Decomposition Of The Time Reversal Operator Research Articles

Nonlinear Through-the-Wall Detection Using DORT Applied With LFM Pulses

The detection of visually obstructed small nonlinear targets in a through-the-wall (TTW) environment is difficult because of linear scatterers and strong wall reflections. In this letter, harmonic-based nonlinear TTW detection is introduced as a method to effectively detect small nonlinear targets behind the wall. Nonlinear TTW detection allows for the suppression of linear scatterer responses and wall reflections by detecting only the harmonics generated from nonlinear targets. Here we apply the decomposition of the time-reversal operator (DORT) for the detection and separation of multiple nonlinear targets behind the wall. DORT extracts the eigenvalues and eigenvectors of nonlinear targets and allows for selective focusing (imaging) of each detected target. In addition, we utilize linear frequency modulated (LFM) pulses, which allow for the compression gain in the detection processing. To validate the proposed concept, we conducted simulation and measurements of various configurations of nonlinear TTW detection. The results demonstrate that nonlinear targets behind the wall can be effectively detected and located.

An Electromagnetic Time-Reversal Imaging Algorithm for Moisture Detection in Polymer Foam in an Industrial Microwave Drying System.

Microwave tomography (MWT) based control is a novel idea in industrial heating systems for drying polymer foam. In this work, an X-band MWT module is designed and developed using a fixed antenna array configuration and integrated with the HEPHAISTOS industrial heating system. A decomposition of the time-reversal operator (DORT) algorithm with a proper Green’s function of multilayered media is utilized to localize the moisture location. The derived Green’s function can be applied to the media with low or high contrast layers. It is shown that the time-reversal imaging (TRI) with the proposed Green’s function can be applied to the multilayered media with a moderately rough surface. Moreover, a single frequency TRI is proposed to decrease the measurement time. Numerical results for different moisture scenarios are presented to demonstrate the efficacy of the proposed method. The developed method is then tested on the experimental data for different moisture scenarios from our developed MWT experimental prototype. Image reconstruction results show promising capabilities of the TRI algorithm in estimating the moisture location in the polymer foam.

Robust and Low-Complexity Time-Reversal Subspace Decomposition Methods for Acoustic Emission Imaging and Localization

This article focuses on the acoustic emission (AE) localization problem in the complex and unknown probed domain. The schemes based on time-reversal (TR) theorem are proposed to achieve accurate imaging and localization, even when there is no accurate priori knowledge of the Green's functions. In the proposed strategies, a signal enhancement method is proposed to de-noise sensor wavefields from single or multiple sources firstly. Then the wideband signal matrix is condensed into a single frequency matrix by coherent processing. The steering vectors are estimated based on minimizing noise variance. And by incorporating the steering vector estimation algorithm into the subspace decomposition-based methods, two novel robust imaging methods, robust coherent Decomposition of the time-reversal operator (R-DORT) and robust coherent time-reversal Multiple signal classification (R-TR-MUSIC), are presented. The performance of the proposed methods is evaluated using simulation studies that consider two background mismatches and different levels of signal-to-noise ratio (SNR) respectively. The simulation results demonstrate the effectiveness and the superiority of the presented methods in locating AE sources under the complex and uncertain circumstances. Moreover, the localization results based on experimental data show the potential of the proposed methods in practical applications.

Localisation and permittivity extraction of an embedded cylinder using decomposition of the time reversal operator

In this study, first, the problem of time reversal imaging of an embedded dielectric or metallic cylinder inside another dielectric cylinder is studied. The direct problem is carried out numerically using the finite-element method. The background dyadic Green function (DGF) is computed analytically by computing radiated fields of an infinitesimal electric dipole near an infinitely long dielectric cylinder. The time reversal technique is then applied using this background DGF to image the embedded cylinder. Results demonstrate that while using a free-space DGF for imaging yields erroneous results, by employing a proper background DGF, the scatterer inside the cylinder is correctly localised. Next, the authors extract permittivities in two different scenarios with two different techniques. In the first case, the permittivity of a background cylinder that contains a metallic cylinder inside it is extracted by calculating the image entropy. In the second case, the permittivity of an embedded cylinder inside a priori known background dielectric cylinder is estimated by a new method based on an optimisation and evaluation of the largest eigenvalues of the multistatic data matrices. The proposed techniques are then verified using simulated and measured data. For measurements, a newly developed combined tapered sectorial antenna is designed, fabricated, and characterised.

