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This paper demonstrates the design steps of a slot-loaded Vivaldi antenna for biomedical microwave imaging applications, showing the influence of the design parameters on the antenna's dimensions and performances. Several antenna miniaturization techniques were taken into consideration during the design: reduction in the electromagnetic wavelength by using a high-permittivity substrate material (relative permittivity ϵ r = 10.2 ), the placement of the antenna inside a coupling medium ( ϵ r = 23 ), and the elongation of the current path by etching slots on each side of the radiator to reduce the antenna's lowest resonant frequency without increasing its physical dimensions. Moreover, an analysis of different antenna slot design scenarios was performed considering different slot lengths, inclination angles, positions, and numbers. Considering the frequency range of microwave imaging (i.e., about 500 MHz–5 GHz) and the array arrangement typical of microwave imaging, the best design was chosen. Finally, the antenna was fabricated and its performances in the coupling medium were characterized. The simulation and measurement results showed good agreement between each other. In comparison with literature antennas, the one developed in this work shows wide bandwidth and compact dimensions. [ABSTRACT FROM AUTHOR]

In this paper, we present a framework for the solution of inverse scattering problems that integrates traditional imaging methods and deep learning. The goal is to image piece-wise homogeneous targets and it is pursued in three steps. First, raw-data are processed via orthogonality sampling method to obtain a qualitative image of the targets. Then, such an image is fed into a U-Net. In order to take advantage of the implicitly sparse nature of the information to be retrieved, the network is trained to retrieve a map of the spatial gradient of the unknown contrast. Finally, such an augmented shape is turned into a map of the unknown permittivity by means of a simple post-processing. The framework is computationally effective, since all processing steps are performed in real-time. To provide an example of the achievable performance, Fresnel experimental data have been used as a validation. [ABSTRACT FROM AUTHOR]

Simple Summary: Non-invasive temperature monitoring during hyperthermia cancer treatment is of paramount importance. It allows physicians to verify the therapeutic temperature is reached in the treated area. Currently, only superficial or invasive thermometry is performed on a clinical level. Magnetic resonance thermometry has been proposed as a a non-invasive alternative but its applicability is limited. Conversely, microwave imaging based thermometry is a potential low cost candidate for non-invasive temperature monitoring. This works presents a computational study in which the use of deep learning is proposed to face the challenges related to the use of microwave imaging in hyperthermia monitoring. The paper deals with the problem of monitoring temperature during hyperthermia treatments in the whole domain of interest. In particular, a physics-assisted deep learning computational framework is proposed to provide an objective assessment of the temperature in the target tissue to be treated and in the healthy one to be preserved, based on the measurements performed by a microwave imaging device. The proposed concept is assessed in-silico for the case of neck tumors achieving an accuracy above 90%. The paper results show the potential of the proposed approach and support further studies aimed at its experimental validation. [ABSTRACT FROM AUTHOR]

Simple Summary: Hyperthermia is a thermal cancer treatment that consists of a selective increase in the tumor temperature to a supra-physiological value for 60–90 min. Heating via microwaves using a phased array applicator proved to be a very useful, non-invasive energy carrier. Although hyperthermia is currently employed for many anatomical sites in combination with standard techniques, there are still open challenges that prevent its more widespread use in the clinic. The aim of this article is to review the work carried out in the framework of a national project concerning the introduction of new tools for microwave hyperthermia and to unify these approaches. The proposed methodologies are interconnected and potentially allow an improvement in treatment planning using a single device. The aim of the article is to provide a summary of the work carried out in the framework of a research project funded by the Italian Ministry of Research. The main goal of the activity was to introduce multiple tools for reliable, affordable, and high-performance microwave hyperthermia for cancer therapy. The proposed methodologies and approaches target microwave diagnostics, accurate in vivo electromagnetic parameters estimation, and improvement in treatment planning using a single device. This article provides an overview of the proposed and tested techniques and shows their complementarity and interconnection. To highlight the approach, we also present a novel combination of specific absorption rate optimization via convex programming with a temperature-based refinement method implemented to mitigate the effect of thermal boundary conditions on the final temperature map. To this purpose, numerical tests were carried out for both simple and anatomically detailed 3D scenarios for the head and neck region. These preliminary results show the potential of the combined technique and improvements in the temperature coverage of the tumor target with respect to the case wherein no refinement is adopted. [ABSTRACT FROM AUTHOR]

