Joe LoVetri

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.

A comparison of numerical techniques for modeling electromagnetic dispersive media

A comparison of various time domain numerical techniques to model material dispersion is presented. Methods that model the material dispersion via a convolution integral as well as those that use a differential equation representation are considered. We have shown how the convolution integral arising in the electromagnetic constitutive relation can be approximated by the trapezoidal rule of numerical integration and implemented using a newly derived one-time-step recursion relation. The superiority of the new method, in terms of accuracy and computer resources, over four previously published techniques is demonstrated on the problem of a transient electromagnetic plane wave propagating in a dispersive media. All of the methods considered are easily incorporated into 3-D codes where the requirement for efficiency is very important.

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.

Overview and Classification of Some Regularization Techniques for the Gauss-Newton Inversion Method Applied to Inverse Scattering Problems

Different regularization techniques used in conjunction with the Gauss-Newton inversion method for electromagnetic inverse scattering problems are studied and classified into two main categories. The first category attempts to regularize the quadratic form of the nonlinear data misfit cost-functional at different iterations of the Gauss-Newton inversion method. This can be accomplished by utilizing penalty methods or projection methods. The second category tries to regularize the nonlinear data misfit cost-functional before applying the Gauss-Newton inversion method. This type of regularization may be applied via additive, multiplicative or additive-multiplicative terms. We show that these two regularization strategies can be viewed from a single consistent framework.

Microwave Biomedical Imaging Using the Multiplicative Regularized Gauss--Newton Inversion

The weighted L2-norm total variation multiplicative regularized Gauss-Newton inversion method, recently developed for inversion of low-frequency deep electromagnetic geophysical measurements, is used for microwave biomedical imaging. This inversion algorithm automatically adjusts the regularization weight and provides edge-preserving characteristics. The accuracy of this method is demonstrated by inverting experimental data of a human forearm and synthetic data taken from brain and breast models, both assuming two-dimensional (2D) transverse magnetic illumination.

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.

Modeling of the seat dip effect using the finite‐difference time‐domain method

In this paper the use of the finite‐difference time‐domain technique for the modeling of the seat dip effect in concert halls is demonstrated. The linear time‐domain acoustic partial differential equations are discretized using a finite‐difference technique. The second‐order accurate differencing scheme is time–space centered, and the velocity and pressure are solved on an interlaced mesh. First‐ and second‐order Mur absorbing boundary conditions, originally formulated for electromagnetic problems, are adapted to the acoustics case and used to truncate the numerical grid. The technique is first verified by comparing the numerical results to the analytic solution of a simple point source. Results from computer simulations of the seat dip phenomena are compared with the findings of previous studies where measurements had been made on scale models and in real concert halls. The computer model successfully predicts the effects associated with the source–receiver distance, the height of the receiver, and the h...

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.