Time Reversal Operator Method Research Articles

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.

Lamb wave-based subwavelength damage imaging using the DORT-MUSIC technique in metallic plates

A Lamb wave-based, subwavelength imaging algorithm is developed for damage imaging in a metallic plate based on a decomposition of the time-reversal operator method together with a multiple signal classification imaging condition in the space-frequency domain. In this study, a hybrid non-contact inspection system was proposed to image damage in an aluminum plate using a piezoelectric linear array for actuation and a laser Doppler vibrometer line-scan perpendicular to the piezoelectric array for sensing. The physics of incident waves, reflection, and reflected waves that underlie the transfer matrix in the decomposition of the time-reversal operator method is mathematically formulated in the context of guided waves based on the first-order Born approximation. Singular value decomposition is then employed to decompose the experimentally measured transfer matrix into three matrices, detailing the incident wave propagation from the linear actuator array, reflection from the damage, and followed by reflected waves toward the linear sensing array for each small damage. The singular value decomposition and multiple signal classification imaging condition enable providing insight on both the damage “reflectivity” and detecting damage smaller than a wavelength (subwavelength). With the flexibility of this inspection system, a considerably large area can be imaged using lower frequency Lamb waves with rapid line-scans. The experimental results showed that the hardware system with a signal processing tools such as the decomposition of the time-reversal operator with multiple signal classification (time-reversal with multiple signal classification) imaging technique can provide robust, highly accurate imaging results as well as providing damage reflectivity estimation with unknown material properties.

Noise Filtering in the Synthetic Transmit Aperture Imaging by Decomposition of the Time Reversal Operator: Application to Flaw Detection in Coarse-grained Stainless Steels

In the present work, the Synthetic Transmit Aperture (STA) imaging is applied on coarse grained steels using a contact phased-array probe. In order to reduce the noise introduced by the heterogeneous structure, as well as artifacts due to surface guided waves, the Decomposition of the Time Reversal Operator method is performed before calculating STA images.

Targets Detection Based on Time Reversal Operator with Uniform Circular Array

In order to detect targets accurately in electromagnetic environment, a decomposition of time reversal operator method for detecting targets with uniform circular array (UCA) is proposed in this paper. In this method, the time reversal operator in UCA is obtained by the transmission functions of targets and antenna array. And then, the eigenvector decomposition of time reversal operator is performed. According to the eigenvectors and the transmission functions of targets and scanning points in the given targets area, the focusing values of all scanning points are calculated, and the direction of scanning points whose focusing values are far greater than others are the direction of targets. Finally, the simulations verify the effectiveness of the proposed method.

A comparison of methods for focusing the field of a HIFU array transducer through human ribs

A forward model, which predicts the scattering by human ribs of a multi-element high-intensity focused ultrasound transducer, was used to investigate the efficacy of a range of focusing approaches described in the literature. This forward model is based on the boundary element method and was described by Gélat et al (2011 Phys. Med. Biol. 56 5553–81; 2012 Phys. Med. Biol. 57 8471–97). The model has since been improved and features a complex surface impedance condition at the surface of the ribs. The inverse problem of focusing through the ribs was implemented on six transducer array-rib topologies and five methods of focusing were investigated, including spherical focusing, binarized apodization based on geometric ray tracing, phase conjugation and the decomposition of the time-reversal operator method. The excitation frequency was 1 MHz and the array was of spherical-section type. Both human and idealized rib topologies were considered. The merit of each method of focusing was examined. It was concluded that the constrained optimization approach offers greater potential than the other focusing methods in terms of maximizing the ratio of acoustic pressure magnitudes at the focus to those on the surface of the ribs whilst taking full advantage of the dynamic range of the phased array.

Spatial diversity in application of the decomposition of the time reversal operator (DORT) method to imaging of an extended target

Taking advantage of the multipath propagation in shallow water waveguide, high resolution can be achieved with the decomposition of the time reversal operator method. In this paper, we investigate how to use the spatial diversity for imaging of an extended target. It is assumed that the target is composed of an infinite number of random, isotropic, and independent scatterers, uniformly distributed over an unknown region. The eigenvalues and eigenvectors associated with the target are first determined. We then employ the frequency characterizations of scatterers from a singular value decomposition of the time reversal operator to localize and image the target. Tank experiments are carried out for a steel cylinder in two kinds of random media: a shallow water waveguide with multiple scatterers and without scatterers. The effects of the random media on the choice of the parameters of the signal processing are also studied.

