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Quantitative inversion of GPR data opens the door to precise characterization of underground environments. However, in order to make the inverse scattering problem solution easier from a computational viewpoint, simplifying assumptions are often applied, i.e., two-dimensional approximations or the consideration of idealized field probes and electromagnetic sources. These assumptions usually produce modeling errors, which can degrade the dielectric reconstruction results considerably. In this article, a processing step based on long short-term memory cells is proposed for the first time to correct the modeling error in a multiantenna GPR setting. In particular, time-domain GPR data are fed into a neural network trained with couples of finite-difference time-domain simulations, where a set of sample targets are simulated in both realistic and idealized configurations. Once trained, the neural network outputs an approximation of multiantenna GPR data as they are collected by an ideal two-dimensional measurement setup. The inversion of the processed data is then accomplished by means of a regularizing Newton-based nonlinear scheme with variable exponent Lebesgue space formulation. A numerical study has been conducted to assess the capabilities of the proposed inversion methodology. The results indicate the possibility of effectively compensating for modeling error in the considered test cases. [ABSTRACT FROM AUTHOR]

A microwave characterization technique to inspect subsurface scenarios is proposed and numerically assessed in this paper. The approach is based on a combination of finite element electromagnetic modeling and an inversion procedure in Lebesgue spaces with variable exponents. The former allows for description of the measurement system and subsurface scenario with high accuracy, while the latter exploits the adaptive definition of exponent function to achieve improved results in the regularized solution of the inverse scattering problem. The method has been assessed with numerical simulations regarding two-layered environments with both planar and non-planar air–soil interfaces. The results show the capabilities of the method of detecting buried objects in different operative conditions. [ABSTRACT FROM AUTHOR]

An innovative nonlinear inverse scattering approach in variable exponent Lebesgue spaces is proposed for microwave imaging purposes. The main objective of the approach is to overcome one of the main problems associated with reconstruction procedures developed in Lebesgue spaces with constant exponent, i.e., the need for the selection of the optimum Lebesgue-space norm parameter, which is critical for obtaining accurate reconstructions, and no exact rules exist for this choice. The approach proposed in this paper is oriented to tomographic imaging applications at microwave frequencies, for which the adopted inversion procedure is based on a Gauss–Newton method, which has been reformulated in the unconventional variable exponent Lebesgue spaces. The capabilities of the approach are demonstrated by a set of numerical simulations, in which cylindrical dielectric targets are inspected. Moreover, an experimental result is reported. [ABSTRACT FROM AUTHOR]

A new microwave tomography prototype for the inspection of wood materials is described and experimentally tested in this paper. The system prototype is composed by a set of microwave antennas, used for both illuminating the sample and collecting field measurements, a custom RF hardware, and a hybrid tomographic inversion scheme. The antennas are placed in contact with the outer structure of the sample, e.g., a tree trunk, and are optimized to radiate inside the inspected region. A switching matrix connects the set of antennas with a custom vector network analyzer, which is used for acquiring multistatic and multiview field measurements at multiple frequencies. The measured data are processed by means of a combined qualitative/quantitative inversion method. In particular, in a first step, the field scattered by the inner inhomogeneities or inclusions is estimated, producing also a qualitative image of the sample. Then, these data are utilized by a deterministic inversion algorithm in order to obtain a quantitative reconstruction of the dielectric properties of the structure under test. [ABSTRACT FROM AUTHOR]

A hybrid approach is proposed to inspect three-dimensional homogeneous dielectric scatterers by using microwaves. Namely, the considered method consists in two steps: first, the supports of the scatterers are retrieved by the linear sampling method; then the permittivities of the targets are estimated by an ant colony optimization algorithm. The described strategy combines the efficiency of the linear sampling method with the global optimization capabilities of the stochastic procedure. Numerical results assess the capabilities of the approach also in the presence of noise. [ABSTRACT FROM AUTHOR]

In this paper, a new inverse-scattering-based reconstruction method is presented. The aim of the approach is to ‘invert’ wavefield samples, which are collected by experimental tomographic systems working at radio frequencies and microwaves. Imaging systems operating in this band require the solution of a nonlinear and highly ill-posed inverse problem. The need to regularize the inverse problem is addressed here by considering an efficient Inexact Newton method that is able to inspect strong scatterers. In this paper, the mathematical formulation of the approach is detailed and discussed. Moreover, the results of several numerical simulations concerning the reconstructions of dielectric structures in noisy environments and in several applicative scenarios are reported. [ABSTRACT FROM AUTHOR]

