Finite-element Contrast Source Inversion Research Articles

Use of Field-Perturbing Elements to Increase Nonredundant Data for Microwave Imaging Systems

Field-perturbing elements (FPEs) are introduced for microwave imaging. These elements affect the imaging performance by increasing the amount of nonredundant data. Although this technique can be implemented in nonmetallic chambers, it is especially effective inside metallic enclosures where small perturbations can change the interrogating fields significantly. Results of simulations and a numerical investigation based on synthetic data are presented. The method is validated using an experimental system comprised of 24 coresident radially oriented monopoles that collect the normal component of the electric field on the inside surface of the enclosure. The measured data are used as input to a finite-element contrast source inversion algorithm. To investigate the effectiveness of the approach, a second experimental example is presented where a simplistic breast phantom with a tumor inclusion is imaged inside a smaller cylindrical chamber with 18 radially oriented monopoles and a single FPE. Because FPEs are easy to manufacture and are low costs, they can reduce the cost of an imaging system significantly by reducing the number of required RF ports, as well as reducing the system complexity and modeling error.

Microwave Imaging Using Normal Electric-Field Components Inside Metallic Resonant Chambers

A novel 3-D microwave imaging approach performed within a resonant air-filled metallic chamber is introduced and investigated. The new method utilizes the measurements of normal electric-field components at discrete points along the metallic chamber’s wall—near the chamber-wall boundary, the normal-field components are dominant, while the tangential components vanish. The inversion algorithm fully incorporates the resonant features of the low-loss chamber. A numerical study is used to quantify the imaging performance of using this technique compared with the traditional unbounded domain imaging. An experimental system is presented where the electric field is collected using 24 antennas distributed in three circumferential layers around an object of interest located inside the circular-cylindrical metallic chamber. For collecting the normal component of the field, two types of linearly polarized antennas are investigated: $\lambda /4$ monopole antennas and specially designed reconfigurable antennas (RAs), both projecting perpendicularly out from the chamber walls into the enclosure. The measured data are calibrated and then inverted using a multiplicatively regularized finite-element contrast source inversion algorithm. Using 3-D reconstructions of simple dielectric targets, it is shown that utilizing the RAs improves imaging performance due to a reduction in the modeling error introduced in the inversion algorithm.

Surface-Current Measurements as Data for Electromagnetic Imaging Within Metallic Enclosures

A 3-D microwave imaging method within metallic enclosures is investigated and improved. This method uses the components of the surface-current vector at receiver points on the enclosure wall as data. At the metallic wall, the normal component of the magnetic field as well as the tangential components of the electric field is negligible, whereas the vectorial surface current, which is directly related to the tangential components of the magnetic field, is dominant. After presenting the results of a numerical investigation based on synthetic data, the method is validated using an experimental system comprised of 24 co-resident shielded, coaxial half-loop antennas, distributed in four layers, within a cylindrical metallic enclosure. These antennas are used in receiver–transmitter pairs to introduce an electromagnetic field into the chamber and collect the magnetic field at the receiver points. The measured data are used as input to a multiplicatively regularized finite-element contrast source inversion algorithm. Due to their relatively small size and minimal protrusion into the chamber, these antennas minimally perturb the field distribution inside the chamber and thereby allow the use of a simple numerical inversion model, which does not need to account for the passive antennas. These attributes are especially useful for large computationally intensive industrial applications. The experimental system described herein is a laboratory-scale prototype for a stored-grain imaging application where metallic silos are utilized.

Grain bin monitoring via electromagnetic imaging

Stored grain monitoring is an important post-harvest stage of the food production chain. Grains are usually stored in large metal containers referred to as bins or silos. During storage, there is a possibility for grain to spoil and become unusable. Therefore, monitoring of grain bins is essential to detect conditions leading to spoilage within the bin. Most current grain bin monitoring techniques lack sensitivity as they require conditions leading to spoilage to surpass a certain limit before detection is possible, and consequently a large amount of stored grain is lost during monitored storage. This paper presents the advances in developing a novel grain-monitoring technique using electromagnetic imaging, a modality that can provide global, quantitative images of grain properties throughout the bin. Side-mounted antennas illuminate the contents of the bin and a set of receivers measures the electromagnetic energy within the bin at discrete locations. Using these measurements an optimization algorithm attempts to reconstruct the contents of the bin – herein a finite-element contrast source inversion (FEM-CSI) algorithm was used. The result is a global map of the electrical properties of the grain throughout the bin. In this work we first present a synthetic validation of the proposed method for a model of a full scale hopper bin using simulations to produce the electromagnetic field data. Next, a scaled experimental system was used to collect data from grain that contained regions of induced contamination. This data was used to produce images that show the applicability of the method in practice. Results suggest that this technology has potential to provide farmers with a reliable and robust method to remotely monitor stored grain, preserving stored food resources and increasing their revenue.

