Cylindrical geometry: a further step in active microwave tomography

A prototype imaging system for active microwave tomography using cylindrical geometry has been developed, making it possible to obtain images of the dielectric properties of biological targets at 2.45 GHz. This configuration allows a fast exploration of body slices placed along the array axis, in a way similar to that of present X-ray scanners. The electromagnetic compatibility (EMC) of this approach is critical because the strongly attenuated received fields are measured on the same array which is being used to emit a high-level illuminating signal. Therefore, carefully designed high-frequency architectures and detection techniques are necessary. The system requires no mechanical movements to illuminate the body from multiple directions (views) and measure the scattered fields. In this way, a complete data set consisting of 64 views is acquired in 3 s using low-power illumination. The system is described, and images obtained with biological phantoms and actual bodies are presented.Peer Reviewe

Microwave Imaging of The Neck by Means of Inverse-Scattering Techniques

In recent decades, in the field of applied electromagnetism, there has been a significant interest in the development of non-invasive diagnostic methods through the use of electromagnetic waves, especially at microwave frequencies [1]. Microwave imaging (MWI) - considered for a long period an emerging technique - has potential- ities in numerous, and constantly increasing, applications in different areas, ranging from civil and industrial engineering, with non-destructive testing and evaluations (example e.g., monitoring contamination in food, sub-surface imaging based on both terrestrial and space platforms; detection of cracks and defects in structures and equipments of various kinds; antennas diagnostics, etc. ), up to the biomedical field [2], [3], [4], [5], [6], [7]. One of the first applications of microwave imaging (MWI) in the medical field was the detection of breast tumors [8], [9], [10], [11], [12], [13], [14], [15], [16], [17]. Subsequently, brain stroke detection has received great attention [18],[19], [20], too. Other possible clinical applications include imaging of torso, arms, and other body parts [21], [22], [23], [24]. The standard diagnostic method are computerized tomography (CT), nuclear magnetic resonance (NMR) and X-rays. Although these consolidated techniques are able to provide extraordinary diagnostic results, some limitations still exist that stimulate the continuous research of new imaging solutions. In this context, MWI can be overcome some limitations of these techniques, such as the ionizing radiations in the CT and X-rays or the disadvantages of being expensive, in the NMR case. This motivates the study of MWI methods and systems, at least as a complementary diagnostic tools. The aim of electromagnetic diagnostic techniques is to determine physical param- eters (such as the electrical conductivity and the dielectric permittivity of materials) and/or geometrics of the objects under test, which are suppose contained within a certain space region, sometimes denoted as "investigation domain". In particular, by means of a properly designed transmitting antenna, the object under test is illuminated by an electromagnetic radiation. The interaction between the incident radiation and the target causes the so-called electromagnetic scattering phenomena. The field generated by this interaction can be measured around the object by means of one or more receiving antennas, placed in what is sometimes defined as the "ob- servation domain". Starting from the measured values of the scattering field, it is possible to reconstruct the fundamental properties of the test object by solving an inverse electromagnetic scattering problem. As it is well known, the inverse problem is non-linear and strongly ill-posed, unless specific approximations are used, which can be applied in specific situations. In several cases, two-dimensional configurations (2D) can be assumed, i.e., the inspected target has a cylindrical shape, at least as a first approximation. More- over, often the target is illuminated by antennas capable of generating a transverse magnetic (TM) electromagnetic field [25]. These assumptions reduces the problem from a vector and three-dimensional problem to a 2D and scalar one, since it turns out that the only significant the field components are those co-polarized with the incident wave and directed along to the cylinder axis. In recent years, several methods and algorithms that allow an efficient resolution of the equations of electromagnetic inverse scattering problem have been developed. The proposed approaches can be mainly grouped into two categories: qualitative and quantitative techniques. Qualitative procedures, such as the delay-and-sum technique [26], the linear sampling method [27], and the orthogonality sampling method [28], usually provides reconstructions that allows to extract only some parameters of the targets, such as position, dimensions and shape. However, they are in most cases fast and computationally efficient.On the contrary, quantitative methods allows in principle to retrieve the full distributions of the dielectric properties of the object under test, which allows to also obtain additional information on the materials composing the inspected scenario. Such approaches are often computationally very demanding [25]. Qualitative and quantitative approaches can be combined in order to develop hybrid algorithms [29], [30], [31], [32], [33], [34]. An example is represented by the combination of a delay-and-sum qualitative focusing technique [35], [36], [37] with a quantitative Newton scheme performing a regularization in the framework of the Lp Banach spaces [38], [39], [40]. Holographic microwave imaging techniques are other important qualitative meth- ods. In this case, the processing of data is performed by using through direct and inverse Fourier transforms in order to obtain a map of the inspected target. As previously mentioned, quantitative approaches aim at retrieving the distributions of the dielectric properties of the scene under test, although they can be significantly more time-consuming especially in 3D imaging. Among them, Newton- type approach are often considered [39], [40]. Recently, artificial neural networks (ANNs) have been considered as powerful tools for quantitative MWI. The first proposed ANNs were developed as shallow network architectures, in which one or at least two hidden layers were considered [41], [42]. Successively, deep neural networks have been proposed, in which more complex fully-connected architecture are adopted. In this framework, Convolutional Neural Networks (CNNs) have been developed as more complex topologies, for classification problems or for solving the inverse scattering problems [43], [44], [45], [46], [47], [48], [49]. In the inverse scattering problems, the CNNs often require a preliminary image retrieved by other techniques [43], [44], [47], [50], [51] and do not allow directly inver- sion from the scattered electric fields collected by the receiving antennas. Standard CNNs are developed for different applications. Examples are represented by Unet [52], ResNet [53] and VGG [54]. This Thesis is devoted to the application of MWI techniques to inspect the human neck. Several pathologic conditions can affect this part of the body, and a non-invasive and nonionizing imaging method can be useful for monitoring patients. The first pathological condition studied in this Thesis is the cervical myelopathy [55], which is a disease that damages the first part of the spinal cord, between the C3 and C7 cervical vertebrae located near the head [56]. The spinal cord has an important function in the body, since it represents the principal actor in the nervous system. For this reason, it is "protected" inside the spinal canal [57]. A first effect of cervical myelopathy is a reduction of the spinal canal sagittal diameter, which may be caused by different factors [58]. Some patients are asymptomatic and for this reason a continuous monitoring could be very helpful for evaluating the pathology progression. To this end, the application of qualitative and quantitative MWI approaches are proposed in this document. The second neck pathology studied in this Thesis is the neck tumor, in particular supraglottic laryngeal carcinoma [59], thyroid cancer [60] and cervical lymph node metastases [61]. These kinds of tumors are frequently occurring and shown a 50% 5-year survival probability [61],[62], [63], [64]. Fully-connected neural network are proposed for neck tumor detection. The Thesis is organized as follows. In Chapter 2, the relevant concepts of the electromagnetic theory are recalled. Chapter 3 describes the developed inversion algorithms. It also reports an extensive validation considering both synthetic and experimental data. Detailed data about the imaging approach based on machine learning are provided in Chapter 4. This chapter also reports the results obtained in a set of simulations and experiments. Finally, some conclusions are drawn in Chapter 5