A DORT-Uniform Diffraction Tomography Algorithm for Through-the-Wall Imaging

Strong reflections of the front wall in a through-the-wall imaging (TWI) system can challenge the detection of the scatterers behind the wall, and cause defocusing and displacement of the images. In this article, a generalized pencil-of-function (GPOF)-based wall mitigation approach is introduced and implemented along with a selective focusing algorithm for TWI. We develop and employ a wideband decomposition of the time-reversal operator (DORT) in conjunction with the uniform diffraction tomographic (UDT) imaging algorithm to image through a stratified medium. Selective focusing is achieved by tracking the singular value decomposition (SVD) of the time-reversal operator over the entire bandwidth of operation. The frequency independent phase of SVD is the main challenge in this process and has been solved by a new approach based on the decomposition formulation of UDT. The formulation of the proposed mitigation algorithm and DORT-UDT are presented along with simulated and measured results for validation. The efficacy of the method is demonstrated on a multistatic TWI system.

Selective remote excitation of complex structures using time reversal in audible frequency range.

Generation of elastic waves is a major issue in nondestructive testing. Structural health monitoring of a thin element can be achieved through the analysis of its resonance spectrum. A time reversal mirror (TRM) operating in the audible frequency range (1-10 kHz) is used to remotely excite thin resonant elastic elements. The generation of elastic waves is studied with respect to the geometry of the TRM. It is observed that the quality of focusing only weakly depends on the number of loudspeakers (LS) in the TRM. When the air/plate coupling is at its maximum, the energetic efficiency of the TRM is estimated to be about 0.02%. The TRM is shown to efficiently and selectively excite a small structure embedded in a complex environment such as a hollow cylinder. Finally, the results are discussed in light of the DORT method (French acronym for "decomposition of the time reversal operator"). In particular, the optimal LS placement and emission signals in this configuration to excite individual eigenmodes of a plate is determined.

A time-reversal imaging system for buried objects in layered media using complex images Green’s functions

In this paper, the three-dimensional problem of detection and localization of buried metallic objects inside a multilayered medium is studied. Decomposition of the time-reversal operator (DORT) is used as the inversion algorithm in the imaging method. In this approach, one has to analyze the time-reversal (TR) operator obtained by using the multistatic data matrix (MDM) of a TR array. To attain MDM in the forward problem, full-wave simulation results from a commercial simulation software are used. For synthetic retransmission of signals in this inverse problem, determination of the appropriate medium Green’s function is required. Here, for the first time the complex images technique is employed in calculating the required Green’s functions. The complex images technique gives a closed-form Green's function, instead of evaluating time-consuming numerical integrals resulting in a fast and accurate Green’s function calculation. Using singular value decomposition of the MDM at a frequency range of 1–3 GHz and synthesized DORT method, images are constructed. Numerical results show the accuracy of the proposed approach in the detection and localization of buried objects. Furthermore, noise effect and sensitivity analysis on layers’ permittivity values are studied. The results confirm the robustness of the method against noise and uncertain layers parameters.