A 3-D Dual-Polarized Near-Field Microwave Imaging System

A novel 3-D dual-polarized microwave imaging system based on the modulated scattering technique (MST) is presented. The system collects the magnitude and phase of the scattered field using 120 MST probes and 12 transmitter/collector antennas distributed around an object-of-interest in the near-field region. The 12 antennas form a middle circumferential layer while the printed MST probes are arranged on three circumferential layers including the middle layer. The antennas are linearly polarized double-layer Vivaldi antennas, each fixed inside its own cylindrical conducting cavity and slanted with respect to the vertical axis of the imaging chamber. The MST probes are etched on both sides of a thin substrate and loaded with five evenly distributed p-i-n diodes along their length. These are positioned vertically and horizontally so that the z- and φ-components of the electric field is measured. Field data are collected using MST, calibrated, and then inverted using a multiplicatively regularized finite-element contrast source inversion algorithm. The system performance is evaluated by collecting and inverting data from different 3-D targets.

BREAST IMAGING USING MICROWAVE TOMOGRAPHY WITH RADAR-BASED TISSUE-REGIONS ESTIMATION

Microwave tomography (MWT) and a radar-based region estimation technique are combined to create a novel algorithm for biomedical imaging with a focus on breast cancer detection and monitoring. The region estimation approach is used to generate a patient-specific spatial map of the breast anatomy that includes skin, adipose and fibroglandular regions, as well as their average dielectric properties. This map is incorporated as a numerical inhomogeneous background into an MWT algorithm based on the finite element contrast source inversion (FEM-CSI) method. The combined approach reconstructs finer structural details of the breast and better estimates the dielectric properties than either technique used separately. Numerical results obtained with the novel combined algorithmic approach, based on synthetically generated breast phantoms, show significant improvement in image quality.

Estimation and Use of Prior Information in FEM-CSI for Biomedical Microwave Tomography

Prior information is used to improve imaging results obtained using the finite-element contrast source inversion ( FEM-CSI ) of a microwave tomography (MWT) dataset collected as part of a forearm imaging study. The data consist of field measurements taken inside a prototype MWT system that uses simple dipole antennas and a saltwater matching medium. Initial images of the 2-D cross-sectional dielectric profile of the individuals' arms are reconstructed using FEM-CSI. These initial “blind” imaging results show that the image quality is dependent on the thickness of the arm's peripheral adipose tissue layer: Thicker layers of adipose tissue lead to poorer overall image quality. The poor image quality for arms with high levels of adipose tissue is not improved by changing the matching fluid's complex dielectric constant. Introducing prior information into the FEM-CSI algorithm in the form of an inhomogeneous background consisting of an adipose layer surrounding a muscle region provides substantial improvement of the image quality: The internal anatomical features of the arm are resolved for each of the five datasets. Two methods are employed to estimate the arm periphery and adipose layer thickness from the blind imaging results: manual estimation and a novel image segmentation algorithm based on global optimization using simulated annealing.

Application of Multiplicative Regularization to the Finite-Element Contrast Source Inversion Method

Multiplicative regularization is applied to the finite-element contrast source inversion (FEM-CSI) algorithm recently developed for microwave tomography. It is described for the two-dimensional (2D) transverse-magnetic (TM) case and tested by inverting experimental data where the fields can be approximated as TM. The unknown contrast, which is to be reconstructed, is represented using nodal variables and first-order basis functions on triangular elements; the same first-order basis functions used in the FEM solution of the accompanying field problem. This approach is different from other MR-CSI implementations where the contrast variables are located on a uniform grid of rectangular cells and represented using pulse basis functions. The linear basis function representation of the contrast makes it difficult to apply the weighted <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$L_{2}$</tex></formula> -norm total variation multiplicative regularization which requires that gradient and divergence operators be applied to the predicted contrast at each iteration of the inversion algorithm; the use of finite-difference operators for this purpose becomes unwieldy. Thus, a new technique is introduced to perform these operators on the triangular mesh.

Finite-element contrast source inversion method for microwave imaging

With respect to the microwave imaging of the dielectric properties in an imaging region, the full derivation of a new inversion algorithm based on the contrast source inversion (CSI) algorithm and a finite-element method (FEM) discretization of the Helmholtz differential operator formulation for the scattered electromagnetic field is presented. The unknown dielectric properties are represented as nodal values on a two-dimensional (2D) arbitrary triangular mesh using linear basis functions. The use of FEM to represent the Helmholtz operator allows for the flexibility of having an inhomogeneous background medium, as well as the ability to accurately model any boundary shape or type: both conducting and absorbing. The resulting sparse and symmetric FEM matrix equation can be solved efficiently, and it is shown how its solution can be used to calculate the gradient operators required in the conjugate-gradient CSI update without storing the inverse of the FEM matrix. The inversion algorithm is applied to conductive-enclosures of various shapes and unbounded-region microwave tomography configurations where the 2D transverse magnetic (TM) approximation can be applied.