask for sidelobe bounds, is presented and discussed. In both cases of linear or planar arrays (with rectangular boundaries), it is first shown that the problem can be formulated, without any loss to performances on the maximum, as a linear programming one, guaranteeing a globally optimal solution. Second, a sufficient uniqueness criterion for the solution of the overall problem is also developed, which shows how the solution may not be unique (as is actually the case) when planar arrays are considered. In addition, further globally effective optimization procedures are proposed for the latter case in order to optimize directivity, smoothness of excitations, or other performance parameters in the set of equivalent solutions. Last, an extension to planar arrays with a nonrectangular boundary is also given. A thorough numerical analysis confirms the effectiveness of the approach proposed and of the solution codes developed.

A hybrid approach to the synthesis of the excitations and locations of non-uniformly spaced arrays, in order to achieve optimal focusing in any given direction, is proposed and discussed. The approach takes definite advantage from the convexity of the problem with respect to the excitation variables, and exploits a simulated annealing procedure as far as the location variables are concerned. The corresponding synthesized patterns outperform previously known results in standard benchmark problems.