Carey M. Rappaport

Time reversal with the FDTD method for microwave breast cancer detection

The feasibility of microwave breast cancer detection with a time-reversal (TR) algorithm is examined. This algorithm is based on the finite-difference time-domain method, and compensates for the wave decay and, therefore, is suitable for lossy media. In this paper, we consider a two-dimensional breast model based on magnetic resonance imaging data, and examine the focusing abilities of a TR mirror comprised of an array of receivers with a single ultra-wideband pulse excitation. In order to resolve small 3-mm-diameter tumors, a very short duration pulse is necessary, and this requirement may restrict the applicability of the system due to hardware limitations. We propose a way to overcome this obstacle based on the observation that the amplitude and phase information of the tumor response is sufficient to achieve focusing. The robustness of the TR algorithm with respect to breast inhomogeneities is demonstrated, and the good performance of the method suggests it is a promising technique for microwave breast cancer detection.

Perfectly matched absorbing boundary conditions based on anisotropic lossy mapping of space

An absorbing boundary condition (ABC), based on the PML BBC of Berenger (1994), used in the frequency domain to terminate the computational grid in electromagnetic scattering simulations is presented. Making use of an impedance-matched lossy layer, with directionally-dependent electric and magnetic conductivity, this ABC is independent of frequency and almost independent of incident angle. Thus it can be placed very close to a scatterer, minimizing the usual buffer of required, uninteresting computational space, and so reduce computer storage and CPU time. With this novel formulation, the ABC can be specified in three dimensions in almost the same manner as the standard FDFD equations, with only a small percentage of increased software overhead. >

A general method for FDTD modeling of wave propagation in arbitrary frequency-dispersive media

A general formulation is presented for finite-difference time-domain (FDTD) modeling of wave propagation in arbitrary frequency-dispersive media. Two algorithmic approaches are outlined for incorporating dispersion into the FDTD time-stepping equations. The first employs a frequency-dependent complex permittivity (denoted Form-1), and the second employs a frequency-dependent complex conductivity (denoted Form-2). A Pade representation is used in Z-transform space to represent the frequency-dependent permittivity (Form-1) or conductivity (Form-2). This is a generalization over several previous methods employing either Debye, Lorentz, or Drude models. The coefficients of the Pade model may be obtained through an optimization process, leading directly to a finite-difference representation of the dispersion relation, without introducing discretization error. Stability criteria for the dispersive FDTD algorithms are given. We show that several previously developed dispersive FDTD algorithms can be cast as special cases of our more general framework. Simulation results are presented for a one-dimensional (1-D) air/muscle example considered previously in the literature and a three-dimensional (3-D) radiation problem in dispersive, lossy soil using measured soil data.

FDTD-based time reversal for microwave breast cancer Detection-localization in three dimensions

In a previous study, a novel time-reversal (TR) algorithm based on the finite-difference time-domain (FDTD) method for ultra-wideband microwave breast cancer detection was presented. The system properties and performance were originally studied for two-dimensional (2-D) simplified models and geometries and, more recently, for a realistic breast model based on magnetic resonance imaging measured data. This paper extends this FDTD TR algorithm to a three-dimensional (3-D) case in order to study localization of the tumor target in 3-D. The FDTD TR algorithm solves the full 3-D wave equation and, thus, takes into account polarization effects. In order to compare the new images with previous results, we consider a 2-D planar receiver array, which is an extension of the line of receivers introduced in the 2-D model. A direct comparison from 3-D to 2-D reconstructions illustrates the advantages of using the fully 3-D algorithm, which counterbalances its additional computational cost.

A matched-filter FDTD-based time reversal approach for microwave breast cancer detection

Based on the finite-difference time-domain (FDTD) method, a numerical time-reversal (TR) algorithm for microwave breast cancer detection, already presented in previous work , , is further examined. In , we assumed that the exact field scattered from the tumor-like anomaly is available for backpropagation, and it was shown that the time reversal process is robust to breast inhomogeneities and uncertainties of the skin thickness or electric properties. In this paper, we use the same time reversal mirror (TRM) and two-dimensional (2-D) breast model based on magnetic resonance imaging (MRI) data, but examine the realistic situation where the target response is not known and can only be estimated from the total signal, which is dominated by clutter. A matched-filter approach to solve this signal processing problem is proposed and applied to the TRM data. Detection and localization is achieved for different target locations, and the ability of the time reversal algorithm to avoid false alarms is demonstrated.