Microwave imaging has been recently proposed as alternative technology for in-line inspection of packaged products in the food industry, thanks to its non-invasiveness and the low-cost of the equipment. In this framework, simple and effective detection/imaging strategies, able to reveal the presence of foreign bodies that may have contaminated the product during the packaging stage, are needed to allow real-time and reliable detection, thus avoiding delays along the production line and limiting occurrence of false detections (either negative or positive). In this work, a novel detection/imaging approach meeting these requirements is presented. The approach performs the detection/imaging of the contaminant by exploiting the symmetries usually characterizing the food items. Such symmetries are broken by the presence of foreign bodies, thereby determining a differential signal that can be processed to reveal their presence. In so doing, the approach does not require the prior measurement of a reference, defect-free, item. With respect to the quite common case of homogeneous food packaged in circular plastic/glass jars, numerical analyses are provided to show the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

Microwave imaging is emerging as an alternative modality to conventional medical diagnostics technologies. However, its adoption is hindered by the intrinsic difficulties faced in the solution of the underlying inverse scattering problem, namely non-linearity and ill-posedness. In this paper, an innovative approach for a reliable and automated solution of the inverse scattering problem is presented, which combines a qualitative imaging technique and deep learning in a two-step framework. In the first step, the orthogonality sampling method is employed to process measurements of the scattered field into an image, which explicitly provides an estimate of the targets shapes and implicitly encodes information in their contrast values. In the second step, the images obtained in the previous step are fed into a neural network (U-Net), whose duty is retrieving the exact shape of the target and its contrast value. This task is cast as an image segmentation one, where each pixel is classified into a discrete set of permittivity values within a given range. The use of a reduced number of possible permittivities facilitates the training stage by limiting its scope. The approach was tested with synthetic data and validated with experimental data taken from the Fresnel database to allow a fair comparison with the literature. Finally, its potential for biomedical imaging is demonstrated with a numerical example related to microwave brain stroke diagnosis. [ABSTRACT FROM AUTHOR]

A novel microwave imaging method to detect and possibly characterize nonaccessible targets concealed into a wall or a floor from the measured backscattered field is proposed. The problem is cast as an inverse scattering one aimed at imaging a piecewise homogeneous target embedded in a layered structure. The proposed method is based on a linear sampling method (LSM), a general and computationally effective shape-reconstruction approach that determines the targets morphology through an indicator defined as the regularized solution of a linear inverse problem. However, LSM cannot discern between homogeneous and inhomogeneous targets; hence, it may retrieve the cache but not characterize its content. To overcome this drawback, we propose a two-step approach in which the cache is first imaged by using the standard LSM indicator. Then, by taking advantage of the physical interpretation of the LSM and of the first step's result, a modified indicator is defined and exploited to detect the inclusions possibly hidden in the retrieved cache. Numerical examples are provided as a proof of concept. Index Terms--Buried object detection, electromagnetic scattering inverse problem, linear sampling method (LSM), microwave imaging, through the wall.

This paper addresses the problem of reconstructing geometrical features of 3-D targets embedded into a nonaccessible region from multiview multistatic scattered field data. Sampling methods (SM) are simple and computationally effective approaches to pursue this task. However, their implementation requires a large number of multipolarization sources and probes. Moreover, their performances are often unsatisfactory for aspect-limited measurement configurations and lossy media. In order to tackle these drawbacks, usually faced in subsurface imaging, we propose a simplified and improved formulation based on the physical interpretation of SM. In particular, such a formulation relies on a small number of single polarization probes and exploits multifrequency data, for the first time in the framework of SM. The performances of the resulting approach are verified by monitoring 3-D regions of large extent. Index Terms--Electromagnetic scattering inverse problems, factorization method (FM), linear sampling method (LSM), microwave imaging, subsurface imaging.