Time-reversal ESPRIT imaging method for the detection of single target

Estimation of signal parameters via rotational invariance techniques (ESPRIT) is employed to time-reversal (TR) imaging for single target in this paper. By the precondition of ESPRIT, the signal subspace is divided into two parts, which are connected with each other by a transfer matrix. This transfer matrix can be used to get the TR-ESPRIT imaging pseudo-spectrum. Two examples corresponding to the noise-free and noise case are considered. The last simulated results show that the proposed TR-ESPRIT method has higher resolution than the conventional decomposition of the time-reversal operator method, and it can keep the efficiency of time reversal operator-based imaging by the signal subspace.

Focusing with the decomposition of the time reversal operator method in noisy environments

This paper presents a detailed analysis of the effects of noise (reverberation) on the focusing performance of decomposition of the time reversal operator (DORT) in a noise-limited case and in a reverberation-limited case, respectively. Quantitative results obtained from simulations and experiments are presented. The results show the DORT method can be efficiently applied to target detection with enough source level to yield significant backscatter. For a target placed on the bottom, the influence of the reverberation on the focusing performance is slight. However, distinguishing between a target and constant backscattering returning from strong local clutter on the bottom (false alarms) needs further research.

Characterization of an elastic target in a shallow water waveguide by decomposition of the time-reversal operator

This paper reports the results of an investigation into extracting of the backscattered frequency signature of a target in a waveguide. Retrieving the target signature is difficult because it is blurred by waveguide reflections and modal interference. It is shown that the decomposition of the time-reversal operator method provides a solution to this problem. Using a modal theory, this paper shows that the first singular value associated with a target is proportional to the backscattering form function. It is linked to the waveguide geometry through a factor that weakly depends on frequency as long as the target is far from the boundaries. Using the same approach, the second singular value is shown to be proportional to the second derivative of the angular form function which is a relevant parameter for target identification. Within this framework the coupling between two targets is considered. Small scale experimental studies are performed in the 3.5 MHz frequency range for 3 mm spheres in a 28 mm deep and 570 mm long waveguide and confirm the theoretical results.

Characterization of targets buried in disordered medium

We consider in this paper the problem of the determination of the permittivity profile of an unknown buried object from measurements of the electromagnetic scattered field. The target under test is assumed to be buried in one of the two involved media while the sources and the receivers are located in the other medium (limited‐aspect data configuration). This ill‐posed and non‐linear inverse scattering problem is reformulated as an optimization problem that is solved iteratively. This method consists in building up a sequence of the parameter of interest by minimizing, at each iteration step, a cost functional representing the discrepancy between the data and those that would be obtained with the best available estimation of the parameter. In addition, when clutter is present, the decomposition of the time reversal operator method is used to improve the signal‐to‐clutter ratio, since it allows us to synthesize a wave that focuses on the scatterer. The data associated with this incident field are included in the iterative minimization procedure.

Extraction of a backscattered target signature in a shallow water waveguide with decomposition of the time reversal operator method

In a shallow water waveguide, detection and characterization of a target is an active field of research. Retrieving the target signature is extremely difficult due to the complex mode coupling between the incident wave and the backscattered wave. One solution consists of deconvolving the target response from the waveguide impulse response. However this method needs an extensive a priori knowledge of the waveguide geometry [Mignerey et al., JASA 1992 and Yang et al., JASA 1994]. To overcome this difficulty, we propose to apply the DORT method (French acronym for decomposition of the time reversal operator). This method is based on time-reversal invariance. Time reversal is commonly known to be an effective means to focus on a target without any a priori knowledge of the propagation medium. In the same way, here we show that the eigenvalues of the time reversal operator are directly proportional to the backscattered target signatures, and the waveguide geometry only acts on the proportionality factor. A theory based on modal waveguide analysis is presented. Ultrasonic scale experiments prove the effectiveness of this method.

Localization and characterization of two-dimensional targets buried in a cluttered environment

In the present paper, we consider a two-dimensional inverse scattering problem involving two semi-infinite media separated by an interface. The targets under test are assumed to be buried in one of the two media while the sources and the receivers are located in the other medium (limited-aspect data configuration). We present an iterative scheme to reconstruct the permittivity distribution of the unknown object. This method consists in building up a sequence of the parameter of interest by minimizing, at each iteration step, a cost functional representing the discrepancy between the data and those that would be obtained with the best available estimation of the parameter. In addition, when clutter is present, the decomposition of the time reversal operator method is used to improve the signal-to-clutter ratio, since it allows us to synthesize a wave that focuses on the scatterer. The data associated with this incident field are included in the iterative minimization procedure.