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.