Starting from the concept of 'degree of non-linearity' of the relationship amongst unknown parameters and scattered fields, we discuss how knowledge of the geometrical features of the targets favorably affects the solution of inverse scattering problems. The same concept is also exploited to optimize the contrast source-extended Born (CS-EB) model, resulting in the optimized CS-EB (O-CS-EB) inversion approach, which remarkably reduces false solutions occurrence. Then, a two-steps approach is proposed as a reliable and effective inversion strategy. The first step consists in retrieving the shape of the targets using the linear sampling method, while in the second step, the estimated shapes and the O-CS-EB are exploited to reconstruct the permittivity profile. The approach has been tested against experimental data, showing that very accurate reconstructions are achieved from monochromatic data. Index Terms--Contrast source-extended Born (CS-EB), electromagnetic inverse scattering problems, shape reconstruction.

Efficient and reliable reconstruction of location and shape of dielectric targets via microwave imaging is relevant in many applications. In this respect, the linear sampling method is an effective candidate to pursue this task. However, despite its simplicity and computational effectiveness, still its use is restricted to the mathematical community wherein it has been originally developed. Starting from this observation, in this paper we propose and test a simple and original 'physical' interpretation of the linear sampling methods, which shows its relationship with electromagnetic focusing problems. Taking advantage of this result we discuss merits and limitations of the method and suggest new guidelines for a successful application. The analysis is supported with results against experimental data. Index Terms--Electromagnetic scattering inverse problems, linear sampling method (LSM), shape reconstruction.

A new, simple, and fast method for the solution of electromagnetic scattering problems for perfectly conducting objects of arbitrary shape is presented. The method is based on an equivalent representation of the conducting object in terms of a circular one having a higher order impedance boundary condition on its surface. As a first result, a new universal relation between the higher order surface impedances and the shape of the object is obtained. Then, by taking advantage of this relationship, the scattering problem related to a conducting object is recast as the solution of a matrix equation whose coefficients are determined from the higher order impedances. Numerical simulations show that the method yields to accurate results, and that, it is computationally effective. Index Terms--Electromagnetic scattering, impedance boundary condition (IBC), numerical methods.

Accurate and reliable evaluation of the electromagnetic field scattered by dielectric objects is a canonical problem in the electromagnetic community. In the framework of integral equation formulations, iterative techniques, and in particular conjugate gradient (CG) schemes, are widely used. However, when the number of parameters grows, CG techniques may become too demanding from a computational point of view. In this paper, we show that many forward scattering problems can be conveniently solved by means of very simple series expansions, which allow a lower computational complexity and memory storage with respect to other iterative schemes. In particular, we consider three different series expansions, namely: 1) the traditional Born series; 2) the contrast source-extended Born series, which is recently introduced by rewriting the traditional source-type integral equations; and 3) a new series, which is a hybridization of the previous ones. Theoretical conditions for the applicability of the series expansions are discussed, and practical tools to foresee that a problem can be solved by means of these simple iterative schemes are provided. Numerical examples are reported for the sake of comparison and to assess performance. Index Terms--Contrast source extend Born model, electric field integral equation, electromagnetic scattering, integral equations.

In this paper, we investigate whether and how one can synthesize given far field patterns by acting on the dielectric profile of a lens antenna. In particular, an approach to design a radiating system consisting of a variable dielectric profile and a single or a low number of feeds is proposed and discussed. To properly take into account physical and practical feasibility issues, the proposed method splits the problem into two steps. The first one is aimed to fix design goals (i.e., the nominal field), in such a way to avoid super-directive or physically unfeasible antennas and properly exploits known properties of electromagnetic fields radiated by finite extent sources. The second step, dealing with the dielectric profile synthesis, is based on suitable modifications of inverse scattering techniques and can take into account constraints on the spatial behavior as well as of dielectric characteristics of the profile to be synthesized. To show the interest of the subject, as well as effectiveness of the proposed approach, the synthesis of new dielectric antennas, such as a high directivity source and a lens radiating a steerable degradation-free Chebyshev pattern, is considered in the two dimensional scalar case. Index Terms--Antenna theory, antennas synthesis, inverse scattering, lens antennas, shaped beam antennas.

