Colin Gilmore

A Wideband Microwave Tomography System With a Novel Frequency Selection Procedure

In this paper, we describe a 2-D wideband microwave imaging system intended for biomedical imaging. The system is capable of collecting data from 3 to 6 GHz, with 24 coresident antenna elements connected to a vector network analyzer via a 2 × 24 port matrix switch. As one of the major sources of error in the data collection process is a result of the strongly coupling 24 coresident antennas, we provide a novel method to avoid the frequencies where the coupling is large enough to prevent successful imaging. Through the use of two different nonlinear reconstruction schemes, which are an enhanced version of the distorted born iterative method and the multiplicative regularized contrast source inversion method, we show imaging results from dielectric phantoms in free space. The early inversion results show that with the frequency selection procedure applied, the system is capable of quantitatively reconstructing dielectric objects, and show that the use of the wideband data improves the inversion results over single-frequency data.

Microwave Biomedical Data Inversion Using the Finite-Difference Contrast Source Inversion Method

We present a contrast source inversion (CSI) technique which is based on a finite-difference (FD) solver for use in microwave biomedical imaging. The algorithm is capable of inverting complex-permittivity biomedical data sets without the explicit use of a forward solver at each iteration. The FD solver is based in the frequency domain, utilizes perfectly matched layer (PML) boundary conditions, and the stiffness matrix is solved via an LU decomposition and Gaussian elimination. An important feature of the FD-CSI algorithm is that the stiffness matrix associated with the FD solver depends only upon the background medium and frequency, and thus the LU decomposition is only performed once, before the iterative inversion process. Unlike the usual integral equation (IE) based inversion techniques, the FD-CSI algorithm is readily capable of utilizing an arbitrary backarbitrary backgroundground medium for the inversion process.

Derivation and comparison of SAR and frequency-wavenumber migration within a common inverse scalar wave problem formulation

Two common Fourier imaging algorithms used in ground penetrating radar (GPR), synthetic aperture radar (SAR), and frequency-wavenumber (F-K) migration, are reviewed and compared from a theoretical perspective. The two algorithms, while arising from seemingly different physical models: a point-scatterer model for SAR and the exploding source model for F-K migration, result in similar imaging equations. Both algorithms are derived from an integral equation formulation of the inverse scalar wave problem, which allows a clear understanding of the approximations being made in each algorithm and allows a direct comparison. This derivation brings out the similarities of the two techniques which are hidden by the traditional formulations based on physical scattering models. The comparison shows that the approximations required to derive each technique from the integral equation formulation of the inverse problem are nearly identical, and hence the two imaging algorithms and physical models are making similar assumptions about the solution to the inverse problem, thus clarifying why the imaging equations are so similar. Sample images of landmine-like targets buried in sand are obtained from experimental GPR data using both algorithms.

Comparison of an Enhanced Distorted Born Iterative Method and the Multiplicative-Regularized Contrast Source Inversion method

For 2D transverse magnetic (TM) microwave inversion, multiplicative-regularized contrast source inversion (MR-CSI), and the distorted Born iterative method (DBIM) are compared. The comparison is based on a computational resource analysis, inversion of synthetic data, and inversion of experimentally collected data from both the Fresnel and UPC Barcelona data sets. All inversion results are blind, but appropriate physical values for the reconstructed contrast are maintained. The data sets used to test the algorithms vary widely in terms of the background media, antennas, and far/near field considerations. To ensure that the comparison is replicable, an automatic regularization parameter selection method is used for the additive regularization within the DBIM, which utilizes a fast implementation of the L-curve method and the Laplacian regularizer. While not used in the classical DBIM, we introduce an MR term to the DBIM in order to provide comparable results to MR-CSI. The introduction of this MR term requires only slight modifications to the classical DBIM algorithm, and adds little computational complexity. The results show that with the addition of the MR term in the DBIM, the two algorithms provide very similar inversion results, but with the MR-CSI method providing advantages for both computational resources and ease of implementation.

On Super-Resolution With an Experimental Microwave Tomography System

The resolution of an experimental microwave tomography (MWT) system is investigated. Using two cylindrical nylon targets and an operating frequency of 5 GHz, a separation resolution of 2 mm, or 1/30 of a wavelength, is achieved. While this resolution is among the highest reported in the literature, it is not a sufficiently robust indicator of the expected resolution obtainable for complex targets, and this is shown with further examples of more complicated targets. However, the basic separation resolution limit obtained is a good way of comparing various aspects of different MWT systems.

Analysis of Incident Field Modeling and Incident/Scattered Field Calibration Techniques in Microwave Tomography

Imaging with microwave tomography systems requires both the incident field within the imaging domain as well as calibration factors that convert the collected data to corresponding data in the numerical model used for inversion. The numerical model makes various simplifying assumptions, e.g., 2-D versus 3-D wave propagation, which the calibration coefficients are meant to take into account. For an air-based microwave tomography system, we study two types of calibration techniques-incident and scattered field calibration-combined with two different incident field models: a 2-D line-source and an incident field from full-wave 3-D simulation of the tomography system. Although the 2-D line-source approximation does not accurately model incident field in our system, the use of scattered field calibration with the 2-D line-source provides similar or better images to incident and scattered field calibration with an accurate incident field. Thus, if scattered field calibration is used, a simple (but inaccurate) incident field is acceptable for our microwave tomography system. While not strictly generalizable, we expect our methodology to be applicable to most other microwave tomography systems.

