Mehmet E. Yavuz

Full time-domain DORT for ultrawideband electromagnetic fields in dispersive, random inhomogeneous media

We investigate the decomposition of the time-reversal operator (DORT under its French language acronym) method applied to ultrawideband electromagnetic pulses propagating in dispersive and (continuous) inhomogeneous random media where volumetric scattering effects are important. We analyze the effects of random medium statistics on the time-reversal operator (TRO) eigenvalues and eigenvectors, and on subsequent selective focusing performance. We develop and employ a full time-domain DORT by tracking the excitation eigenvectors from a singular value decomposition of the TRO over the entire bandwidth of operation. We also study effects of frequency dispersion and conduction losses on the TRO and consider dispersion/loss compensation techniques to improve DORT operation in those cases

Space–Frequency Ultrawideband Time-Reversal Imaging

We introduce time-reversal ultrawideband (UWB) imaging functionals based on the simultaneous utilization of spatial and UWB frequency data acquired by limited-aspect antenna arrays. The targets are discrete scatterers embedded in homogeneous or continuous random inhomogeneous media. Singular value decomposition is applied to space-frequency multistatic scattering data matrices indexed by sensor location and frequency data, and the resulting singular values and vectors are employed to construct time-domain excitation signals for UWB imaging of the embedded scatterer(s) via synthetic backpropagation (reverse migration). Spatial information needed for focusing on the embedded scatterer(s) is provided by either the left singular vectors or the eigenvectors of the space-space multistatic data matrices. The resulting UWB imaging functionals can yield statistical stability in random media.

On the Sensitivity of Time-Reversal Imaging Techniques to Model Perturbations

Time-reversal (TR) techniques involve physical or synthetic retransmission of signals acquired by a set of transceivers in a time-reversed fashion, and can be used for a host of applications, including ultrawideband imaging of obscured targets. This work investigates the performance of some TR-based techniques under non-ideal conditions, and is divided into three main parts. In the first part, we investigate the robustness of TR-based imaging techniques via the decomposition of TR operator (DORT) algorithm and the multiple signal classification (MUSIC) algorithm under clutter and (additive) noise. In the second part, we examine the effect of TR-invariance breaking (due to losses in the intervening media) on the performance of both DORT and (TR-based) MUSIC. In the third part, effects of translational perturbations of the TR array are examined, as a class of model perturbations. These ensuing effects are then exploited, in a controlled manner, as a means to extract second-order spatial statistics of the probed media.

Ultrawideband Microwave Sensing and Imaging Using Time-Reversal Techniques: A Review

This paper provides an overview of some time-reversal (TR) techniques for remote sensing and imaging using ultrawideband (UWB) electromagnetic signals in the microwave and millimeter wave range. The TR techniques explore the TR invariance of the wave equation in lossless and stationary media. They provide superresolution and statistical stability, and are therefore quite useful for a number of remote sensing applications. We first discuss the TR concept through a prototypal TR experiment with a discrete scatterer embedded in continuous random media. We then discuss a series of TR-based imaging algorithms employing UWB signals: DORT, space-frequency (SF) imaging and TR-MUSIC. Finally, we consider a dispersion/loss compensation approach for TR applications in dispersive/lossy media, where TR invariance is broken.

A numerical study of time-reversed UWB electromagnetic waves in continuous random media

We investigate superresolution effects on ultrawideband (UWB) electromagnetic waves (EM) produced by time-reversal (TR) arrays in continuous random media. The investigation is done via numerical simulations employing the finite-difference time-domain (FDTD) method. A Gaussian random background medium is considered. We compare the effect of statistical parameters, viz. variance, and correlation length, on the focusing resolution of transmitted waves by the TR array (TRA). The effect of depolarization is also briefly considered.

Frequency dispersion compensation in time reversal techniques for UWB electromagnetic waves

The invariance of the wave equation under time reversal enables optimal refocusing of ultrawideband waves by time-reversal (TR) arrays. This forms the basis of recently developed TR techniques for selective (re-)focusing and inverse scattering applications. However, in electromagnetic sensing applications involving lossy or dispersive media, such as earth media, time invariance is lost and TR techniques can be significantly degraded. To alleviate this problem, a method to compensate dispersion in TR applications is proposed here. The method is based on short-time Fourier transforms and is shown to improve refocusing.

GPR Signal Enhancement Using Sliding-Window Space-Frequency Matrices

Ground penetrating radar (GPR) has shown to provide useful results for detection of buried objects. However, its performance sufiers from strong re∞ection from ground surface especially for shallowly buried targets. In such cases, the detection problem depends on the separation of the target signal from the ground backscatter such as landmines and unexploded ordnances. In this paper, we discuss and analyze the use of space-frequency time-reversal matrices for the enhancement of ground penetrating radar signals and potential clutter reduction. Through the use of sliding windows, submatrices from a given B-scan (radargram) are utilized to extract localized scattering information of a given detection scenario. Each sub-B-scan is decomposed to its singular vectors and later used to render synthetic aperture time-domain singular vector distributions corresponding to difierent scattering mechanisms. Later, they are weighted by the singular values and subtracted from the full B-scan to achieve reduced clutter and enhanced target response. The method shows satisfactory results for shallowly buried dielectric targets even in the presence of rough surface proflles.

Continuous Wavelet Transform-Based Frequency Dispersion Compensation Method for Electromagnetic Time-Reversal Imaging

The invariance of wave equations in lossless media allows the time reversal (TR) technique to spatiotemporally refocus back-propagated signals in a given ultrawideband imaging scenario. However, the existence of dispersion and loss in the propagation medium breaks this invariance and the resultant TR focusing exhibits frequency and propagation duration dependent degradation. We propose an algorithm based on the continuous wavelet transform that tackles this degradation to improve focusing resolution under such conditions. The developed algorithm has been successfully applied to the scenario for localization of lung cancer.

Frequency Dispersion Compensation Through Variable Window Utilization in Time-Reversal Techniques for Electromagnetic Waves

In microwave imaging applications, propagating signals undergo additional attenuation in dispersive and lossy media compared to the nondispersive and lossless media. In this communication, we introduce a threshold approach and short-time Fourier transform (STFT)-based inverse filters to compensate for such additional attenuation in time-reversal (TR)-based imaging algorithms. The method introduced here is utilized to reduce the unwanted noise amplification in the received signals during the compensation stage. Additionally, optimum settings for window type and length in the STFT method are obtained through a scanning operation in the propagation medium. Different window types and lengths are studied to achieve the best focusing resolution in TR applications. While utilizing a large number of windows with short spatial lengths provides an improved TR focusing performance, it also increases the overall cost and complexity of the imaging system. The threshold method introduced here achieves improved TR focusing performance without increasing the cost by utilizing a lower number of inverse filters.

Effects of array restriction on time-reversal methods

In this work, we consider two TR-based algorithms: DORT (decomposition of the TR operator) (Prada et al., 1994) and TR-MUSIC (TR-multiple signal classification).