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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.

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)

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.

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 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.