Through-the-Wall Imaging and Multipath Exploitation

We consider the problem of using electromagnetic sensing to estimate targets in complex environments, such as when they are hidden behind walls and other opaque objects. The often unknown electromagnetic interactions between the target and the surrounding area, make the problem challenging. To improve our results, we exploit information in the multipath of the objects surrounding both the target and the sensors. First, we estimate building layouts by using the jump-diffusion algorithm and employing prior knowledge about typical building layouts. We also take advantage of a detailed physical model that captures the scattering by the inner walls and efficiently utilizes the frequency bandwidth. We then localize targets hidden behind reinforced concrete walls. The sensing signals reflected from the targets are significantly distorted and attenuated by the embedded metal bars. Using the surface formulation of the method of moments, we model the response of the reinforced walls, and incorporate their transmission coefficients into the beamforming method to achieve better estimation accuracy. In a related effort, we utilize the sparsity constraint to improve electromagnetic imaging of hidden conducting targets, assuming that a set of equivalent sources can be substituted for the targets. We derive a linear measurement model and employ l1 regularization to identify the equivalent sources in the vicinity of the target surfaces. The proposed inverse method reconstructs the target shape in one or two steps, using single-frequency data. Our results are experimentally verified. Finally, we exploit the multipath from sensor-array platforms to facilitate direction finding. This in contrast to the usual approach, which utilizes the scattering close to the targets. We analyze the effect of the multipath in a statistical signal processing framework, and compute the Cramer-Rao bound to obtain the system resolution. We conduct experiments on a simple array platform to support our theoretical approach

Microwave Tomography With LSTM-Based Processing of the Scattered Field

The quantitative inspection of unknown targets or bodies by means of microwave tomography requires a proper modeling of the field scattered by the structures under test, which in turn depends on several factors related to the adopted antennas and measurement configuration. In this article, a multifrequency tomographic approach in nonconstant-exponent Lebesgue spaces is enhanced by a preliminary step that processes the measured scattered field with a neural network based on long short-term memory cells. In the considered cases, this approach allows dealing with measurements in three-dimensional settings obtained with non-ideal antennas and measurement points, while retaining a canonical two-dimensional formulation of the inverse problem. The adopted data-driven model is trained with a set of simulations of cylindrical targets performed with a finite-difference time domain method, considering a simplified bistatic measurement configuration as an initial case study. The inversion procedure is then validated with numerical simulations involving cylindrical and spherical structures

Experimental Investigation of the Accuracy of an Ultrawideband Time-Domain Microwave-Tomographic System