This work presents the design and numerical assessment of a novel microwave imaging (MWI) system, capable of providing a full 3-D image of food/beverage products content in order to disclose the possible presence of physical contaminants, such as plastic fragments. The system here presented exploits the dielectric contrast between the food content and possible intrusions at microwave frequencies; it is based on an antenna array architecture inspecting the items in motion along a conveyor belt without interrupting the production process. The inversion problem is solved by means of linearization, assuming the viability of the Born approximation thanks to the localized intrusions, and regularization, based on the singular value decomposition of the discretized scattering operator. Furthermore, an algorithm, to balance the illumination of the considered scenario due to the nonuniform radiation of the employed antennas, is presented to enhance imaging. The system is first assessed considering an ideal case and then extended to a more realistic approach, for two different kinds of food products, with completely different dielectric properties and considering the performance of existing instrumentation for the purpose. The obtained results lay the foundations for the realization of an actual prototype. [ABSTRACT FROM AUTHOR]

In this article, an innovative approach to microwave imaging, which combines a qualitative imaging technique and deep learning (DL), is presented. The goal is to develop a tool for reliable and user-independent retrieval of the shape of unknown targets from the knowledge of the scattered fields. Qualitative imaging methods are powerful inverse scattering tools, as they provide morphological information in real time. However, their outcome is a continuous map, which has to be hard-thresholded to clearly identify the targets. This thresholding unavoidably results in case-dependent, often user-biased, results. To deal with this issue, a DL approach, based on a physics-assisted deep neural network, is proposed to automatically classify image pixels, i.e., to generate binary masks, separating the targets (foreground) from the background. In particular, the proposed network binarizes the output of a qualitative imaging inversion technique known as the orthogonality sampling method. For the sake of comparison, a DL method is also exploited, which generates the binary masks directly from the scattered fields without any qualitative imaging aid. A quantitative assessment of the performances of both methods and a test on experimental data are provided. [ABSTRACT FROM AUTHOR]

Magnetic scaffolds have been investigated as promising tools for the interstitial hyperthermia treatment of bone cancers, to control local recurrence by enhancing radio- and chemotherapy effectiveness. The potential of magnetic scaffolds motivates the development of production strategies enabling tunability of the resulting magnetic properties. Within this framework, deposition and drop-casting of magnetic nanoparticles on suitable scaffolds offer advantages such as ease of production and high loading, although these approaches are often associated with a non-uniform final spatial distribution of nanoparticles in the biomaterial. The implications and the influences of nanoparticle distribution on the final therapeutic application have not yet been investigated thoroughly. In this work, poly-caprolactone scaffolds are magnetized by loading them with synthetic magnetic nanoparticles through a drop-casting deposition and tuned to obtain different distributions of magnetic nanoparticles in the biomaterial. The physicochemical properties of the magnetic scaffolds are analyzed. The microstructure and the morphological alterations due to the reworked drop-casting process are evaluated and correlated to static magnetic measurements. THz tomography is used as an innovative investigation technique to derive the spatial distribution of nanoparticles. Finally, multiphysics simulations are used to investigate the influence on the loading patterns on the interstitial bone tumor hyperthermia treatment. [ABSTRACT FROM AUTHOR]

This paper presents a novel method for three-dimensional microwave imaging based on sparse processing. To enforce the sparsity of the unknown function, we take advantage of the fact that arbitrary three-dimensional electromagnetic fields can be decomposed into two components with respect to the radial direction: one with transverse-magnetic polarization and the other with transverse-electric polarization. Each component can be further expressed as a sum of spherical harmonics, which provide the dictionary exploited by the sparse processing algorithm. Our measurement model relates the data and the parameters of the spherical harmonics' sources, which are uniformly distributed on a grid sampling the imaging domain. By relying on the theory of degrees of freedom of electromagnetic fields, it can be shown that only a few harmonics are sufficient to accurately represent the measured scattered field from objects whose diameter is of the order of the wavelength, thus allowing reducing the dimension of the adopted dictionary. We analyze several imaging scenarios to assess the algorithm's performance, including different object shapes, sensor orientations, and signal-to-noise ratios. Moreover, we compare the obtained results with other state-of-the-art linear imaging techniques. Notably, thanks to the adopted dictionary, the proposed algorithm can yield accurate images of both convex and concave objects. [ABSTRACT FROM AUTHOR]