Through the Wall Imaging Using Ultrawideband Frequency Domain Sampling Method

In this paper, a novel ultrawideband (UWB) time reversal technique for through-the-wall imaging (TWI) is introduced. The proposed algorithm is based on utilization of spatial and UWB frequency data acquired by antenna array. Scattering data are obtained by transmitting a short pulse from the central transmitter and recording the received signal at each array element. Individual multistatic scattering data matrix according to each antenna is formed by casting the fine and coarse frequency samples of the scattering information. The resulting matrix is calibrated based on transmitter signal and fed into the DORT (French acronym for decomposition of the time reversal operator) algorithm. The performance of the proposed method is investigated numerically by applying it to discrete scatterers embedded in homogeneous and continuously random medium. Numerical results are presented to show the effectiveness and high efficiency of the proposed algorithm for TWI.

Effects of target resonances on ultrawideband-DORT

In this paper, we investigate the effects of target (scatterer) resonances on the decomposition of the time reversal operator (DORT) applied to ultrawideband (UWB) electromagnetic scattering. When UWB-DORT is applied to well-resolved point-like scatterers, the frequency responses of the scatterers remain mostly identical and the detected targets appear as a set of distinct eigenvalues over the entire frequency band of operation. However, this may not be the case for targets with strong resonances, since the strongest eigenvalue may not correspond to the same scatterer at different frequency points depending on the resonance characteristics of each target, rendering the eigenstructure inconsistent over the band. Such an effect limits the ability to characterize the targets and construct UWB signals for selective focusing. We examine this phenomenon via numerical experiment considering various target configurations. We also demonstrate a method to overcome this eigenstructure ‘mixing’ by simply correlating adjacent frequency points when applying UWB-DORT. A robust UWB-DORT process applicable to various types of targets would enhance the capability of DORT as a method of target characterization/identification in addition to selective focusing.

Cancer Detection in Highly Dense Breasts Using Coherently Focused Time-Reversal Microwave Imaging

Detection of tumors in highly dense breasts is a critical but challenging issue for early-stage breast cancer detection. We present the application of coherent focusing for time-reversal (TR) microwave imaging in beamspace for the detection and localization of multiple tumors in highly dense 3-D breast phantoms. We propose a novel coherent beamspace time reversal maximum likelihood (C-B-TR-ML) technique to obtain accurate tumor locations with reduced computational burden. To compare the performance, the coherent beamspace processing is also extended for conventional decomposition of the TR operator (DORT) and TR-MUSIC algorithms. A novel hybrid technique involving time of arrival and entropy is also proposed for early-time artifact removal as well as for estimating the Green's function of an equivalent virtual medium required for the TR operation. Finite-difference time-domain computations on anatomically realistic 3-D numerical breast phantoms are used to obtain the backscattered data. The results demonstrate the superior capabilities of the proposed C-B-TR-ML microwave-imaging technique in detecting and localizing multiple tumors embedded inside highly dense breast phantoms.

Nonlinear Lamb wave based DORT method for detection of fatigue cracks

This research reports a selective detecting and focusing approach for fatigue cracks through use of decomposition of the time reversal operator (DORT) in combination with nonlinear Lamb waves. In the proposed approach, the time reversal operator (TRO) is only decomposed at the second-harmonic frequency, which has been widely utilized in recent years to evaluate micro-damage, rather than the fundamental frequency in the traditional DORT method. Further, an imaging algorithm based on the total focus method is introduced to locate nonlinear scatterers. The proposed approach is experimentally investigated to locate two fatigue cracks with different fatigue cycles in an aluminum plate with a set of surface bounded piezoelectric (PZT) transducers. The results show that the significant eigenvalues are related to the fatigue cycles of fatigue cracks when the TRO is decomposed at the second-harmonic frequency, and the number of significant eigenvalues is exactly equal to the number of fatigue cracks. The two fatigue cracks are selectively located accurately and are also distinguished from linear scatterer by use of the proposed method.

Ultrasonic Imaging in Highly Attenuating Materials With Hadamard Codes and the Decomposition of the Time Reversal Operator.