A new approach to noninvasive inspection of dielectric targets at microwave frequencies is proposed. Cylindrical dielectric objects are reconstructed under the second-order Born approximation. A multi-illumination configuration is considered. The continuous model is discretized by the moment method and an efficient inexact-Newton method is applied. The dielectric profile is iteratively reconstructed starting from the measured scattered data, which are related to the unknown target through the inverse scattering equations written in a variational setting. Several numerical results are reported, which are aimed at assessing the capabilities of the approach in dealing with the nonlinear illeposed inverse problem associated to the short-range microwave imaging. Single, multilayer, and separate cylinders are reconstructed in noiseless and noisy environments. [ABSTRACT FROM AUTHOR]

A hybrid inversion scheme for through-the-wall imaging is proposed in this paper. The approach is based on a linearized model of the inverse-scattering problem, employing the Green's function developed for a layered background. The reconstruction is obtained by means of a Landweber-like iterative method performing a regularization in the framework of variable-exponent Lebesgue spaces. Thanks to the non-conventional geometrical properties of such spaces, it is possible to enhance the reconstruction capabilities, e.g., by promoting sparseness and reducing over-smoothing. The exponent function defining the specific space adopted in the inversion procedure is adaptively obtained directly from the measured data, through a truncated-singular value decomposition method. In this way, it is possible to precompute and reuse in both steps, for a given scenario, all the matrices necessary in the inversion process, thus leading to a computationally efficient solving strategy. The effectiveness of the approach is evaluated by using experimental data obtained with a commercial GPR apparatus employing a pulsed source field. A fast Fourier transform is applied to the time-domain measurements to extract frequency-domain data at a set of frequencies in the source spectrum, which are fed in input to the imaging scheme. Very good reconstruction capabilities are obtained both with a single metallic target, as well as in a challenging two targets layout including both a metallic object and a low-permittivity target. [ABSTRACT FROM AUTHOR]

Microwave imaging of targets enclosed in circular metallic cylinders represents an interesting scenario, whose applications range from biomedical diagnostics to nondestructive testing. In this paper, the theoretical bases of microwave tomographic imaging inside circular metallic pipes are reviewed and discussed. A nonlinear quantitative inversion technique in non-Hilbertian Lebesgue spaces is then applied to this kind of problem for the first time. The accuracy of the obtained dielectric reconstructions is assessed by numerical simulations in canonical cases, aimed at verifying the dependence of the result on the size of the conducting enclosure and comparing results with the conventional free space case. Numerical results show benefits in lossy environments, although the presence and the type of resonances should be carefully taken into account. [ABSTRACT FROM AUTHOR]

The imaging of dielectric targets hidden behind a wall is addressed in this paper. An analytical solver for a fast and accurate computation of the forward scattered field by the targets is proposed, which takes into account all the interactions of the electromagnetic field with the interfaces of the wall. Furthermore, an inversion procedure able to address the full underlying non-linear inverse scattering problem is introduced. This technique exploits a regularizing scheme in Lebesgue spaces in order to reconstruct an image of the hidden targets. Preliminary numerical results are provided in order to initially assess the capabilities of the developed solvers. [ABSTRACT FROM AUTHOR]

An overview of the recent advancements in the development of microwave imaging procedures based on the exploitation of the regularization theory in Lebesgue spaces is reported in this paper. Such inversion schemes have been found to provide accurate results in several microwave imaging scenarios, thanks to the different geometrical properties that Lebesgue spaces can exhibit with respect to the more classical Hilbert ones. Moreover, the recent extension to the more general case of variable-exponent Lebesgue spaces is also addressed. Experimental results involving reference data are shown for supporting the theoretical description of the approaches. [ABSTRACT FROM AUTHOR]

The subject of this paper is the possible use of a network of microwave sensors to achieve a map of the electromagnetic properties of unknown targets. The basic idea is to use a set of microwave sensors to illuminate a region of interest and to measure the resulting axial component of the electric field. Measurements are then processed by means of a technique based on inverse-scattering, which provides an estimate map of the dielectric values of the area under examination, allowing to discriminate among possible targets. In order to initially evaluate the feasibility of the proposed approach, numerical results in a simulated environment are preliminarily considered and discussed. Furthermore, an initial test on experimental data in a simplified configuration is also presented. [ABSTRACT FROM AUTHOR]