In a virtual experiment (VE), the data available to solve an inverse scattering problem are linearly combined in order to make the inversion task simpler. This goal is achieved by conditioning contrast sources radiating the scattered fields and exploiting their properties in the inversion procedure, for instance, by devising data-driven approximations or regularization schemes. In this framework, the design of a VE amounts to determine the coefficients ruling the recombination of the available data. In this article, we present a general and simple procedure to design VEs capable of enforcing contrast sources with desired properties. The proposed procedure is computationally straightforward and stable, as it does not require an explicit inversion and regularization process, and just consists in the evaluation of the adjoint solution of an auxiliary problem. The design approach is tested in the case of VE enforcing circularly symmetric contrast sources, and the corresponding inversion procedure is assessed using both simulated and experimental data. [ABSTRACT FROM AUTHOR]

The orthogonality sampling method (OSM) is a recently introduced qualitative inverse scattering approach for the estimation of the morphological properties of unknown targets. Both the simplicity of implementation and the applicability to various measurement configurations make this method very effective. In this article, a general physical understanding of this otherwise “pure mathematical” method is given for the first time. Such an interpretation is derived from the relationship between the currents induced in the investigated scenario and the so-called reduced scattered field, which is the core of the orthogonality sampling indicator function. Interestingly, the nature of such a relationship implies that the reduced scattered field can be related to the radiating component of the induced currents. A direct consequence of such a result is that the OSM is capable of imaging discontinuities within the unknown targets and hence identify regions with different electromagnetic properties. This possibility represents a unique feature among qualitative inverse scattering methods, as these latter have been introduced as tools to image just the external shape of the unknown targets. The new interpretation as well as the above distinctive capability of the OSM are proved with examples on both simulated and experimental data. [ABSTRACT FROM AUTHOR]

In this article, a method is presented to estimate the effective electrical parameters of the scatterers for multi-view multi-static two dimensional transverse electric (2D-TE) scattering configurations. The derived method needs the shape and position information of scatterers a-priorly to model the targets as circular cylinders (i.e., an effective radius and center is determined for each target) with constant electrical parameters. Next, the method employs the virtual experiments to focus the incident magnetic field as a $J_{0}$ on a specific target. After focusing the excitation and neglecting the multiple scattering between targets, the scattered field is in $H_{1}^{(1)}$ form. Next, the error between the simulated and the virtual fields is calculated. Then, the effective electrical parameter is estimated as the minimizer of the error. Lastly, for the cases where the shape and/or position information are noisy, the introduced method links the deviation of the electrical parameters to deviations of the effective radius and center. From this relation, the method presents a way to estimate the maximum deviations in the electrical parameters, given the maximum deviations in effective radius and center. The efficiency and accuracy of the proposed formulations are tested with both numerical and experimental examples. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present and experimentally verify the first prototype of a microwave imaging system specifically designed and realized for the continuous monitoring of patients affected by brain stroke, immediately after its onset and diagnosis. The device is a 2D version of the 3D system, currently under construction, and consists of an array of 12 printed monopole antennas connected to a two-port vector network analyzer through a switching matrix so that each antenna can act as a transmitter or receiver, thereby allowing the acquisition of the entire multistatic multiview scattering matrix required for the imaging. The system has been experimentally tested on 2D phantoms with electric properties mimicking the brain. The presence and the evolution of the stroke have been reproduced by filling a proper cavity in the phantom with a liquid having the electric properties of blood. A differential approach has been adopted by acquiring the scattering matrix before and after the filling of the blood cavity. The so achieved differential dataset has been processed by means of a linear imaging algorithm in order to reconstruct the stroke location and dimension. Moreover, the effect of pre- and postprocessing operations on the measured data is investigated. A good agreement has been obtained between the reconstructions and the actual scenario. As a final remark, it is worth noting that the entire data acquisition and processing are sufficiently fast to allow a real-time monitoring. [ABSTRACT FROM AUTHOR]