In this paper, defects in a high density polyethylene pipe are imaged with the total focusing method. The viscoelastic attenuation of this material greatly reduces the signal level and leads to a poor signal-to-noise ratio (SNR) due to electronic noise. To improve the image quality, the decomposition of the time reversal operator method is combined with the spatial Hadamard coded transmissions before calculating images in the time domain. Because the Hadamard coding is not compatible with conventional imaging systems, this paper proposes two modified coding methods based on sparse Hadamard matrices with +1/0 coefficients. The SNRs expected with the different spatial codes are demonstrated, and then validated on both simulated and experimental data. Experiments are performed with a transducer array in contact with the base material of a polyethylene pipe. In order to improve the noise filtering procedure, the singular values associated with electronic noise are expressed on the basis of the random matrix theory. This model of noise singular values allows a better identification of the defect response in noisy experimental data. Finally, the imaging method is evaluated in a more industrial inspection configuration, where an immersion array probe is used to image defects in a butt fusion weld with a complex geometry.

Evaluation of a multiple scattering filter to enhance defect detection in heterogeneous media

Ultrasonic evaluation of coarse-grain materials generates multiple scattering at high frequency and large depth. Recent academic experiments with array probes showed the ability of a random matrix method [multiple scattering filter (MSF)] to reduce multiple scattering, hence improving detection. Here, MSF is applied to an industrial nickel-based alloy with coarse-grain structure. Two samples with average grain sizes 90 ± 60 μm and 750 ± 400 μm are inspected with wide-band 64-element arrays at central frequencies 2, 3, and 5 MHz. They contain cylindrical through-holes (1-mm radius) at various depths. The array transfer matrix is recorded and post-processed both in the flawless area and for eleven positions above each defect, which allows for a statistical analysis. MSF is compared with two conventional imaging techniques: the total focusing method (TFM) and the decomposition of the time-reversal operator (DORT). Several parameters to assess the performance of detection techniques are proposed and discussed. The results show the benefit of MSF, especially at high frequencies and for deep defects: at 5 MHz and 70 mm depth, i.e., more than three scattering mean-free paths, the detection rate for MSF ranges between 55% and 100% while it is found to be 0% both for TFM and DORT.

Eigenspace Time-Reversal Robust Capon Beamforming for Target Localization in Continuous Random Media

We propose a novel eigenspace time-reversal robust Capon beamformer (E-TR-RCB) for improved target localization in continuous random media. We also derive the Beamspace-TR-RCB (B-TR-RCB) algorithm and compare their localization performances by varying the medium characteristic and excitation bandwidth. Finite-difference time-domain (FDTD) method is used to numerically obtain the multistatic scattered field data from the continuous random dielectric medium. The results indicate that the E-TR-RCB has superior performance over the B-TR-RCB and outperforms the conventional (elementspace) TR-RCB and decomposition of the time-reversal operator (DORT) imaging techniques.

Locating small structural damages in pipes using space-frequency DORT processing

A new imaging algorithm is introduced and applied for inspection of damages in pipes employing ultrasonic guided waves. The algorithm is based on the decomposition of the time-reversal operator (DORT, in its French acronym) and is demonstrated using both simulations and experiments. Its performance is compared against more traditional time-reversal imaging algorithms. The proposed algorithm is shown to be effective to determine the number and relative location of multiple small damages in pipes with good resolution.

Improving three-dimensional target reconstruction in the multiple scattering regime using the decomposition of the time-reversal operator

The singular vectors of the time reversal operator (décomposition de l'opérateur de retournement temporel, time reversal operator decomposition (DORT) processing) are often used for localizing small echogeneous targets in a cluttered environment. In this work, we show that they can also improve the imaging of relatively large and contrasted targets in a homogeneous environment. It is observed that non-linear inversion schemes, minimizing iteratively the discrepancy between experimental data and simulated field scattered by target estimates, are more efficient when the illuminations correspond to the DORT singular vectors. In addition, DORT preprocessing permits a drastic diminution of the data load and computer burden. This study is conducted with experimental microwave data of targets with size comparable or greater than the wavelength.