Subsurface Sensing of Buried Objects Under a Randomly Rough Surface Using Scattered Electromagnetic Field Data

This paper proposes a new inverse method for microwave-based subsurface sensing of lossy dielectric objects embedded in a dispersive lossy ground with an unknown rough surface. An iterative inversion algorithm is employed to reconstruct the geometry and dielectric properties of the half-space ground as well as that of the buried object. B-splines are used to model the shape of the object as well as the height of the rough surface. In both cases, the control points for the spline function represent the unknowns to be recovered. A single-pole rational transfer function is used to capture the dispersive nature of the background. Here, the coefficients in the numerator and denominator are the unknowns. The approach presented in this paper is based on the state-of-the-art semianalytic mode matching forward model, which is a fast and efficient algorithm to determine the scattered electromagnetic fields. Numerical experiments involving two-dimensional geometries and TM incident plane waves demonstrate the accuracy and reliability of this inverse method

Modeling with the FDTD method for microwave breast cancer detection

This paper addresses important issues related to finite-difference time-domain modeling for microwave breast cancer detection. We present a simple and efficient way of modeling dispersion for various types of biological tissue, in the range of 30 MHz-20 GHz. Propagation and absorbing boundary conditions are modified accordingly. Results from three-dimensional simulations of a semiellipsoid geometric representation of the breast terminated by a planar chest wall illustrate the effect of certain important aspects of the detection problem including: 1) the pulse distorting effects of propagation in frequency-dependent tissue; 2) the choice of the surrounding medium; and 3) the transmitter location relative to the breast and chest wall. In particular, it is shown that the presence of the chest wall can affect greatly the systems detection abilities, even for tumors that are not located in the proximity of the chest wall.

An FPGA implementation of the two-dimensional finite-difference time-domain (FDTD) algorithm

Understanding and predicting electromagnetic behavior is needed more and more in modern technology. The Finite-Difference Time-Domain (FDTD) method is a powerful computational electromagnetic technique for modelling the electromagnetic space. The 3D FDTD buried object detection forward model is emerging as a useful application in mine detection and other subsurface sensing areas. However, the computation of this model is complex and time consuming. Implementing this algorithm in hardware will greatly increase its computational speed and widen its use in many other areas. We present an FPGA implementation to speedup the pseudo-2D FDTD algorithm which is a simplified version of the 3D FDTD model. The pseudo-2D model can be upgraded to 3D with limited modification of structure. We implement the pseudo-2D FDTD model for layered media and complete boundary conditions on an FPGA. The computational speed on the reconfigurable hardware design is about 24 times faster than a software implementation on a 3.0GHz PC. The speedup is due to pipelining, parallelism, use of fixed point arithmetic, and careful memory architecture design.

Three-dimensional subsurface analysis of electromagnetic scattering from penetrable/PEC objects buried under rough surfaces: use of the steepest descent fast multipole method

The electromagnetic scattering from a three-dimensional (3D) shallow object buried under a two-dimensional (2D) random rough dielectric surface is analyzed. The buried object can be a perfect electric conductor (PEC) or can be a penetrable dielectric with size and burial depth comparable to the free-space wavelength. The random rough ground surface is characterized with Gaussian statistics for surface height and for surface autocorrelation function. The Poggio, Miller, Chang, Harrington, and Wu (PMCHW) integral equations are implemented and extended. The integral equation-based steepest descent fast multipole method (SDFMM), that was originally developed at UIUC, has been used and the computer code based on this algorithm has been successfully modified to handle the current application. The significant potential of the SDFMM code is that it calculates the unknown moment method surface electric and magnetic currents on the scatterer in a dramatically fast, efficient, and accurate manner. Interactions between the rough surface interface and the buried object are fully taken into account with this new formulation. Ten incident Gaussian beams with the same elevation angle and different azimuth angles are generated for excitation as one possible way of having multiple views of a given target. The scattered electric fields due to these ten incident beams are calculated in the near zone and their complex vector average over the multiple views is computed. The target signature is obtained by subtracting the electric fields scattered from the rough ground only from those scattered from the ground with the hurled anti-personnel mine.

Statistical method to detect subsurface objects using array ground-penetrating radar data

We introduce a combination of high-dimensional analysis of variance (HANOVA) and sequential probability ratio test (SPRT) to detect buried objects from an array ground-penetrating radar (GPR) surveying a region of interest in a progressive manner. Using HANOVA, we exploit the transient characteristic of GPR signals in the time domain to extract information about buried objects at fixed positions of the array. Based on the output of the HANOVA, the SPRT is employed to make detection decisions recursively as the array moves downtrack. The method is on-line implementable and of low computational complexity. Our approach is validated using field-data from two quite different GPR sensing systems designed for landmine detection applications.