Enhancement of microwave tomography through the use of electrically conducting enclosures

We consider microwave tomography (MWT) where the imaging region is surrounded by an electrically conducting surface. This surface acts as both a shield from outside interference, holding tank for any possible matching media, and, in certain cases, serves to enhance the performance of electromagnetic (EM) inversion algorithms. For the 2D transverse magnetic (TM) case and where the surface consists of a perfect electrical conductor (PEC) in the shape of a circular cylinder, we formulate an appropriate Greens function which is amenable to implementation in the existing EM inversion codes. We utilize this Greens function in the multiplicative-regularized contrast source inversion (MR-CSI) method. Several different synthetic examples are used to test the performance of the inversion when the PEC surface is present and the results show that in many cases, the tomographic image is significantly improved. The reasons for the improved inversion results are an area of active research, but are likely to be due to the increased interrogation energy deposited into the imaging region. Results are also shown which demonstrate the problems which may arise if the unbounded domain Greens function is used in an MWT system that utilizes a matching medium of finite extent—a problem which is overcome by the inclusion of a PEC surface on the exterior of the MWT system.

Microwave imaging of human forearms: pilot study and image enhancement

We present a pilot study using a microwave tomography system in which we image the forearms of 5 adult male and female volunteers between the ages of 30 and 48. Microwave scattering data were collected at 0.8 to 1.2 GHz with 24 transmitting and receiving antennas located in a matching fluid of deionized water and table salt. Inversion of the microwave data was performed with a balanced version of the multiplicative-regularized contrast source inversion algorithm formulated using the finite-element method (FEM-CSI). T1-weighted MRI images of each volunteers forearm were also collected in the same plane as the microwave scattering experiment. Initial “blind” imaging results from the utilized inversion algorithm show that the image quality is dependent on the thickness of the arms peripheral adipose tissue layer; thicker layers of adipose tissue lead to poorer overall image quality. Due to the exible nature of the FEM-CSI algorithm used, prior information can be readily incorporated into the microwave imaging inversion process. We show that by introducing prior information into the FEM-CSI algorithm the internal anatomical features of all the arms are resolved, significantly improving the images. The prior information was estimated manually from the blind inversions using an ad hoc procedure.

Hardware invariant protocol disruptive interference for 100BaseTX Ethernet communications

In this paper, we introduce a new concept that we refer to as hardware invariant protocol disruptive interference (HIPDI). Such interference would pose a severe threat as intentional EMI to the corresponding protocol for which it was designed. In this paper, we consider only the 100BaseTX Ethernet protocol over UTP CAT-5 cable which is used extensively in local-area networks. We show that low power, narrowband, differential-mode voltage levels on a 100BaseTX Ethernet twisted-pair can seriously degrade network throughput independent of the physical features of the network or the protocol interpreter hardware. Moreover, we show that the required parameters of disruptive interference can be derived from the protocol itself using a concept we call hardware aperture. The experimental results reported herein indicate that creating such interference is practically feasible and therefore, is a possible threat to existing communication networks.

A study of matching fluid loss in a biomedical microwave tomography system

PURPOSE Effective imaging of human tissue with microwave tomography systems requires a matching fluid to reduce the wave reflections at the tissue boundary. Further, in order to match the idealized mathematical model used for imaging with the complicated physical measurement environment, loss must be added to the matching fluid. Both too little and too much loss result in low-quality images, but due to the nonlinear nature of the imaging problem, the exact nature of loss-to-image quality cannot be predicted a priori. Possible optimal loss levels include a single, highly sensitive value, or a broad range of acceptable losses. Herein, the authors outline a process of determining an appropriate level of loss inside the matching fluid and attempt to determine the bounds for which the images are the highest quality. METHODS Our biomedical microwave tomography system is designed for 2D limb imaging, operating from 0.8 to 1.2 GHz. Our matching fluid consists of deionized water with various levels of loss introduced by the addition of table salt. Using two homogeneous tissue-mimicking phantoms, and eight different matching fluids of varying salt concentrations, the authors introduce quantitative image quality metrics based on L-norms, mean values, and standard deviations to test the tomography system and assess image quality. Images are generated with a balanced multiplicative regularized contrast source inversion algorithm. The authors further generate images of a human forearm which may be analyzed qualitatively. RESULTS The image metrics for the phantoms support the claim that the worst images occur at the extremes of high and low salt concentrations. Importantly, the image metrics show that there exists a broad range of salt concentrations that result in high-quality images, not a single optimal value. In particular, 2.5-4.5 g of table salt per liter of deionized water provide the best reconstruction quality for simple phantoms. The authors argue that qualitatively, the human forearm data provide the best images at approximately the same salt concentrations. CONCLUSIONS There exists a relatively large-range of matching fluid losses (i.e., salt concentrations) that provide similar image quality. In particular, it is not necessary to spend time highly optimizing the level of loss in the matching fluid.