Ultrasonic imaging of defects in coarse-grained steels with the decomposition of the time reversal operator.

In the present work, the Synthetic Transmit Aperture (STA) imaging is combined with the Decomposition of the Time Reversal Operator (DORT) method to image a coarse grained austenitic-ferritic steel using a contact transducer array. The highly heterogeneous structure of this material produces a strong scattering noise in ultrasound images. Furthermore, the surface waves guided along the array interfere with the bulk waves backscattered by defects. In order to overcome these problems, the DORT method is applied before calculating images with the STA algorithm. The method consists in analyzing in the frequency domain the singular values and singular vectors of the full array transfer matrix. This paper first presents an analysis of the singular values of different waves contained in the data acquisition, which facilitates the identification of the subspace associated with the surface guided waves for filtering operations. Then, a filtered matrix is defined where the contribution of structural noise and guided waves are reduced. Finally, in the time domain, the STA algorithm is applied to this matrix in order to calculate an image with reduced structural noise. Experiments demonstrate that this filtering improves the signal-to-noise ratio by more than 12 dB in comparison with the STA image before filtering.

An efficient technique based on DORT method to locate multiple soft faults in wiring networks

Decomposition of the time reversal operator (DORT) recently adapted to wiring fault detection and location presented effectual results when dealing with a single soft fault along with complex network configurations. On the other hand, it failed to handle the task of locating multiple faults within even simple ones. In this article, we propose an enhanced version of the standard DORT technique (EDORT) based on a complementary procedure that enables the accurate and selective location of multiple soft faults in various wiring systems.

The detection of flaws in austenitic welds using the decomposition of the time-reversal operator.

The non-destructive testing of austenitic welds using ultrasound plays an important role in the assessment of the structural integrity of safety critical structures. The internal microstructure of these welds is highly scattering and can lead to the obscuration of defects when investigated by traditional imaging algorithms. This paper proposes an alternative objective method for the detection of flaws embedded in austenitic welds based on the singular value decomposition of the time-frequency domain response matrices. The distribution of the singular values is examined in the cases where a flaw exists and where there is no flaw present. A lower threshold on the singular values, specific to austenitic welds, is derived which, when exceeded, indicates the presence of a flaw. The detection criterion is successfully implemented on both synthetic and experimental data. The datasets arising from welds containing a flaw are further interrogated using the decomposition of the time-reversal operator (DORT) method and the total focusing method (TFM), and it is shown that images constructed via the DORT algorithm typically exhibit a higher signal-to-noise ratio than those constructed by the TFM algorithm.

Electromagnetic Time-Reversal Imaging of Pinholes in Pipes

We have designed and implemented a structural health monitoring (SHM) system to detect and localize multidefects in semi-infinite cylindrical metal pipelines simultaneously. The system utilizes electromagnetic decomposition of the time-reversal operator (known under French acronym DORT) signal processing method. The magnificent performance of the DORT detector against signal-to-noise ratio (SNR), and its ability to detect and localize multidefects simultaneously, are the main advantages of the DORT time-reversal method. In the DORT time-reversal method, the reversed wave would precisely retrace back the exact intricate received path to converge coherently at the original source location by using the proper Green’s function. We have utilized the operating frequencies which are far enough from the (highly dispersive) band near the waveguide $TE_{11}$ cut-off frequency. The radius of the pipe is assumed to be ${\text{a}}=10{\text{cm}}$ . Hence, in order to excite the first two modes, frequency bandwidth is considered to be 300 MHz at the center frequency of 1.15 GHz. This system is tested to localize two rectangular holes of the area $(0.13\, \lambda_{0})^{2}$ , where $\lambda_{0}$ is the free-space wavelength at the central frequency. In addition, required parameters such as the minimum number of antennas for detection, the DORT detector performance analysis, the equivalent reflection coefficients of the holes with different sizes and shapes, and the maximum distance of detection of small holes are calculated.