This paper presents the design of a novel low-complexity microwave imaging system for monitoring brain stroke. In particular, the design is concerned with the determination of the optimal layout of the antennas array, namely, minimum number, positions, and polarization of the radiating elements, enabling the acquisition of an amount of data such to assure a reliable imaging. This goal is achieved by adopting a rigorous design procedure based on the inspection of the singular value decomposition of the relevant discretized scattering operator and taking into account the actual dynamics and signal-to-noise ratio of the measurement system. The design is first carried out in the case of ideal dipoles and then extended and assessed for actual printed monopole antennas, developed for the imaging system. The resulting system is a helmet equipped with 24 antennas, whose performances have been numerically validated in terms of both spatial resolution and reconstruction capabilities, by employing full-wave numerical simulations, realistic 3-D phantoms of the human head, and an accurate modeling of the actual antennas employed in the system. [ABSTRACT FROM AUTHOR]

Generating given 3-D field intensity distributions in a non-homogeneous scenario is a canonical problem which is of interest in many applications. On the other side, due to its very challenging nature, very few methods have been proposed up to now in the literature. In this communication, starting from the well-known time reversal (TR) technique, a simple innovative approach, the so-called optimized multi-target TR (O-mt-TR), is presented. The strategy is based on the optimization of the phase shifts between the time-reversed fields in a number of control points within the target region. In doing so, the proposed method outperforms the simple juxtaposition of time-reversed fields pursued by the so-called mt-TR, or even succeed in cases in which the latter fails completely. This capability of the proposed method is assessed through a numerical analysis concerned with a 3-D inhomogeneous scenario, in which the results are quantitatively appraised in terms of coverage of the target areas. [ABSTRACT FROM AUTHOR]

Magnetic nanoparticle-aided microwave imaging is recently gaining an increasing interest as a potential tool for breast cancer diagnostics. This is due to the peculiar features of magnetic nanoparticles, which are biocompatible, can be selectively targeted to the tumor, and may change their microwave magnetic response when modulated by a polarizing magnetic field. This latter aspect is particularly appealing, as it enables the physical separation of the microwave signal due the malignancy, targeted by the nanoparticles, from that due to healthy tissue. This increases the specificity of the diagnostic tool, in principle allowing a diagnosis based solely on the detection of the signal due to the nanoparticles response. In this respect, a proper choice of the polarizing field modulation can remarkably increase the detection performances. This paper deals with this issue, by providing the mathematical framework for such an optimization and a procedure for estimating the required quantities from a set of proper measurements. The procedure is then experimentally demonstrated by applying it to a recently developed ultrawideband radar system for the magnetic nanoparticle-aided detection of breast cancer. For such a system, the optimal magnetic field modulation is determined. [ABSTRACT FROM AUTHOR]

Due to the plethora of possible applicative fallouts, in the recent years several efforts have been made to develop three-dimensional (3-D) field intensity shaping methods. While many approaches able to focus a wave-field into a target point are available, few strategies have been instead developed to generate a field having a given intensity spatial distribution. This is probably due to the higher challenging nature of such a problem. In this letter, with reference to scalar fields, we present an innovative 3-D shaping procedure, which casts the problem as the solution of a finite number of convex programming problems. An example of the performance of the proposed procedure in a 3-D inhomogeneous scenario is given to show the capability of ensuring uniform field intensity within a target area while keeping it arbitrarily bounded elsewhere. [ABSTRACT FROM AUTHOR]

Microwave thermal ablation is a cancer treatment that exploits local heating caused by a microwave electromagnetic field to induce coagulative necrosis of tumor cells. Recently, such a technique has significantly progressed in the clinical practice. However, its effectiveness would dramatically improve if paired with a noninvasive system for the real-time monitoring of the evolving dimension and shape of the thermally ablated area. In this respect, microwave imaging can be a potential candidate to monitor the overall treatment evolution in a noninvasive way, as it takes direct advantage from the dependence of the electromagnetic properties of biological tissues from temperature. This paper explores such a possibility by presenting a proof of concept validation based on accurate simulated imaging experiments, run with respect to a scenario that mimics an ex vivo experimental setup. In particular, two model-based inversion algorithms are exploited to tackle the imaging task. These methods provide independent results in real-time and their integration improves the quality of the overall tracking of the variations occurring in the target and surrounding regions. [ABSTRACT FROM AUTHOR]