The measurement accuracy of an ultrawideband (UWB) time-domain microwave-tomographic system is investigated. In order to make an assessment of the random variation of the measurements, the measurement repeatability of the system is evaluated by comparison with an UWB frequency-domain system. A phantom is imaged with the time-domain microwave-tomographic system, and the reconstructed images are compared with those obtained by using the frequency-domain system. The results suggest that with the averaging tens of measurements, the time-domain system can achieve the same level of measurement repeatability as that of the frequency-domain system in the interesting frequency range of microwave tomography. The imaging results, however, indicate that the phantom reconstruction does not require such high measurement accuracy. The permittivity profile of the phantom reconstructed from the nonaveraging time-domain measurements is very similar with that obtained by means of the frequency-domain system

On the 3D electromagnetic quantitative inverse scattering problem: algorithms and regularization

In this thesis, 3D quantitative microwave imaging algorithms are developed with emphasis on efficiency of the algorithms and quality of the reconstruction. First, a fast simulation tool has been implemented which makes use of a volume integral equation (VIE) to solve the forward scattering problem. The solution of the resulting linear system is done iteratively. To do this efficiently, two strategies are combined. First, the matrix-vector multiplications needed in every step of the iterative solution are accelerated using a combination of the Fast Fourier Transform (FFT) method and the Multilevel Fast Multipole Algorithm (MLFMA). It is shown that this hybridMLFMA-FFT method is most suited for large, sparse scattering problems. Secondly, the number of iterations is reduced by using an extrapolation technique to determine suitable initial guesses, which are already close to the solution. This technique combines a marching-on-in-source-position scheme with a linear extrapolation over the permittivity under the form of a Born approximation. It is shown that this forward simulator indeed exhibits a better efficiency. The fast forward simulator is incorporated in an optimization technique which minimizes the discrepancy between measured data and simulated data by adjusting the permittivity profile. A Gauss-Newton optimization method with line search is employed in this dissertation to minimize a least squares data fit cost function with additional regularization. Two different regularization methods were developed in this research. The first regularization method penalizes strong fluctuations in the permittivity by imposing a smoothing constraint, which is a widely used approach in inverse scattering. However, in this thesis, this constraint is incorporated in a multiplicative way instead of in the usual additive way, i.e. its weight in the cost function is reduced with an improving data fit. The second regularization method is Value Picking regularization, which is a new method proposed in this dissertation. This regularization is designed to reconstruct piecewise homogeneous permittivity profiles. Such profiles are hard to reconstruct since sharp interfaces between different permittivity regions have to be preserved, while other strong fluctuations need to be suppressed. Instead of operating on the spatial distribution of the permittivity, as certain existing methods for edge preservation do, it imposes the restriction that only a few different permittivity values should appear in the reconstruction. The permittivity values just mentioned do not have to be known in advance, however, and their number is also updated in a stepwise relaxed VP (SRVP) regularization scheme. Both regularization techniques have been incorporated in the Gauss-Newton optimization framework and yield significantly improved reconstruction quality. The efficiency of the minimization algorithm can also be improved. In every step of the iterative optimization, a linear Gauss-Newton update system has to be solved. This typically is a large system and therefore is solved iteratively. However, these systems are ill-conditioned as a result of the ill-posedness of the inverse scattering problem. Fortunately, the aforementioned regularization techniques allow for the use of a subspace preconditioned LSQR method to solve these systems efficiently, as is shown in this thesis. Finally, the incorporation of constraints on the permittivity through a modified line search path, helps to keep the forward problem well-posed and thus the number of forward iterations low. Another contribution of this thesis is the proposal of a new Consistency Inversion (CI) algorithm. It is based on the same principles as another well known reconstruction algorithm, the Contrast Source Inversion (CSI) method, which considers the contrast currents – equivalent currents that generate a field identical to the scattered field – as fundamental unknowns together with the permittivity. In the CI method, however, the permittivity variables are eliminated from the optimization and are only reconstructed in a final step. This avoids alternating updates of permittivity and contrast currents, which may result in a faster convergence. The CI method has also been supplemented with VP regularization, yielding the VPCI method. The quantitative electromagnetic imaging methods developed in this work have been validated on both synthetic and measured data, for both homogeneous and inhomogeneous objects and yield a high reconstruction quality in all these cases. The successful, completely blind reconstruction of an unknown target from measured data, provided by the Institut Fresnel in Marseille, France, demonstrates at once the validity of the forward scattering code, the performance of the reconstruction algorithm and the quality of the measurements. The reconstruction of a numerical MRI based breast phantom is encouraging for the further development of biomedical microwave imaging and of microwave breast cancer screening in particular

Microwave Sensing and Imaging

In recent years, microwave sensing and imaging have acquired an ever-growing importance in several applicative fields, such as non-destructive evaluations in industry and civil engineering, subsurface prospection, security, and biomedical imaging. Indeed, microwave techniques allow, in principle, for information to be obtained directly regarding the physical parameters of the inspected targets (dielectric properties, shape, etc.) by using safe electromagnetic radiations and cost-effective systems. Consequently, a great deal of research activity has recently been devoted to the development of efficient/reliable measurement systems, which are effective data processing algorithms that can be used to solve the underlying electromagnetic inverse scattering problem, and efficient forward solvers to model electromagnetic interactions. Within this framework, this Special Issue aims to provide some insights into recent microwave sensing and imaging systems and techniques